ICAS Algebra and Patterns 5

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?

Accepted Answer

19

Answer

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?

Accepted Answer

(5, 10)

Answer

Set 2x = x + 5, so x = 5 and y = 10; check: 10 = 5 + 5 ✓.

Question 3

The expression 5x − 2(x − 3) simplifies to:

Accepted Answer

3x + 6

Answer

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)?

Accepted Answer

25

Answer

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?

Accepted Answer

A = 2w²

Answer

Substitute l = 2w into A = lw: A = (2w)(w) = 2w².

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