PAT Algebraic Thinking 1 — Questions and Answers
Question 1: Which of the following represents the rule for the pattern: 3, 6, 12, 24, ...?
- Add 3 each time
- Multiply by 2 each time (Correct answer)
- Add 6 each time
- Multiply by 3 each time
Correct answer: Multiply by 2 each time
Each term is obtained by multiplying the previous term by 2 (3×2=6, 6×2=12, 12×2=24).
Question 2: If n = 5, what is the value of 3n + 4?
- 12
- 17
- 19 (Correct answer)
- 22
Correct answer: 19
Substituting n = 5: 3(5) + 4 = 15 + 4 = 19.
Question 3: Which equation best describes this function table? Input: 1, 2, 3, 4 | Output: 5, 8, 11, 14
- y = 2x + 3
- y = 3x + 2 (Correct answer)
- y = 4x + 1
- y = x + 4
Correct answer: y = 3x + 2
The output increases by 3 for each increase of 1 in input, and when x=1, y=3(1)+2=5, confirming y=3x+2.
Question 4: Solve for x: x − 7 = 15
- 8
- 22 (Correct answer)
- 21
- 23
Correct answer: 22
Adding 7 to both sides: x = 15 + 7 = 22.
Question 5: A sequence starts at 100 and each term decreases by 8. What is the 6th term?
- 52
- 60 (Correct answer)
- 56
- 48
Correct answer: 60
Starting at 100: term1=100, term2=92, term3=84, term4=76, term5=68, term6=60.
Question 6: Which expression is equivalent to 2(x + 5)?
- 2x + 5
- x + 10
- 2x + 10 (Correct answer)
- 2x + 7
Correct answer: 2x + 10
Applying the distributive property: 2(x + 5) = 2·x + 2·5 = 2x + 10.
Question 7: If a bag holds 8 apples and you have b bags, which expression represents the total number of apples?
- b + 8
- 8 − b
- 8b (Correct answer)
- b ÷ 8
Correct answer: 8b
Each of the b bags holds 8 apples, so the total is 8 multiplied by b, written as 8b.
PAT Algebraic Thinking 1
Which of the following represents the rule for the pattern: 3, 6, 12, 24, ...?