AQL Number Sense and Algebraic Thinking 1 — Questions and Answers
Question 1: Which of the following best represents the value of 2³ × 2⁴?
- 2⁷ (Correct answer)
- 2¹²
- 4⁷
- 8⁷
Correct answer: 2⁷
When multiplying exponential expressions with the same base, you add the exponents: 2³ × 2⁴ = 2^(3+4) = 2⁷.
Question 2: If a store sells apples for $1.25 each and oranges for $0.75 each, how much does it cost to buy 4 apples and 6 oranges?
- $9.50 (Correct answer)
- $8.00
- $9.00
- $7.50
Correct answer: $9.50
4 × $1.25 = $5.00 and 6 × $0.75 = $4.50, so the total is $5.00 + $4.50 = $9.50.
Question 3: Which number is a prime number?
- 51
- 57
- 53 (Correct answer)
- 55
Correct answer: 53
53 is prime because it has no divisors other than 1 and itself; 51 = 3×17, 55 = 5×11, and 57 = 3×19.
Question 4: Solve for x: 3x - 7 = 14
- x = 7 (Correct answer)
- x = 3
- x = 9
- x = 21
Correct answer: x = 7
Adding 7 to both sides gives 3x = 21, then dividing by 3 gives x = 7.
Question 5: What is the least common multiple (LCM) of 8 and 12?
- 48
- 24 (Correct answer)
- 96
- 4
Correct answer: 24
The LCM of 8 and 12 is 24 because 24 is the smallest number that both 8 and 12 divide into evenly.
Question 6: A number is increased by 40% and then decreased by 20%. What is the net percentage change?
- 12% increase (Correct answer)
- 20% increase
- 20% decrease
- No change
Correct answer: 12% increase
Starting with 100, a 40% increase gives 140, and a 20% decrease gives 140 × 0.80 = 112, which is a 12% net increase.
Question 7: Which of the following is an example of an irrational number?
- √9
- √25
- √2 (Correct answer)
- 0.75
Correct answer: √2
√2 ≈ 1.41421… is irrational because it cannot be expressed as a ratio of two integers, while √9 = 3, √25 = 5, and 0.75 = 3/4 are all rational.
AQL Number Sense and Algebraic Thinking 1
Which of the following best represents the value of 2³ × 2⁴?