Mathematics Challenge

Simplify the algebraic expression: 3x + 2y - 5x + 4y

• -2x + 2y

• 8y - 2x

• 5x - 6y

• -2x + 6y

Answer explanation

Combine like terms by adding the coefficients of x and y separately: 3x - 5x = -2x and 2y + 4y = 6y. Therefore, the simplified expression is -2x + 6y.

Calculate the area of a rectangle with length 8 cm and width 5 cm.

• 42 square cm

• 40 square cm

• 30 square cm

• 13 square cm

Answer explanation

To calculate the area of a rectangle, multiply the length by the width. In this case, 8 cm * 5 cm = 40 square cm. Therefore, the correct answer is 40 square cm.

Convert the fraction 3/4 to a decimal.

• 1.25

• 0.50

• 0.75

• 0.25

Answer explanation

To convert the fraction 3/4 to a decimal, divide 3 by 4 which equals 0.75. Therefore, the correct answer is 0.75.

In a survey, 60% of students prefer pizza over burgers. If there are 150 students in total, how many prefer pizza?

• 75

• 100

• 120

• 90

Answer explanation

If 60% prefer pizza out of 150 students, then 0.6 * 150 = 90 students prefer pizza. Therefore, the correct answer is 90.

What is the probability of rolling a prime number on a standard six-sided die?

• 1/5

• 1/2

• 1/4

• 1/3

Answer explanation

To find the probability of rolling a prime number on a standard six-sided die, we identify the prime numbers on a die which are 2, 3, and 5. There are 3 prime numbers out of 6 possible outcomes, so the probability is 3/6 which simplifies to 1/2.

If a rectangle has a length of 12 cm and a width of 5 cm, what is its perimeter?

• 22 cm

• 40 cm

• 15 cm

• 34 cm

Answer explanation

To find the perimeter of a rectangle, we use the formula 2*(length + width). Substituting the values, we get 2*(12+5) = 2*17 = 34 cm. Therefore, the correct answer is 34 cm.

Solve for x: 2(x + 3) = 16

• x = 5

• x = 3

• x = 8

• x = 10

Answer explanation

To solve the equation, first distribute the 2: 2x + 6 = 16. Then, subtract 6 from both sides: 2x = 10. Finally, divide by 2 to find x = 5. Therefore, the correct answer is x = 5.

Find the volume of a cube with a side length of 4 cm.

• 64 cubic cm

• 100 cubic cm

• 16 cubic cm

• 36 cubic cm

Answer explanation

To find the volume of a cube, you cube the length of one side. In this case, 4 cm cubed equals 64 cubic cm. Therefore, the correct answer is 64 cubic cm.

Add 1/3 and 2/5, then simplify the result.

• 5/8

• 7/15

• 9/13

• 11/15

Answer explanation

To add 1/3 and 2/5, find a common denominator which is 15. Then, convert both fractions to have the denominator 15. 1/3 becomes 5/15 and 2/5 becomes 6/15. Adding them gives 11/15, which is the simplified result.

Given the data set: 5, 7, 8, 10, 12, find the mean.

• 8.4

• 9.2

• 11.8

• 7.5

Answer explanation

To find the mean, add all numbers together and divide by the total count. (5 + 7 + 8 + 10 + 12) / 5 = 42 / 5 = 8.4. Therefore, the mean is 8.4.