NBT Algebra and Functions 1 — Questions and Answers
Question 1: Solve for x: 3x + 7 = 22
- x = 3
- x = 5 (Correct answer)
- x = 7
- x = 4
Correct answer: x = 5
Subtract 7 from both sides to get 3x = 15, then divide both sides by 3. This gives x = 5.
Question 2: What is the value of f(3) if f(x) = 2x² - 4x + 1?
- 7 (Correct answer)
- 5
- 10
- 13
Correct answer: 7
Substitute x = 3: f(3) = 2(9) - 4(3) + 1 = 18 - 12 + 1 = 7. Careful substitution into the quadratic function gives the correct value.
Question 3: Which of the following represents a linear function?
- y = x² + 3
- y = 4x - 2 (Correct answer)
- y = 1/x
- y = √x
Correct answer: y = 4x - 2
A linear function has the form y = mx + c, where the variable x has an exponent of 1. Only y = 4x - 2 fits this form, with m = 4 and c = -2.
Question 4: If 2(x - 3) + 5 = 3(x + 1), what is x?
- -4 (Correct answer)
- 2
- -2
- 4
Correct answer: -4
Expand: 2x - 6 + 5 = 3x + 3, simplify: 2x - 1 = 3x + 3, so -1 - 3 = 3x - 2x, giving x = -4.
Question 5: What is the gradient (slope) of the line 3y - 6x = 12?
- -6
- 2 (Correct answer)
- 4
- -2
Correct answer: 2
Rearrange to y = mx + c form: 3y = 6x + 12, so y = 2x + 4. The gradient is the coefficient of x, which is 2.
Question 6: Factorise completely: x² - 9
- (x - 3)(x - 3)
- (x + 9)(x - 1)
- (x + 3)(x - 3) (Correct answer)
- (x - 9)(x + 1)
Correct answer: (x + 3)(x - 3)
This is a difference of two squares: x² - 9 = x² - 3². The formula a² - b² = (a + b)(a - b) gives (x + 3)(x - 3).
NBT Algebra and Functions 1
Solve for x: 3x + 7 = 22