NJGPA Algebra I and Geometry Concepts 3 — Questions and Answers
Question 1: What are the solutions to x² - 5x + 6 = 0?
- x = 1 and x = 6
- x = 2 and x = 3 (Correct answer)
- x = -2 and x = -3
- x = -1 and x = 6
Correct answer: x = 2 and x = 3
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?
- 13
- 14
- 15 (Correct answer)
- 17
Correct answer: 15
By the Pythagorean theorem: c² = 9² + 12² = 81 + 144 = 225, so c = 15.
Question 3: Which inequality represents 'x is at most 7'?
- x > 7
- x ≥ 7
- x < 7
- x ≤ 7 (Correct answer)
Correct answer: x ≤ 7
'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?
- 47
- 60 (Correct answer)
- 35
- 24
Correct answer: 60
Volume = length × width × height = 5 × 4 × 3 = 60.
Question 5: Simplify: (3x²y)(4xy³)
- 7x³y⁴
- 12x²y³
- 12x³y⁴ (Correct answer)
- 7x²y³
Correct answer: 12x³y⁴
Multiply coefficients (3 × 4 = 12) and add exponents: x^(2+1) = x³ and y^(1+3) = y⁴, giving 12x³y⁴.
Question 6: What is the midpoint of the segment connecting (1, 3) and (7, 9)?
- (3, 5)
- (4, 6) (Correct answer)
- (5, 7)
- (6, 8)
Correct answer: (4, 6)
Midpoint = ((1+7)/2, (3+9)/2) = (4, 6).
Question 7: A quadrilateral has interior angles of 90°, 85°, 110°, and x°. What is x?
- 65°
- 75° (Correct answer)
- 85°
- 95°
Correct answer: 75°
The sum of interior angles of a quadrilateral is 360°, so x = 360 - 90 - 85 - 110 = 75.
NJGPA Algebra I and Geometry Concepts 3
What are the solutions to x² - 5x + 6 = 0?