NJGPA Algebra I and Geometry Concepts 3

Question 1

What are the solutions to x² - 5x + 6 = 0?

Accepted Answer

x = 2 and x = 3

Answer

Factor as (x - 2)(x - 3) = 0, giving x = 2 or x = 3.

Question 2

A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?

Accepted Answer

15

Answer

By the Pythagorean theorem: c² = 9² + 12² = 81 + 144 = 225, so c = 15.

Question 3

Which inequality represents 'x is at most 7'?

Accepted Answer

x ≤ 7

Answer

'At most 7' means x can equal 7 or be less, so x ≤ 7.

Question 4

What is the volume of a rectangular prism with length 5, width 4, and height 3?

Accepted Answer

60

Answer

Volume = length × width × height = 5 × 4 × 3 = 60.

Question 5

Simplify: (3x²y)(4xy³)

Accepted Answer

12x³y⁴

Answer

Multiply coefficients (3 × 4 = 12) and add exponents: x^(2+1) = x³ and y^(1+3) = y⁴, giving 12x³y⁴.

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test