Core Plus (Math Version Flashcards

A classroom has 24 students. If 3/8 of them scored above 90% on a test, how many students scored above 90%?

Answer: 9

3/8 × 24 = 9 students scored above 90%.

Which of the following is equivalent to 2³ × 2⁴?

Answer: 2⁷

When multiplying powers with the same base, add the exponents: 2³ × 2⁴ = 2^(3+4) = 2⁷.

A rectangle has a length of 15 cm and a width of 8 cm. What is its perimeter?

Answer: 46 cm

Perimeter = 2(length + width) = 2(15 + 8) = 2(23) = 46 cm.

If y = 3x − 5 and x = 4, what is the value of y?

Answer: 7

Substitute x = 4: y = 3(4) − 5 = 12 − 5 = 7.

A store marks up items by 25%. If an item costs $48, what is the selling price?

Answer: $60

Markup = 25% × $48 = $12; selling price = $48 + $12 = $60.

What is the least common multiple (LCM) of 6 and 10?

Answer: 30

The LCM of 6 and 10 is 30, as it is the smallest number divisible by both.

A number line shows points at −3, 0, and 4. What is the distance between −3 and 4?

Answer: 7

Distance = |4 − (−3)| = |4 + 3| = 7.

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of randomly picking a blue marble?

Answer: 3/10

P(blue) = 3 blue / 10 total = 3/10.

Which expression is equivalent to 4(x + 3) − 2x?

Answer: 2x + 12

Distribute: 4x + 12 − 2x = 2x + 12.

A triangle has angles measuring 45°, 90°, and x°. What is the value of x?

Answer: 45

The sum of angles in a triangle is 180°, so x = 180 − 45 − 90 = 45.

Convert 0.375 to a fraction in simplest form.

Answer: 3/8

0.375 = 375/1000, which simplifies to 3/8 by dividing by 125.

A recipe calls for 2½ cups of flour. If you want to make 3 batches, how many cups of flour do you need?

Answer: 7½

2½ × 3 = 5/2 × 3 = 15/2 = 7½ cups.

On a coordinate plane, what quadrant contains the point (−4, 6)?

Answer: Quadrant II

A negative x-value and positive y-value place the point in Quadrant II.

If 5n + 7 = 32, what is the value of n?

Answer: 5

5n = 32 − 7 = 25, so n = 25 ÷ 5 = 5.

A car travels 270 miles in 4.5 hours. What is its average speed in miles per hour?

Answer: 60 mph

Speed = distance ÷ time = 270 ÷ 4.5 = 60 mph.

What is the area of a circle with a radius of 7 cm? (Use π ≈ 3.14)

Answer: 153.86 cm²

Area = πr² = 3.14 × 7² = 3.14 × 49 ≈ 153.86 cm².

Which of the following sets of numbers is ordered from least to greatest?

Answer: −1, −0.5, 0, 0.25

On the number line, −1 < −0.5 < 0 < 0.25 is the correct ascending order.

A student scored 78, 85, 91, 74, and 82 on five tests. What is the mean score?

Answer: 82

Mean = (78 + 85 + 91 + 74 + 82) / 5 = 410 / 5 = 82.

Which property is illustrated by the equation 5 × (2 + 3) = 5 × 2 + 5 × 3?

Answer: Distributive property

The distributive property states that a(b + c) = ab + ac.

A map has a scale of 1 inch = 50 miles. If two cities are 3.5 inches apart on the map, what is the actual distance?

Answer: 175 miles

Actual distance = 3.5 × 50 = 175 miles.