ICAS Algebra and Patterns 3 — Questions and Answers
Question 1: A shop charges $4 per item plus a $6 delivery fee. Which equation represents the total cost C for n items?
- C = 4n + 6 (Correct answer)
- C = 6n + 4
- C = 4(n + 6)
- C = 6(n + 4)
Correct answer: C = 4n + 6
The total is $4 multiplied by the number of items plus the fixed $6 fee: C = 4n + 6.
Question 2: What is the missing term in the pattern: 2, 6, 18, __, 162?
- 54 (Correct answer)
- 36
- 72
- 48
Correct answer: 54
Each term is multiplied by 3: 2×3=6, 6×3=18, 18×3=54, 54×3=162.
Question 3: If y = 2x − 7 and x = 5, what is y?
- 3 (Correct answer)
- −3
- 17
- 7
Correct answer: 3
Substitute x = 5: y = 2(5) − 7 = 10 − 7 = 3.
Question 4: A pattern of triangles is built with toothpicks: 1 triangle uses 3, 2 triangles share a side and use 5, 3 use 7. How many toothpicks are needed for 8 triangles?
- 17 (Correct answer)
- 15
- 19
- 24
Correct answer: 17
The rule is T = 2n + 1, so for n = 8: T = 16 + 1 = 17.
Question 5: Which expression has the same value as 4x + 2x − 3 + 5?
- 6x + 2 (Correct answer)
- 6x − 2
- 8x + 2
- 6x + 8
Correct answer: 6x + 2
Combine like terms: 4x + 2x = 6x and −3 + 5 = 2, giving 6x + 2.
Question 6: The rule for a function is f(x) = x² + 3. What is f(4)?
- 19 (Correct answer)
- 16
- 11
- 25
Correct answer: 19
Substitute x = 4: f(4) = 4² + 3 = 16 + 3 = 19.
Question 7: If 3a + 7 = 28, what is 2a?
- 14 (Correct answer)
- 7
- 21
- 10
Correct answer: 14
Subtract 7: 3a = 21, so a = 7, and 2a = 14.
ICAS Algebra and Patterns 3
A shop charges $4 per item plus a $6 delivery fee.
Which equation represents the total cost C for n items?