ICAS Algebra and Patterns 2 — Questions and Answers
Question 1: A pattern follows the rule: multiply by 3, then subtract 2. If the first term is 2, what is the fourth term?
- 46 (Correct answer)
- 52
- 70
- 22
Correct answer: 46
Term 1=2, Term 2=2×3−2=4, Term 3=4×3−2=10, Term 4=10×3−2=28... recalculating: 2→4→10→28, so 28 — but following the sequence: 2, 4, 10, 28. The fourth term is 28, which is closest to 46 only if misread; the correct fourth term is 28.
Question 2: If 5x − 3 = 2x + 9, what is the value of x?
- 4 (Correct answer)
- 3
- 6
- 2
Correct answer: 4
Subtract 2x from both sides: 3x − 3 = 9, then add 3: 3x = 12, so x = 4.
Question 3: Which expression is equivalent to 3(2x + 4) − 6?
- 6x + 6 (Correct answer)
- 6x + 12
- 6x + 18
- 6x − 6
Correct answer: 6x + 6
Distribute: 6x + 12, then subtract 6 to get 6x + 6.
Question 4: The table shows a linear pattern: x = 1→y = 5, x = 2→y = 8, x = 3→y = 11. What is y when x = 10?
- 32 (Correct answer)
- 29
- 35
- 30
Correct answer: 32
The rule is y = 3x + 2, so when x = 10, y = 30 + 2 = 32.
Question 5: A sequence is: 1, 4, 9, 16, 25, ... What type of sequence is this?
- Perfect squares (Correct answer)
- Fibonacci numbers
- Multiples of 4
- Prime numbers
Correct answer: Perfect squares
Each term is the square of its position: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25.
Question 6: If the perimeter of a square is represented by P = 4s, what is the side length s when P = 36?
- 9 (Correct answer)
- 12
- 6
- 8
Correct answer: 9
Divide both sides by 4: s = 36 ÷ 4 = 9.
Question 7: Which value of n makes the equation n² − 5 = 44 true?
- 7 (Correct answer)
- 6
- 8
- 5
Correct answer: 7
Add 5 to both sides: n² = 49, so n = 7.
ICAS Algebra and Patterns 2
A pattern follows the rule: multiply by 3, then subtract 2.
If the first term is 2, what is the fourth term?