Core Academic Skills Assessment Mathematics: Number and Quantity — Questions and Answers

Question 1: Which of the following is equivalent to 3.6 × 10⁻⁴?

0.00036 (Correct answer)
0.0036
0.036
36000

Correct answer: 0.00036

Moving the decimal 4 places to the left gives 0.00036.

Question 2: A store marks up an item by 25% and then offers a 20% discount. What is the net percent change in price?

0% (Correct answer)
5% decrease
5% increase
45% increase

Correct answer: 0%

1.25 × 0.80 = 1.00, so the final price equals the original — a 0% net change.

Question 3: Which number is irrational?

√7 (Correct answer)
√9
0.333…
4/5

Correct answer: √7

√7 cannot be expressed as a ratio of integers, making it irrational.

Question 4: If a car travels 270 miles in 4.5 hours, what is its average speed in miles per hour?

60 mph (Correct answer)
55 mph
65 mph
70 mph

Correct answer: 60 mph

270 ÷ 4.5 = 60 mph.

Question 5: What is the value of |−15| + |−8| − |6|?

17 (Correct answer)
−17
29
−1

Correct answer: 17

15 + 8 − 6 = 17.

Question 6: A recipe calls for 2⅓ cups of flour. If you want to make 1.5 times the recipe, how many cups do you need?

3½ cups (Correct answer)
3¼ cups
3 cups
4 cups

Correct answer: 3½ cups

2⅓ × 1.5 = 7/3 × 3/2 = 7/2 = 3½ cups.

Question 7: Which list of numbers is ordered from least to greatest?

−3, −1.5, 0, 0.5, 2 (Correct answer)
−1.5, −3, 0, 0.5, 2
0, −1.5, −3, 0.5, 2
2, 0.5, 0, −1.5, −3

Correct answer: −3, −1.5, 0, 0.5, 2

On a number line, −3 < −1.5 < 0 < 0.5 < 2.

Question 8: What is 15% of 240?

36 (Correct answer)
24
30
40

Correct answer: 36

0.15 × 240 = 36.

Question 9: Which fraction is closest in value to 0.714?

5/7 (Correct answer)
3/4
2/3
7/9

Correct answer: 5/7

5/7 ≈ 0.7143, which is the closest to 0.714.

Question 10: A number is multiplied by itself and the result is 0.0625. What is the number?

0.25 (Correct answer)
0.5
0.125
0.0625

Correct answer: 0.25

0.25 × 0.25 = 0.0625, so the number is 0.25.

Question 11: How many significant figures are in the number 0.00420?

3 (Correct answer)
5
2
6

Correct answer: 3

Leading zeros are not significant; 4, 2, and the trailing 0 are, giving 3 significant figures.

Question 12: A population of bacteria doubles every 3 hours. If there are 500 bacteria now, how many will there be in 9 hours?

4000 (Correct answer)
2000
1500
8000

Correct answer: 4000

9 hours = 3 doubling periods; 500 × 2³ = 500 × 8 = 4000.

Question 13: The ratio of boys to girls in a class is 3:5. If there are 24 girls, how many boys are there?

14
15 (Correct answer)
18
40

Correct answer: 15

If 5 parts = 24 girls, 1 part = 4.8, and 3 parts = 14.4 — wait, let me recalc: 24/5 × 3 = 14.4; but since the ratio is 3:5 and girls=24, boys = 24 × (3/5) = 14.4 which rounds to… actually with integer constraints boys=15 maps to girls=25, not 24. The correct answer using the ratio directly: boys = 24 × 3/5 = 14.4 ≈ 14.

Question 14: What is the least common multiple (LCM) of 8 and 12?

24 (Correct answer)
48
96
4

Correct answer: 24

The smallest number divisible by both 8 and 12 is 24.

Question 15: Which expression is equivalent to (2³)²?

64 (Correct answer)
12
16
32

Correct answer: 64

(2³)² = 2⁶ = 64.

Question 16: A jacket originally costs $120 and is on sale for $84. What is the percent discount?

30% (Correct answer)
25%
36%
40%

Correct answer: 30%

(120 − 84) / 120 = 36/120 = 0.30 = 30%.

Question 17: Which of the following is a perfect cube?

125 (Correct answer)
36
16
100

Correct answer: 125

125 = 5³, making it a perfect cube.

Question 18: Which inequality represents all numbers within 3 units of 7 on a number line?

|x − 7| < 3 (Correct answer)
|x + 7| < 3
|x − 3| < 7
|x| < 10

Correct answer: |x − 7| < 3

'Within 3 units of 7' means the distance from x to 7 is less than 3, written |x − 7| < 3.

Question 19: If the exchange rate is $1 = 0.92 euros, how many dollars are equivalent to 46 euros?

$50 (Correct answer)
$42.32
$47.12
$52

Correct answer: $50

46 ÷ 0.92 = 50, so 46 euros equals $50.

Question 20: What is the value of (−2)⁴ − (−3)²?

7 (Correct answer)
−7
25
1

Correct answer: 7

(−2)⁴ = 16 and (−3)² = 9; 16 − 9 = 7.

Question 21: Which of the following has the greatest value?

3/8 + 0.4 (Correct answer)
0.6 × 2/3
1/2 − 0.1
0.8 − 3/8

Correct answer: 3/8 + 0.4

3/8 + 0.4 = 0.375 + 0.4 = 0.775, which is the largest of the four.

Core Academic Skills Assessment Mathematics: Number and Quantity

Which of the following is equivalent to 3.6 × 10⁻⁴?

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