NBT Algebra and Functions

Question 1

Solve for x: 3x + 7 = 22

Accepted Answer

x = 5

Answer

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?

Accepted Answer

7

Answer

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?

Accepted Answer

y = 4x - 2

Answer

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?

Accepted Answer

-4

Answer

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?

Accepted Answer

2

Answer

Rearrange to y = mx + c form: 3y = 6x + 12, so y = 2x + 4. The gradient is the coefficient of x, which is 2.

(NBT) National Benchmark Test Practice Test