NBT Mathematics Algebra — Questions and Answers
Question 1: Solve for x: 3x + 7 = 22.
- x = 5 (Correct answer)
- x = 7
- x = 3
- x = 15
Correct answer: x = 5
Subtract 7: 3x = 15. Divide by 3: x = 5.
Question 2: Simplify: 2(x + 4) + 3x.
- 6x + 8
- 5x + 8 (Correct answer)
- 5x + 4
- 2x + 7
Correct answer: 5x + 8
Expand: 2x + 8 + 3x. Combine like terms: 5x + 8.
Question 3: Factorise fully: x^2 - 9.
- x(x - 9)
- (x + 9)(x - 1)
- (x + 3)(x - 3) (Correct answer)
- (x - 3)(x - 3)
Correct answer: (x + 3)(x - 3)
x^2 - 9 is a difference of two squares: x^2 - 3^2 = (x + 3)(x - 3).
Question 4: If f(x) = 2x - 5, what is f(4)?
- 1
- 13
- 8
- 3 (Correct answer)
Correct answer: 3
Substitute x = 4: f(4) = 2(4) - 5 = 8 - 5 = 3.
Question 5: Solve the inequality: x - 6 < 2.
- x < 4
- x > 8
- x < 8 (Correct answer)
- x > -4
Correct answer: x < 8
Add 6 to both sides: x < 8.
Question 6: Solve for x: x^2 = 49.
- x = 7 or x = -7 (Correct answer)
- x = 7 only
- x = -7 only
- x = 24.5
Correct answer: x = 7 or x = -7
Both 7 and -7 squared equal 49, so x = 7 or x = -7.
Question 7: Make y the subject: 2y + x = 10.
- y = (10 - x)/2 (Correct answer)
- y = 10 - 2x
- y = (x - 10)/2
- y = 10 - x
Correct answer: y = (10 - x)/2
Subtract x: 2y = 10 - x. Divide by 2: y = (10 - x)/2.
Question 8: Expand: (x + 2)(x + 3).
- x^2 + 6
- x^2 + 5x + 6 (Correct answer)
- x^2 + 5x + 5
- x^2 + 6x + 5
Correct answer: x^2 + 5x + 6
FOIL: x^2 + 3x + 2x + 6 = x^2 + 5x + 6.
NBT Mathematics Algebra
Solve for x: 3x + 7 = 22.