PAT Algebraic Thinking 2 — Questions and Answers
Question 1: What is the missing number in the pattern: 2, 5, __, 11, 14?
- 7
- 8 (Correct answer)
- 9
- 6
Correct answer: 8
The pattern adds 3 each time: 2+3=5, 5+3=8, 8+3=11, 11+3=14.
Question 2: Solve for y: 4y = 36
- 8
- 9 (Correct answer)
- 32
- 40
Correct answer: 9
Dividing both sides by 4: y = 36 ÷ 4 = 9.
Question 3: Which value of x makes the inequality 2x + 1 > 9 true?
- x = 3
- x = 4
- x = 5 (Correct answer)
- x = 2
Correct answer: x = 5
Substituting x=5: 2(5)+1=11>9 is true; for x=3: 7>9 false; x=4: 9>9 false (not strictly greater); x=2: 5>9 false.
Question 4: A plumber charges a $25 call-out fee plus $15 per hour. Which equation shows the total cost C for h hours of work?
- C = 15h
- C = 25h + 15
- C = 15h + 25 (Correct answer)
- C = 25 + 15
Correct answer: C = 15h + 25
The total cost is the hourly rate (15h) added to the fixed call-out fee (25), giving C = 15h + 25.
Question 5: Which value of x makes the equation 5x − 3 = 22 true?
- 4
- 5 (Correct answer)
- 6
- 7
Correct answer: 5
Adding 3 to both sides: 5x = 25, then dividing by 5: x = 5. Check: 5(5)−3=22 ✓
Question 6: The number of chairs in a row follows the pattern: Row 1 has 3, Row 2 has 5, Row 3 has 7. How many chairs are in Row 10?
- 19
- 21 (Correct answer)
- 23
- 25
Correct answer: 21
The rule is 2n + 1: Row 10 = 2(10) + 1 = 21.
Question 7: Simplify the expression: 4a + 3b − 2a + b
- 2a + 4b (Correct answer)
- 6a + 4b
- 2a + 2b
- 6a + 2b
Correct answer: 2a + 4b
Combining like terms: (4a − 2a) + (3b + b) = 2a + 4b.
PAT Algebraic Thinking 2
What is the missing number in the pattern: 2, 5, __, 11, 14?