Mathematics Quiz

Which of the following is an example of the commutative property of addition?

• 6 x (4 + 2) = (6 x 4) + (6 x 2)

• (1 + 7) + 4 = 1 + (7 + 4)

• 5 x 3 = 3 x 5

• 8 + 9 = 9 + 8

Answer explanation

The commutative property of addition states that changing the order of the addends does not change the sum. In this case, 8 + 9 = 9 + 8 illustrates this property, while the other options represent different properties.

A school bus has the following riders: 20 students in ninth grade, 10 students in tenth grade, 9 students in eleventh grade, and 7 students in twelfth grade. Approximately what percent of the students on the bus are in ninth grade?

• 23%

• 43%

• 46%

• 76%

Answer explanation

To find the percentage of ninth graders, divide the number of ninth graders (20) by the total number of students (20 + 10 + 9 + 7 = 46). Thus, 20/46 ≈ 0.4348, or about 43%. Therefore, the correct answer is 43%.

To make fruit punch, Edie mixes two kinds of juices in the following ratio: 1 cup of pineapple juice to 3 cups of orange juice. How many cups of orange juice will Edie need in order to make 48 cups of fruit punch?

• 12

• 16

• 24

• 36

Answer explanation

The ratio of pineapple to orange juice is 1:3. For 48 cups of fruit punch, divide by 4 (1+3=4), giving 12 cups of pineapple and 36 cups of orange juice. Thus, Edie needs 36 cups of orange juice.

The only prime factors of a certain product are 2, 3, and 7. Which of the following could be the product?

• 18 x 28

• 20 x 21

• 22 x 63

• 24 x 35

Answer explanation

The product 18 x 28 equals 504, which has prime factors 2, 3, and 7. The other options include prime factors outside of 2, 3, and 7, making 18 x 28 the only valid choice.

After a lesson on rounding and estimation, a teacher tells students that 157 rulers will be distributed to 4 teachers. The teacher asks the students to estimate the number of rulers each teacher will receive if the rulers are shared as equally as possible among the teachers. Which of the following students produces the best estimate of the number of rulers each teacher will receive?

• Student A: about 30

• Student B: about 35

• Student C: about 40

• Student D: about 45

Answer explanation

To estimate, divide 157 by 4. 157 is close to 160, and 160 divided by 4 equals 40. Thus, Student C's estimate of about 40 is the best choice, as it accurately reflects the distribution of rulers.

What is the value of the expression 4x² + 7 when x = 3.2?

Answer explanation

To find the value of 4x² + 7 when x = 3.2, substitute 3.2 into the expression: 4(3.2)² + 7 = 4(10.24) + 7 = 40.96 + 7 = 47.96. The correct answer is not listed, indicating a possible error in the answer choices.

Jack had three babysitting jobs this week. He worked the same number of hours H on each job. He was paid at a rate of $12 for every hour at his first job, $4 for every half hour at his second job, and $5 for every 20 minutes at his third job. Which of the following expressions represents the total amount, in dollars, Jack was paid this week?

• 12 x H + 4 x H + 5 x H

• 12 x H + 8 x H + 15 x H

• 12 x H + 4 x H + 20 x H

• 12 x H + 4 x ½ x H + 5 x ⅓ x H

Answer explanation

Jack's total pay is calculated by multiplying hours worked by the pay rate for each job. For the first job: 12H, second job: 4 per half hour (8H), and third job: 5 per 20 minutes (15H). Thus, the total is 12H + 8H + 15H.

Which of the following is equivalent to the inequality $5 \leq 7 - p$?

• p \leq 2

• p \geq 2

• p \leq -2

• p \geq -2

Answer explanation

To solve the inequality $5 \leq 7 - p$, subtract 7 from both sides: $5 - 7 \leq -p$ simplifies to $-2 \leq -p$. Multiplying by -1 reverses the inequality: $p \leq 2$. Thus, the correct choice is $p \leq 2$.

Which of the following equations could represent the relationship shown in the preceding table?

• y = -8x + 4

• y = -7x + 4

• y = -6x + 4

• y = -5x + 4

Answer explanation

To find the correct equation, we can check the slope and y-intercept. The equation y = -6x + 4 has a slope of -6, which matches the rate of change in the table, making it the correct choice.

Which of the following terms best describes the preceding polygon?

• Hexagon

• Parallelogram

• Pentagon

• Trapezoid

Answer explanation

A pentagon is a polygon with five sides. The question asks for the term that best describes the polygon, and since a pentagon fits this definition, it is the correct choice over hexagon (6 sides), parallelogram (4 sides), and trapezoid (4 sides).