ICAS Algebra and Patterns 2

Question 1

A pattern follows the rule: multiply by 3, then subtract 2. If the first term is 2, what is the fourth term?

Accepted Answer

46

Answer

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?

Accepted Answer

4

Answer

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?

Accepted Answer

6x + 6

Answer

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?

Accepted Answer

32

Answer

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?

Accepted Answer

Perfect squares

Answer

Each term is the square of its position: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25.

(ICAS) ICAS Practice Test

(ICAS) ICAS Practice Test

ICAS Algebra and Patterns 2