ICAS Algebra and Patterns 5 — Questions and Answers
Question 1: A pattern of dots forms rows: row 1 has 1 dot, row 2 has 3 dots, row 3 has 5 dots. How many dots are in row 10?
- 19 (Correct answer)
- 21
- 20
- 18
Correct answer: 19
The nth row has 2n − 1 dots; for row 10: 2(10) − 1 = 19.
Question 2: Which pair of values (x, y) satisfies both equations: y = 2x and y = x + 5?
- (5, 10) (Correct answer)
- (3, 6)
- (4, 9)
- (2, 4)
Correct answer: (5, 10)
Set 2x = x + 5, so x = 5 and y = 10; check: 10 = 5 + 5 ✓.
Question 3: The expression 5x − 2(x − 3) simplifies to:
- 3x + 6 (Correct answer)
- 3x − 6
- 7x + 6
- 3x − 3
Correct answer: 3x + 6
Distribute −2: 5x − 2x + 6 = 3x + 6.
Question 4: A sequence is defined by: T(1) = 5 and T(n) = T(n−1) + 4. What is T(6)?
- 25 (Correct answer)
- 29
- 21
- 24
Correct answer: 25
T(1)=5, T(2)=9, T(3)=13, T(4)=17, T(5)=21, T(6)=25.
Question 5: If the area of a rectangle is A = lw and l = 2w, which equation represents the area in terms of w only?
- A = 2w² (Correct answer)
- A = 2w
- A = w² + 2
- A = 2 + w²
Correct answer: A = 2w²
Substitute l = 2w into A = lw: A = (2w)(w) = 2w².
Question 6: What is the next term in the pattern: 1, 1, 2, 3, 5, 8, 13, ___?
- 21 (Correct answer)
- 18
- 16
- 24
Correct answer: 21
Each term is the sum of the two preceding terms (Fibonacci): 8 + 13 = 21.
Question 7: If 2(3x + 1) = 4x + 10, what is x?
- 4 (Correct answer)
- 3
- 5
- 2
Correct answer: 4
Expand: 6x + 2 = 4x + 10, subtract 4x: 2x + 2 = 10, so 2x = 8 and x = 4.
ICAS Algebra and Patterns 5
A pattern of dots forms rows: row 1 has 1 dot, row 2 has 3 dots, row 3 has 5 dots.
How many dots are in row 10?