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Show that an element and its inverse have the same order in any group. A cubic block of wood, 10.0 cm on each side, floats at the interface between... An ice cube tray of negligible mass contains 0.315 kg of water at17.7∘. How much... An open tank has a vertical partition and on one side contains gasoline with a... A 100g cube of ice at 0C is dropped into 1.0kg of water thatwas originally... Complete the equation of the line through (2, 1) and (5, -8). Use exact numbers. Write a function based on the given parent function and transformations in the given order.... How many solutions does the equationx1+x2+x3=13have wherex1,x2,andx3are non negative integers less than 6. Determine whether f : Z×Z→Z is onto if a) f(m,n)=2m−nb) b) f(m,n)=m2−n2 c) f(m,n)=m+n+1 d)... The base of S is an elliptical region with boundary curve 9x2+4y2=36. Cross-sections perpendicular to... Create a graph of y=2x−6. Construct a graph corresponding to the linear equation y=2x−6. Use the graphs of f and g to graph h(x) = (f + g)(x). (Graph... find expressions for the quadratic functions whose graphs are shown. f(x)=? g(x)=? Find the volume V of the described solid S. A cap of a sphere with... Find a counterexample to show that each statement is false. The sum of any three... Read the numbers and decide what the next number should be. 5 15 6 18... In how many different orders can five runners finish a race if no ties are... A farmer plants corn and wheat on a 180 acre farm. He wants to plant... Find the distance between (0, 0) and (-3, 4) pair of points. If needed, show... Whether each of these functions is a bijection from R to R.a)f(x)=−3x+4b)f(x)=−3x2+7c)f(x)=x+1x+2d)f(x)=x5+1 Find two numbers whose difference is 100 and whose product is a minimum. Find an expression for the function whose graph is the given curve. The line segment... Prove or disprove that if a and b are rational numbers, then ab is also... How to find a rational number halfway between any two rational numbers given infraction form... Fill in the blank with a number to make the expression a perfect square x2−6x+? Look at this table: x y 1–2 2–4 3–8 4–16 5–32 Write a linear (y=mx+b),... Part a: Assume that the height of your cylinder is 8 inches. Think of A... The graph of a function f is shown. Which graph is an antiderivative of f? A rectangle has area 16m2 . Express the perimeter of the rectangle as a function... Find the equation of the quadratic function f whose graph is shown below. (5, −2) Use the discriminant, b2−4ac, to determine the number of solutions of the following quadratic equation.... How many solutions does the equation ||2x-3|-m|=m have if m>0? If a system of linear equations has infinitely many solutions, then the system is called... A bacteria population is growing exponentially with a growth factor of 16 each hour.By what... A system of linear equations with more equations than unknowns is sometimes called an overdetermined... Express the distance between the numbers 2 and 17 using absolute value. Then find the... Find the Laplace transform of f(t)=(sint–cost)2 Express the interval in terms of an inequality involving absolute value. (0,4) A function is a ratio of quadratic functions and has a vertical asymptote x =4... how do you graph y > -2 Find the weighted average of a data set where 10 has a weight of 5,... The population of California was 29.76 million in 1990 and 33.87 million in 2000. Assume... The population of a region is growing exponentially. There were 10 million people in 1980... Two cables BG and BH are attached to the frame ACD as shown.Knowing that the... A bird flies in the xy-plane with a position vector given by r→=(αt−βt3)i^+γt2j^, with α=2.4... A movie stuntman (mass 80.0kg) stands on a window ledge 5.0 mabove the floor. Grabbing... Solve the following linear congruence, 25x≡15(bmod29) For the equation, a. Write the value or values of the variable that make a... Which of the following statements is/are correct about logistic regression? (There may be more than... Compute 4.659×104−2.14×104. Round the answer appropriately. Express your answer as an integer using the proper... Find the 52nd term of the arithmetic sequence -24,-7, 10 Find the 97th term of the arithmetic sequence 17, 26, 35, An equation that expresses a relationship between two or more variables, such as H=910(220−a), is... The football field is rectangular. a. Write a polynomial that represents the area of the... The equation 1.5r+15=2.25r represents the number r of movies you must rent to spend the... While standing on a ladder, you drop a paintbrush. The function represents the height y... When does data modeling use the idea of a weak entity? Give definitions for the... Write an equation of the line passing through (-2, 5) and parallel to the line... Find a polar equation for the curve represented by the given Cartesian equation. y =... Find c such that fave=f(c) List five integers that are congruent to 4 modulo 12. A rectangular package to be sent by a postal service can have a maximum combined... A juggler throws a bowling pin straight up with an initial speed of 8.20 m/s.... The One-to-One Property of natural logarithms states that if ln x = ln y, then... Find an equation of a parabola that has curvature 4 at the origin. Find a parametric representation of the solution set of the linear equation. 3x − 1/2y... Find the product of the complex number and its conjugate. 2-3i Find the prime factorization of 10!. Find a polynomial f(x) of degree 5 that has the following zeros. -3, -7, 5... True or False. The domain of every rational function is the set of all real... What would be the most efficient step to suggest to a student attempting to complete... Write a polynomial, P(x), in factored form given the following requirements. Degree: 4 Leading coefficient... Give a geometric description of the set of points in space whose coordinates satisfy the... Use the Cauchy-Riemann equations to show that f(z)=z― is not analytic. Find the local maximum and minimum values and saddle points of the function. If you... a) Evaluate the polynomial y=x3−7x2+8x−0.35 at x=1.37 . Use 3-digit arithmetic with chopping. Evaluate the... The limit represents f'(c) for a function f and a number c. Find f and... A man 6 feet tall walks at a rate of 5 feet per second away... Find the Maclaurin series for the function f(x)=cos4x. Use the table of power series for... Suppose that a population develops according to the logistic equation dPdt=0.05P−0.0005P2 where t is measured... Find transient terms in this general solution to a differential equation, if there are any... Find the lengths of the sides of the triangle PQR. Is it a right triangle?... Use vectors to decide whether the triangle with vertices P(1, -3, -2), Q(2, 0, -4),... Find a path that traces the circle in the plane y=5 with radius r=2 and... a. Find an upper bound for the remainder in terms of n.b. Find how many... Find two unit vectors orthogonal to both j−k and i+j. Obtain the Differential equations: parabolas with vertex and focus on the x-axis. The amount of time, in minutes, for an airplane to obtain clearance for take off... Use the row of numbers shown below to generate 12 random numbers between 01 and... Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!)... A random sample of 1200 U.S. college students was asked, "What is your perception of... The two intervals (114.4, 115.6) and (114.1, 115.9) are confidence intervals (The same sample data... How many different 10 letter words (real or imaginary) can be formed from the following... Assume that σ is unknown, the lower 100(1−α)% confidence bound on μ is: a) μ≤x―+tα,n−1sn... A simple random sample of 60 items resulted in a sample mean of 80. The... Decresing the sample size, while holding the confidence level and the variance the same, will... A privately owned liquor store operates both a drive-n facility and a walk-in facility. On... Show that the equation represents a sphere, and find its center and radius. x2+y2+z2+8x−6y+2z+17=0 Describe in words the region of R3 represented by the equation(s) or inequality. x=5 Suppose that the height, in inches, of a 25-year-old man is a normal random variable... Find the value and interest earned if $8906.54 is invested for 9 years at %... Which of the following statements about the sampling distribution of the sample mean is incorrect?... The random variable x stands for the number of girls in a family of four... The product of the ages, in years, of three (3) teenagers os 4590. None of... A simple random sample size of 100 is selected from a population with p=0.40 What... Which of the following statistics are unbiased estimators of population parameters? Choose the correct answer... The probability distribution of the random variable X represents the number of hits a baseball... Let X be a random variable with probability density function.f(x)={c(1−x2)−1<x<10otherwise(a) What is the value of... A survey of 4826 randomly selected young adults (aged 19 to 25) asked, "What do... The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is... Given that z is a standard normal random variable, compute the following probabilities.a.P(z≤−1.0)b.P(z≥−1)c.P(z≥−1.5)d.P(−2.5≤z)e.P(−3<z≤0) Given a standard normal distribution, find the area under the curve that lies(a) to the... Chi-square tests are best used for which type of dependent variable? nominal, ordinal ordinal interval... True or False 1.The goal of descriptive statistics is to simplify, summarize, and organize data.... What is the difference between probability distribution and sampling distribution? A weather forecaster predicts that the temperature in Antarctica will decrease 8∘F each hour for... The tallest person who ever lived was approximately 8 feet 11 inches tall. a) Write... An in-ground pond has the shape of a rectangular prism. The pond has a depth... The average zinc concentration recovered from a sample of measurements taken in 36 different locations... Why is it important that a sample be random and representative when conducting hypothesis testing?... Which of the following is true about the sampling distribution of means? A. Shape of... Give an example of a commutative ring without zero-divisors that is not an integral domain. List all zero-divisors in Z20. Can you see relationship between the zero-divisors of Z20 and... Find the integer a such that a≡−15(mod27) and −26≤a≤0 Explain why the function is discontinuous at the given number a. Sketch the graph of... Two runners start a race at the same time and finish in a tie. Prove... Which of the following graphs represent functions that have inverse functions? find the Laplace transform of f (t). f(t)=tsin3t Find Laplace transforms of sinh3t cos22t find the Laplace transform of f (t). f(t)=t2cos2t The Laplace transform of the product of two functions is the product of the Laplace... The Laplace transform of u(t−2) is (a) 1s+2 (b) 1s−2 (c) e2ss(d)e−2ss Find the Laplace Transform of the function f(t)=eat Explain First Shift Theorem & its properties? Solve f(t)=etcost Find Laplace transform of the given function te−4tsin3t Reduce to first order and solve:x2y″−5xy′+9y=0 y1=x3 (D3−14D+8)y=0 A thermometer is taken from an inside room to the outside ,where the air temperature... Find that solution of y′=2(2x−y) which passes through the point (0, 1). Radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg... Let A, B, and C be sets. Show that (A−B)−C=(A−C)−(B−C) Suppose that A is the set of sophomores at your school and B is the... In how many ways can a 10-question true-false exam be answered? (Assume that no questions... Is 2∈{2}? How many elements are in the set { 2,2,2,2 } ? How many elements are in the set { 0, { { 0 } }? Draw the Hasse diagram representing the partial ordering {(a, b) | a divides b} on... Flux through a Cube (Eigure 1) A cube has one corner at the origin and... A well-insulated rigid tank contains 3 kg of saturated liquid-vapor mixture of water at 200... A water pump that consumes 2 kW of electric power when operating is claimed to... A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius... In a truck-loading station at a post office, a small 0.200-kg package is released from... The magnetic fieldB→in acertain region is 0.128 ,and its direction is that of the z-axis... A marble moves along the x-axis. The potential-energy functionis shown in Fig. 1a) At which... A proton is released in a uniform electric field, and it experiences an electric force... A potters wheel having a radius of 0.50 m and a moment of inertia of12kg⋅m2is... Two spherical objects are separated by a distance of 1.80×10−3m. The objects are initially electrically... An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h.... Resolve the force F2 into components acting along the u and v axes and determine... A conducting sphere of radius 0.01m has a charge of1.0×10−9Cdeposited on it. The magnitude of... Starting with an initial speed of 5.00 m/s at a height of 0.300 m, a... In the figure a worker lifts a weightωby pulling down on a rope with a... A stream of water strikes a stationary turbine bladehorizontally, as the drawing illustrates. The incident... Until he was in his seventies, Henri LaMothe excited audiences by belly-flopping from a height... A radar station, located at the origin of xz plane, as shown in the figure... 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Raindrops make an angle theta with the vertical when viewed through a moving train window.... A 0.50 kg ball that is tied to the end of a 1.1 m light... If the coefficient of static friction between your coffeecup and the horizontal dashboard of your... A car is initially going 50 ft/sec brakes at a constant rate (constant negative acceleration),... A swimmer is capable of swimming 0.45m/s in still water (a) If sheaim her body... A block is hung by a string from inside the roof of avan. When the... A race driver has made a pit stop to refuel. Afterrefueling, he leaves the pit... A relief airplane is delivering a food package to a group of people stranded on... The eye of a hurricane passes over Grand Bahama Island. It is moving in a... An extreme skier, starting from rest, coasts down a mountainthat makes an angle25.0∘with the horizontal.... Four point charges form a square with sides of length d, as shown in the... In a scene in an action movie, a stuntman jumps from the top of one... The spring in the figure (a) is compressed by length delta x . It launches... An airplane propeller is 2.08 m in length (from tip to tip) and has a... A helicopter carrying dr. evil takes off with a constant upward acceleration of5.0ms2. Secret agent... A 15.0 kg block is dragged over a rough, horizontal surface by a70.0 N force... A box is sliding with a speed of 4.50 m/s on a horizontal surface when,... 3.19 Win the Prize. In a carnival booth, you can win a stuffed giraffe if... A car is stopped at a traffic light. It then travels along a straight road... a. When the displacement of a mass on a spring is12A, what fraction of the... At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy... A jet plane lands with a speed of 100 m/s and can accelerate at a... In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints... 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Find the area of the parallelogram with vertices A(-3, 0), B(-1 , 3), C(5, 2),... If the atomic radius of lead is 0.175 nm, find the volume of its unit... At one point in a pipeline the water’s speed is 3.00 m/s and the gauge... Find the volume of the solid in the first octant bounded by the coordinate planes,... A paper cup has the shape of a cone with height 10 cm and radius... A light wave has a 670 nm wavelength in air. Its wavelength in a transparent... An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50... Find the equation of the sphere centered at (-9, 3, 9) with radius 5. Give... Determine whether the congruence is true or false. 5≡8 mod 3 Find all whole number solutions of the congruence equation. (2x+1)≡5 mod 4 Determine whether the congruence is true or false. 100≡20 mod 8 I want example of an undefined term and a defined term in geometry and explaining... Two fair dice are rolled. Let X equal the product of the 2dice. Compute P{X=i}... Suppose that two defective refrigerators have been included in a shipment of six refrigerators. The... Based on the Normal model N(100, 16) describing IQ scores, what percent of peoples The probability density function of the net weight in pounds of a packaged chemical herbicide... Let X represent the difference between the number of heads and the number of tails... An urn contains 3 red and 7 black balls. Players A and B withdraw balls... 80% A poll is given, showing are in favor of a new building project. 8... The probability that the San Jose Sharks will win any given game is 0.3694 based... Find the value of P(X=7) if X is a binomial random variable with n=8 and... Find the value of P(X=8) if X is a binomial random variable with n=12 and... On a 8 question multiple-choice test, where each question has 2 answers, what would be... If you toss a fair coin 11 times, what is the probability of getting all... A coffee connoisseur claims that he can distinguish between a cup of instant coffee and... Two firms V and W consider bidding on a road-building job, which may or may... Two cards are drawn without replacement from an ordinary deck, find the probability that the... In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the... A local bank reviewed its credit card policy with the intention of recalling some of... The accompanying table gives information on the type of coffee selected by someone purchasing a... A batch of 500 containers for frozen orange juice contains 5 that are defective. Two... The probability that an automobile being filled with gasoline also needs an oil change is... Let the random variable X follow a normal distribution with μ=80 and σ2=100. a. Find... A card is drawn randomly from a standard 52-card deck. Find the probability of the... The next number in the series 38, 36, 30, 28, 22 is ? What is the coefficient of x8y9 in the expansion of (3x+2y)17? A boat on the ocean is 4 mi from the nearest point on a straight... How many different ways can you make change for a quarter? (Different arrangements of the... Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and... Approximately 80,000 marriages took place in the state of New York last year. Estimate the... The probability that a student passes the Probability and Statistics exam is 0.7. (i)Find the... Customers at a gas station pay with a credit card (A), debit card (B), or... It is conjectured that an impurity exists in 30% of all drinking wells in a... Assume that the duration of human pregnancies can be described by a Normal model with... According to a renowned expert, heavy smokers make up 70% of lung cancer patients. If... Two cards are drawn successively and without replacement from an ordinary deck of playing cards... Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L),... A bag contains 6 red, 4 blue and 8 green marbles. How many marbles of... A normal distribution has a mean of 50 and a standard deviation of 4. Please... Seven women and nine men are on the faculty in the mathematics department at a... An automatic machine in a manufacturing process is operating properly if the lengths of an... Three cards are drawn without replacement from the 12 face cards (jacks, queens, and kings)... Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a... A TIRE MANUFACTURER WANTS TO DETERMINE THE INNER DIAMETER OF A CERTAIN GRADE OF TIRE.... Differentiate the three measures of central tendency: ungrouped data. Find the mean of the following data: 12,10,15,10,16,12,10,15,15,13 A wallet containing four P100 bills, two P200 bills, three P500 bills, and one P1,000... The number of hours per week that the television is turned on is determined for... Data was collected for 259 randomly selected 10 minute intervals. For each ten-minute interval, the... Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in... A normal distribution has a mean of 80 and a standard deviation of 14. Determine... True or false: a. All normal distributions are symmetrical b. All normal distributions have a... Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or... Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. 8408 1374 1872 8879... The velocity function (in meters per second) is given for a particle moving along a... Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1) What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4),... The integral represents the volume of a solid. Describe the solid. π∫01(y4−y8)dy a) The integral... Two components of a minicomputer have the following joint pdf for their useful lifetimes X... Use the table of values of f(x,y) to estimate the values of fx(3,2), fx(3,2.2), and... Calculate net price factor and net price. Dollars list price −435.20$ Trade discount rate −26%,15%,5%. Represent the line segment from P to Q by a vector-valued function and by a... (x2+2xy−4y2)dx−(x2−8xy−4y2)dy=0 If f is continuous and integral 0 to 9 f(x)dx=4, find integral 0 to 3... Find the parametric equation of the line through a parallel to ba=[3−4],b=[−78] Find the velocity and position vectors of a particle that has the given acceleration and... If we know that the f is continuous and integral 0 to 4f(x)dx=10, compute the... Integration of (y⋅tanxy) For the matrix A below, find a nonzero vector in the null space of A... Find a nonzero vector orthogonal to the plane through the points P, Q, and R.... Suppose that the augmented matrix for a system of linear equations has been reduced by... Find two unit vectors orthogonal to both (3 , 2, 1) and (- 1, 1,... What is the area of the parallelogram whose vertices are listed? (0,0), (5,2), (6,4), (11,6) Using T defined by T(x)=Ax, find a vector x whose image under T is b,... Use the definition of Ax to write the matrix equation as a vector equation, or... We need to find the volume of the parallelepiped with only one vertex at the... List five vectors in Span {v1,v2}. For each vector, show the weights on v1 and... (1) find the projection of u onto v and (2) find the vector component of... Find the area of the parallelogram determined by the given vectors u and v. u... (a) Find the point at which the given lines intersect. r = 2,... (a) find the transition matrix from B toB′,(b) find the transition matrix fromB′to B,(c) verify... A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If... Given the following vector X, find anon zero square marix A such that AX=0; You... Construct a matrix whose column space contains (1, 1, 5) and (0, 3.1) and whose... At what point on the paraboloid y=x2+z2 is the tangent plane parallel to the plane... Label the following statements as being true or false. (a) If V is a vector... Find the Euclidean distance between u and v and the cosine of the angle between... Write an equation of the line that passes through (3, 1) and (0, 10) There are 100 two-bedroom apartments in the apartment building Lynbrook West.. The montly profit (in... State and prove the linearity property of the Laplace transform by using the definition of... The analysis of shafts for a compressor is summarized by conformance to specifications. Suppose that... The Munchies Cereal Company combines a number of components to create a cereal. Oats and... Movement of a Pendulum A pendulum swings through an angle of 20∘ each second. If... If sinx+siny=aandcosx+cosy=b then find tan(x−y2) Find the values of x such that the angle between the vectors (2, 1, -1),... Find the dimensions of the isosceles triangle of largest area that can be inscribed in... Suppose that you are headed toward a plateau 50 meters high. If the angle of... Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport.... Find an equation of the plane. The plane through the points (2, 1, 2), (3,... Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following... two small spheres spaced 20.0cm apart have equal charges. How many extra electrons must be... The base of a pyramid covers an area of 13.0 acres (1 acre =43,560 ft2)... Find out these functions' domain and range. To find the domain in each scenario, identify... Your bank account pays an interest rate of 8 percent. You are considering buying a... Whether f is a function from Z to R ifa)f(n)=±n.b)f(n)=n2+1.c)f(n)=1n2−4. The probability density function of X, the lifetime of a certain type of electronic device... A sandbag is released by a balloon that is rising vertically at a speed of... A proton is located in a uniform electric field of2.75×103NCFind:a) the magnitude of the electric... A rectangular plot of farmland are finite on one facet by a watercourse and on... A solenoid is designed to produce a magnetic field of 0.0270 T at its center.... I want to find the volume of the solid enclosed by the paraboloidz=2+x2+(y−2)2and the planesz=1,x=−1y=0,andy=4 Let W be the subspace spanned by the u’s, and write y as the sum... Can u find the point on the planex+2y+3z=13that is closest to the point (1,1,1). You... A spring of negligible mass stretches 3.00 cm from its relaxed length when a force... A force of 250 Newtons is applied to a hydraulic jack piston that is 0.01... Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface... A credit card contains 16 digits between 0 and 9. However, only 100 million numbers... Every real number is also a complex number? True of false? Let F be a fixed 3x2 matrix, and let H be the set of all... Find a vector a with representation given by the directed line segment AB. Draw AB... Find A such that the given set is Col A. {[2s+3tr+s−2t4r+s3r−s−t]:r,s,t real} Find the vector that has the same direction as (6, 2, -3) but is four... For the matrices (a) find k such that Nul A is a subspace of Rk,... How many subsets with an odd number of elements does a set with 10 elements... In how many ways can a set of five letters be selected from the English... Suppose that f(x) = x/8 for 3 < x < 5. Determine the following probabilities:... Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to... Find two vectors parallel to v of the given length. v=PQ→ with P(1,7,1) and Q(0,2,5);... A dog in an open field runs 12.0 m east and then 28.0 m in... Can two events with nonzero probabilities be both independent and mutually exclusive? Explain your reasoning. Use the Intermediate Value Theorem to show that there is a root of the given... In a fuel economy study, each of 3 race cars is tested using 5 different... A company has 34 salespeople. A board member at the company asks for a list... A dresser drawer contains one pair of socks with each of the following colors: blue,... A restaurant offers a $12 dinner special with seven appetizer options, 12 choices for an... A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17... Suppose E(X)=5 and E[X(X–1)]=27.5, find ∈(x2) and the variance. A Major League baseball diamond has four bases forming a square whose sides measure 90... Express f(x)=4x3+6x2+7x+2 in term of Legendre Polynomials. Find a basis for the space of 2×2 diagonal matrices. Basis ={[],[]} Which of the following expressions are meaningful? Which are meaningless? Explain. a) (a⋅b)⋅c (a⋅b)⋅c has... Vectors V1 and V2 are different vectors with lengths V1 and V2 respectively. Find the... Find an equation for the plane containing the two (parallel) lines v1=(0,1,−2)+t(2,3,−1) and v2=(2,−1,0)+t(2,3,−1). Find, correct to the nearest degree, the three angles of the triangle with the given... Find the vector, not with determinants, but by using properties of cross products. (i+j)×(i−j) Find the curve’s unit tangent vector. Also, find the length of the indicated portion of... Construct a 4×3 matrix with rank 1 Find x such that the matrix is equal to its inverse.A=[7x−8−7] Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3... Write in words how to read each of the following out loud.a.{x∈R′∣0<x<1}b.{x∈R∣x≤0orx⇒1}c.{n∈Z∣nisafactorof6}d.{n∈Z⋅∣nisafactorof6} Pets Plus and Pet Planet are having a sale on the same aquarium. At Pets... Find the average value of F(x, y, z) over the given region. F(x,y,z)=x2+9 over the... Find the trace of the plane in the given coordinate plane. 3x−9y+4z=5,yz Determine the level of measurement of the variable. Favorite color Choose the correct level of... How wide is the chasm between what men and women earn in the workplace? According... Write an algebraic expression for: 6 more than a number c. Please, can u convert 3.16 (6 repeating) to a fraction. Evaluate the expression. P(8, 3) In a poker hand consisting of 5 cards, find the probability of holding 3 aces. Give an expression that generates all angles coterminal with each angle. Let n represent any... An ideal Otto cycle has a compression ratio of 10.5, takes in air at 90... A piece of wire 10 m long is cut into two pieces. One piece is... Put the following equation of a line into slope intercept form, simplifying all fractions 3x+3y=24 Find the point on the hyperbola xy = 8 that is closest to the point... Water is pumped from a lower reservoir to a higher reservoir by a pump that... A piston–cylinder device initially contains 0.07m3 of nitrogen gas at 130 kPa and 180∘. The... Write an algebraic expression for each word phrase. 4 more than p A club has 25 members. a) How many ways are there to choose four members... For each of the sets below, determine whether {2} is an element of that set.... Which expression has both 8 and n as factors? If repetitions are not permitted (a) how many 3 digit number can be formed from... To determine the sum of all multiples of 3 between 1 and 1000 On average, there are 3 accidents per month at one intersection. We need to find... One number is 2 more than 3 times another. Their sum is 22. Find the... The PMF for a flash drive with X (GB) of memory that was purchased is... An airplane needs to reach a velocity of 203.0 km/h to takeoff. On a 2000... A racquetball strikes a wall with a speed of 30 m/s and rebounds with a... Assuming that the random variable x has a cumulative distribution function,F(x)={0,x<00.25x,0≤x<51,5≤xDetermine the following:a)p(x<2.8)b)p(x>1.5)c)p(x<−z)d)p(x>b) At t = 0 a grinding wheel has an angular velocity of 24.0 rad/s. It... How many 3/4's are in 1? You’re driving down the highway late one night at 20 m/s when a deer steps... Table salt contains 39.33 g of sodium per 100 g of salt. The U.S. Food... The constant-pressure heat capacity of a sample of a perfect gas was found to vary... Coffee is draining from a conical filter into a cylindrical coffepot at the rate of... Cart is driven by a large propeller or fan, which can accelerate or decelerate the... A vending machine dispenses coffee into an eight-ounce cup. The amounts of coffee dispensed into... On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a... The gage pressure in a liquid at a depth of 3 m is read to... Consider a cylindrical specimen of a steel alloy 8.5 mm (0.33 in.) in diameter and... Calculate the total kinetic energy, in Btu, of an object with a mass of 10... A 0.500-kg mass on a spring has velocity as a function of time given by... An Australian emu is running due north in a straight line at a speed of... Another pitfall cited is expecting to improve the overall performance of a computer by improving... You throw a glob of putty straight up toward the ceiling, which is 3.60 m... A 0.150-kg frame, when suspended from a coil spring, stretches the spring 0.070 m. A... A batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips.... A rock climber stands on top of a 50-m-high cliff overhanging a pool of water.... A tank whose bottom is a mirror is filled with water to a depth of... Two sites are being considered for wind power generation. In the first site, the wind... 0.250 kilogram of water at75.0∘Care contained in a tiny, inert beaker. How much ice, at... Two boats start together and race across a 60-km-wide lake and back. Boat A goes... A roller coaster moves 200 ft horizontally and the rises 135 ft at an angle... A tow truck drags a stalled car along a road. The chain makes an angle... Consider the curve created by2x2+3y2–4xy=36(a) Show thatdydx=2y−2x3y−2x(b) Calculate the slope of the line perpendicular to... The current entering the positive terminal of a device is i(t)=6e−2t mA and the voltage... The fastest measured pitched baseball left the pitcher’s hand at a speed of 45.0 m/s.... Calculate the total potential energy, in Btu, of an object that is 20 ft below... A chemist in an imaginary universe, where electrons have a different charge than they do... When jumping, a flea reaches a takeoff speed of 1.0 m/s over a distance of... Determine the energy required to accelerate a 1300-kg car from 10 to 60 km/h on... The deepest point in the ocean is 11 km below sea level, deeper than MT.... A golfer imparts a speed of 30.3 m/s to a ball, and it travels the... Calculate the frequency of each of the following wavelengths of electromagnetic radiation. A) 632.8 nm... Prove that there is a positive integer that equals the sum of the positive integers... A hurricane wind blows across a 6.00 m×15.0 m flat roof at a speed of... If an electron and a proton are expelled at the same time,2.0×10−10mapart (a typical atomic... The speed of sound in air at 20 C is 344 m/s. (a) What is... Which of the following functions f has a removable discontinuity at a? If the discontinuity... A uniform steel bar swings from a pivot at one end with a period of... A wind farm generator uses a two-bladed propellermounted on a pylon at a height of... A copper calorimeter can with mass 0.100 kg contains 0.160 kgof water and 0.018 kg... Jones figures that the total number of thousands of miles that a used auto can... Assign a binary code in some orderly manner to the 52 playingcards. Use the minimum... A copper pot with mass 0.500 kg contains 0.170 kg of water ata temperature of... Ea for a certain biological reaction is 50 kJ/mol, by what factor ( how many... When a person stands on tiptoe (a strenuous position), the position of the foot is... A solution was prepared by dissolving 1210 mg of K3Fe(CN)6 (329.2 g/mol) in sufficient waterto... A 58-kg skier is going down a slope oriented 35 degree abovethe horizontal. The area... The mechanics at lincoln automotive are reboring a 6-in deepcylinder to fit a new piston.... A 0.48 kg piece of wood floats in water but is found to sinkin alcohol... A 50-g ice cube at 0oC is heated until 45-g hasbecome water at 100oC and... A solution containing 6.23 ppm of KMnO4 had a transmittance of 0.195 in a 1.00-cm... A black body at 7500K consists of an opening of diameter 0.0500mm, looking into an... A new absolute temperature scale is proposed. On thisscale the ice point of water is... A 65.0 mm focal length converging lens is 78.0 mm away from a sharp image.... A crate of fruit with mass 35.0 kg and specific heat capacity 3650 J/Kg .... A freezer has a thermal efficiency of 2.40. Thefreezer is to convert 1.80 kg of... A horizontal force of 210N is exerted on a 2.0 kg discus as it rotates... Lead has a specific heat of 0.030 cal/gC. In an insulated container, 300 grams of... A parachutist relies on air resistance mainly on her parachute to decrease her downward velocity.... The distance between a carbon atom (m=12 u) and an oxygen atom (m + 16... A car heading north collides at an intersection with a truckheading east. If they lock... Water stands at a depth H in a large, open tank whose sidewalls are vertical.... The heaviest invertebrate is the giant squid, which is estimated to have a weight of... Which of the following is a correct comment? */ Comments */ ** Comment ** /*... The concentrated sulfuric acid we use in the laboratory is 98% H2SO4 by mass. Calculate... Consider the reaction N2(g)+3H2(g)→2NH3(g) suppose that a particular moment during the reaction molecular hydrogen on... use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F... - High School Questions
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120 Math Word Problems To Challenge Students Grades 1 to 8Written by Marcus Guido - Subtraction
- Multiplication
- Mixed operations
- Ordering and number sense
- Comparing and sequencing
- Physical measurement
- Ratios and percentages
- Probability and data relationships
You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems. A jolt of creativity would help. But it doesn’t come. Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge. This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes . ( See our entire list of back to school resources for teachers here .) There are 120 examples in total. The list of examples is supplemented by tips to create engaging and challenging math word problems. 120 Math word problems, categorized by skillAddition word problems. Best for: 1st grade, 2nd grade 1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total? 2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now? 3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now? 4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total? 5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies? 6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June? 7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now? 8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total? Subtraction word problemsBest for: 1st grade, second grade 9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left? 10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing? 11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now? Practice math word problems with Prodigy MathJoin millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade! 12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half? 13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now? 14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month? 15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left? 16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left? Multiplication word problemsBest for: 2nd grade, 3rd grade 17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have? 18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total? 19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year? 20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total? 21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn? Division word problemsBest for: 3rd grade, 4th grade, 5th grade 22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag? 23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on? 24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total? 25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost? 26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible? Mixed operations word problems27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now? 28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order? 29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have? 30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag? Ordering and number sense word problems31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total? 32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total? 33. Composing Numbers: What number is 6 tens and 10 ones? 34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I? 35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points? Fractions word problemsBest for: 3rd grade, 4th grade, 5th grade, 6th grade 36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar? 37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait? 38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total? 39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink? 40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total? 41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left? 42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete? 43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use? 44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction. 45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make? 46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number. Decimals word problemsBest for: 4th grade, 5th grade 47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total? 48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left? 49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked? 50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower? 51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo? 52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week? Comparing and sequencing word problemsBest for: Kindergarten, 1st grade, 2nd grade 53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more? 54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more? 55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs? 56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers? 57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20? 58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36? 59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April? Time word problems66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her? 69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school? 70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for? 71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home? Money word problemsBest for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade 60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total? 61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left? 62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times? 63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost? 64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total? 65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left? 67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional. 68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year? Physical measurement word problemsBest for: 1st grade, 2nd grade, 3rd grade, 4th grade 72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler? 73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres? 74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years? 75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year? 76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink? 77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get? 78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy? 79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total? 80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres? 81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction? Ratios and percentages word problemsBest for: 4th grade, 5th grade, 6th grade 82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have? 83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers? 84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players? 85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport? 86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population? 87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there? 88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average? Probability and data relationships word problemsBest for: 4th grade, 5th grade, 6th grade, 7th grade 89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased? 90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1? 91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction. 92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni? 93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test? 94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal? 95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y . Geometry word problemsBest for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade 96. Introducing Perimeter: The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter? 97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total? 98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume? 99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw? 100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter? 101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area? 102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw? 103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm? 104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy? 105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle? 106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it? 107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it? 108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it? 109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides? 110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units? 111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side? 112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter? 113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield? 114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius? Variables word problemsBest for: 6th grade, 7th grade, 8th grade 115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent? 116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored. 117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast. 118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored. 119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive. 120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours? How to easily make your own math word problems & word problems worksheetsArmed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do: - Link to Student Interests: By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
- Make Questions Topical: Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
- Include Student Names: Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
- Be Explicit: Repeating keywords distills the question, helping students focus on the core problem.
- Test Reading Comprehension: Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
- Focus on Similar Interests: Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
- Feature Red Herrings: Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.
A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones. Final thoughts about math word problemsYou’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students. Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments. The result? A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach. Try ProdigyThere's no cost to you or your students and Prodigy is fully aligned with state standards for grades 1-8 math. Share this article Table of Contents Popular Posts Related Categories - Teacher Activities (5)
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Hey teachers! 👋Use Prodigy to spark a love for math in your students – including when solving word problems! Please ensure that your password is at least 8 characters and contains each of the following: - a special character: @$#!%*?&
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What can QuickMath do?QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. - The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
- The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
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Have an account? Suggestions for you See moreKindergarten Fact Face OffMultiplication and division, describing and identifying shapes, compare decimals, divide decimals by whole numbers, prepositions, ordinal numbers, multiplication. Math Problem SolvingMathematics. 8 questions Introducing new Paper modeNo student devices needed. Know more - 1. Multiple Choice Edit 30 seconds 1 pt #1: What was the number sentence for your problem? 62-38=? 72-38=? 76-36= 37+?=73
- 2. Multiple Choice Edit 30 seconds 1 pt #2: What was the number sentence for your problem? 81+47= 36+73= 81-42= 73-36=
- 3. Multiple Choice Edit 30 seconds 1 pt #3: What was the number sentence for your problem? 81-47= 81-46= 47-81= 59-22=
- 4. Multiple Choice Edit 30 seconds 1 pt #4: What was the number sentence for your problem? 29+52 52+29 52-29= 52-49=
- 5. Multiple Choice Edit 30 seconds 1 pt #1: What was your answer? 24 34 37 23
- 6. Multiple Choice Edit 30 seconds 1 pt #2: What was your answer? 24 34 37 23
- 7. Multiple Choice Edit 30 seconds 1 pt #3: What was your answer? 24 34 37 23
- 8. Multiple Choice Edit 30 seconds 1 pt #4: What was your answer? 24 34 37 23
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Problem Solving Quizzes, Questions & AnswersTop trending quizzes. Popular TopicsRecent quizzes. 30 Fun Maths Questions with AnswersTable of Contents IntroductionMathematics can be fun if you treat it the right way. Maths is nothing less than a game, a game that polishes your intelligence and boosts your concentration. Compared to older times, people have a better and friendly approach to mathematics which makes it more appealing. The golden rule is to know that maths is a mindful activity rather than a task. There is nothing like hard math problems or tricky maths questions, it’s just that you haven’t explored mathematics well enough to comprehend its easiness and relatability. Maths tricky questions and answers can be transformed into fun math problems if you look at it as if it is a brainstorming session. With the right attitude and friends and teachers, doing math can be most entertaining and delightful. Math is interesting because a few equations and diagrams can communicate volumes of information. Treat math as a language, while moving to rigorous proof and using logical reason for performing a particular step in a proof or derivation. Treating maths as a language totally eradicates the concept of hard math problems or tricky maths questions from your mind. Introducing children to fun maths questions can create a strong love and appreciation for maths at an early age. This way you are setting up the child’s successful future. Fun math problems will urge your child to choose to solve it over playing bingo or baking. Apparently, there are innumerable methods to make easy maths tricky questions and answers. This includes the inception of the ideology that maths is simpler than their fear. This can be done by connecting maths with everyday life. Practising maths with the aid of dice, cards, puzzles and tables reassures that your child effectively approaches Maths. If you wish to add some fun and excitement into educational activities, also check out - Check out some mind-blowing Math Magic Tricks!
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Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12 . Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs. Fun Maths Questions with answers - PDFHere is the Downloadable PDF that consists of Fun Math questions. Click the Download button to view them. Here are some fun, tricky and hard to solve maths problems that will challenge your thinking ability. Answer: is 3, because ‘six’ has three letters What is the number of parking space covered by the car? This tricky math problem went viral a few years back after it appeared on an entrance exam in Hong Kong… for six-year-olds. Supposedly the students had just 20 seconds to solve the problem! Believe it or not, this “math” question actually requires no math whatsoever. If you flip the image upside down, you’ll see that what you’re dealing with is a simple number sequence. Replace the question mark in the above problem with the appropriate number. Which number is equivalent to 3^(4)÷3^(2) This problem comes straight from a standardized test given in New York in 2014. There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete? This question comes directly from a second grader's math homework. To figure out how many small dogs are competing, you have to subtract 36 from 49 and then divide that answer, 13 by 2, to get 6.5 dogs, or the number of big dogs competing. But you’re not done yet! You then have to add 6.5 to 36 to get the number of small dogs competing, which is 42.5. Of course, it’s not actually possible for half a dog to compete in a dog show, but for the sake of this math problem let’s assume that it is. Add 8.563 and 4.8292. Adding two decimals together is easier than it looks. Don’t let the fact that 8.563 has fewer numbers than 4.8292 trip you up. All you have to do is add a 0 to the end of 8.563 and then add like you normally would. I am an odd number. Take away one letter and I become even. What number am I? Answer: Seven (take away the ‘s’ and it becomes ‘even’). Using only an addition, how do you add eight 8’s and get the number 1000? Answer: 888 + 88 + 8 + 8 + 8 = 1000 Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother times her age? 41 years ago, when Sally was 13 and her mother was 39. Which 3 numbers have the same answer whether they’re added or multiplied together? There is a basket containing 5 apples, how do you divide the apples among 5 children so that each child has 1 apple while 1 apple remains in the basket? 4 children get 1 apple each while the fifth child gets the basket with the remaining apple still in it. There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number? Fill in the question mark Two girls were born to the same mother, at the same time, on the same day, in the same month and the same year and yet somehow they’re not twins. Why not? Because there was a third girl, which makes them triplets! A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each rung in 20cm and the bottom rung touches the water. The tide rises at a rate of 10cm an hour. When will the water reach the fifth rung? The tide raises both the water and the boat so the water will never reach the fifth rung. The day before yesterday I was 25. The next year I will be 28. This is true only one day in a year. What day is my Birthday? You have a 3-litre bottle and a 5-litre bottle. How can you measure 4 litres of water by using 3L and 5L bottles? Solution 1 : First, fill 3Lt bottle and pour 3 litres into 5Lt bottle. Again fill the 3Lt bottle. Now pour 2 litres into the 5Lt bottle until it becomes full. Now empty 5Lt bottle. Pour remaining 1 litre in 3Lt bottle into 5Lt bottle. Now again fill 3Lt bottle and pour 3 litres into 5Lt bottle. Now you have 4 litres in the 5Lt bottle. That’s it. Solution 2 : First, fill the 5Lt bottle and pour 3 litres into 3Lt bottle. Empty 3Lt bottle. Pour remaining 2 litres in 5Lt bottle into 3Lt bottle. Again fill the 5Lt bottle and pour 1 litre into 3 Lt bottle until it becomes full. 3 Friends went to a shop and purchased 3 toys. Each person paid Rs.10 which is the cost of one toy. So, they paid Rs.30 i.e. total amount. The shop owner gave a discount of Rs.5 on the total purchase of 3 toys for Rs.30. Then, among Rs.5, Each person has taken Rs.1 and remaining Rs.2 given to the beggar beside the shop. Now, the effective amount paid by each person is Rs.9 and the amount given to the beggar is Rs.2. So, the total effective amount paid is 9*3 = 27 and the amount given to beggar is Rs.2, thus the total is Rs.29. Where has the other Rs.1 gone from the original Rs.30? The logic is payments should be equal to receipts. We cannot add the amount paid by persons and the amount given to the beggar and compare it to Rs.30.The total amount paid is ₹27. So, from ₹27, the shop owner received 25 rupees and beggar received ₹ 2. Thus, payments are equal to receipts. How to get a number 100 by using four sevens (7’s) and a one (1)? Answer 1: 177 – 77 = 100 ; Answer 2: (7+7) * (7 + (1/7)) = 100 Move any four matches to get 3 equilateral triangles only (don’t remove matches) Find the area of the red triangle. To solve this fun maths question, you need to understand how the area of a parallelogram works. If you already know how the area of a parallelogram and the area of a triangle are related, then adding 79 and 10 and subsequently subtracting 72 and 8 to get 9 should make sense. How many feet are in a mile? Solve - 15+ (-5x) =0 What is 1.92÷3 A man is climbing up a mountain which is inclined. He has to travel 100 km to reach the top of the mountain. Every day He climbs up 2 km forward in the day time. Exhausted, he then takes rest there at night time. At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined. Then how many days does it take him to reach the mountain top? If 72 x 96 = 6927, 58 x 87 = 7885, then 79 x 86 = ? Answer: Look at this series: 36, 34, 30, 28, 24, … What number should come next? Look at this series: 22, 21, 23, 22, 24, 23, … What number should come next? If 13 x 12 = 651 & 41 x 23 = 448, then, 24 x 22 =? Look at this series: 53, 53, 40, 40, 27, 27, … What number should come next? The ultimate goals of mathematics instruction are students understanding the material presented, applying the skills, and recalling the concepts in the future. There's little benefit in students recalling a formula or procedure to prepare for an assessment tomorrow only to forget the core concept by next week. Teachers must focus on making sure that the students understand the material and not just memorize the procedures. After you learn the answers to a fun maths question, you begin to ask yourself how you could have missed something so easy. The truth is, most trick questions are designed to trick your mind, which is why the answers to fun maths questions are logical and easy. About CuemathCuemath, a student-friendly mathematics and coding platform, conducts regular Online Classes for academics and skill-development, and their Mental Math App, on both iOS and Android , is a one-stop solution for kids to develop multiple skills. Understand the Cuemath Fee structure and sign up for a free trial. Brain Teaser: Think You're a High IQ Individual? Solve This Math Puzzle to Prove It!Brain teaser: it’s a tough challenge only the brightest high-iq individuals can beat this math puzzle. are you one of them you have 19 seconds on the clock to beat this challenge. Brainteasers are more than just riddles wrapped in a package. They're a mental gym, a challenging playground where you can push your cognitive abilities. These puzzles come in all shapes and sizes, like a well-stocked toy box for the mind. From logic puzzles that test your reasoning skills to wordplay challenges that make you think outside the box, there's a brainteaser out there for everyone, regardless of age or background. Try: Wordmoji Puzzle: Can Your Emoji Mastery Crack This Chocolate Mystery in 9 Seconds? But what exactly makes a brainteaser a brainteaser? It all comes down to the unconventional thinking they require. This particular brainteaser is a siren song for all math enthusiasts! Get ready to flex your cognitive muscles and test your mathematical prowess. Below, you'll find an image featuring a monkey and various other objects with numerical values assigned to them. Your mission is to decipher the value written against the objects and decode the final equation mentioned in the image. Here's the catch: you only have 19 seconds! The pressure is on, but fear not, math whizzes! By utilising lateral thinking and approaching the problem from a creative angle, you'll be well on your way to cracking the code. Are you ready to embark on this mathematical adventure? Set your timer, focus your mind, and let the brainteasing begin! Remember, the key lies in unconventional thinking. Brain Teaser: Find the Values in 19 Seconds Source: Pinterest (Vera Pavlovskaya) Brainteasers are more than just mind games; they're a playground for your brain, offering a delightful blend of challenge and amusement. Not only can they keep your mind sharp, but they can also provide an opportunity to impress your friends with your problem-solving prowess. The brainteaser we're about to tackle involves deciphering various equations. This isn't your ordinary math problem. It's a test of both logic and creative thinking. By examining the equations provided and utilising your basic arithmetic skills, you'll be well on your way to unlocking the secret. Time is of the essence! Being under pressure can actually benefit your brain. It forces you to focus your attention and think more quickly, honing your ability to recognise patterns and make logical connections. But fear not, even if the clock runs out before you crack the code, all is not lost! So, how many equations did you solve? Congratulations if you managed to find them all! Your logical skills deserve a round of applause. If you're still stumped, don't worry! The beauty of brainteasers is that you can always revisit them and try again. Simply scroll back up and give it another shot. Find the Values: Solution The image shows two Monkeys valued at 6 in the first equation Let's take the value of one Monkey to be A So, we get: A=6/2 So the value of one Monkey is 3 Coming to the second equation we have a Monkey and two bananas subtracting and giving the value of 13 Let's take the value of Bananas to be B So, the value of Bananas is 16 Coming to the third equation we have Bananas and a Coconut Tree valued at 20 Let's take the value of Coconut Tree to be C So we have: B+C=20 16+C=20 Coming to the fourth equation we have Deriving the values from the above we get: 3+4=7 So, the value of the final equation is 7 Hope you liked this puzzle! Keep trying your hands on these puzzles and you will surely emerge as a true puzzle master! Must Try: Logic Puzzle: Only High IQ Thinkers Can Find the Hidden Word in 13 Seconds—Will You? Get here current GK and GK quiz questions in English and Hindi for India , World, Sports and Competitive exam preparation. 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This isn't your ordinary math problem. It's a test of both logic and creative thinking. By examining the equations provided and utilising your basic arithmetic skills, you'll be well on your way ...