NCDAP Algebraic Concepts & Quantitative Reasoning 4

Question 1

Solve the system: x + y = 10 and x - y = 4. What is x?

Accepted Answer

7

Answer

Adding the equations: 2x = 14 → x = 7.

Question 2

What is the y-intercept of the line 3x - 2y = 12?

Accepted Answer

-6

Answer

Set x = 0: -2y = 12 → y = -6.

Question 3

A population of bacteria doubles every 3 hours. If there are 200 bacteria now, how many will there be in 9 hours?

Accepted Answer

1600

Answer

After 9 hours = 3 doubling periods: 200 × 2³ = 200 × 8 = 1600.

Question 4

Which expression is equivalent to (2x²)³?

Accepted Answer

8x⁶

Answer

(2x²)³ = 2³ · x^(2·3) = 8x⁶.

Question 5

Maria scored 78, 85, 92, and 89 on her first four tests. What score does she need on the fifth test to have an average of 87?

Accepted Answer

91

Answer

(78 + 85 + 92 + 89 + x)/5 = 87 → 344 + x = 435 → x = 91.

(NCDAP) North Carolina Diagnostic Placement Test Practice Test