SAT Math 9A Volume 2

Functions

100

If f(x) = 4x - 3, what is f(2)?

5

200

If f(x) = x² - 2x and g(x) = x + 1, what is f(g(2))?

f(3) = 9 - 6 = 3

300

f(x) = x² - 4x + 4. What is the value of f(2)?

0

400

If f(x) = x² and g(x) = 2x - 1, find (f ∘ g)(1)

f(g(1)) = f(1) = 1

500

If f(x) = 1 / (x - 2), for what value of x is f(x) undefined?

x=2

Easy polynomials

100

Simplify:(x + 1)(x + 4)

x² + 5x + 4

200

What is the degree of the polynomial: 3x⁴ - 7x² + 2?

4

300

Factor: x² + 7x + 10

(x + 2)(x + 5)

400

Expand and simplify: (2x + 3)(x - 1)

2x² + x - 3

500

If (x + a)(x + b) = x² + 9x + 20, what are a and b?

a = 4, b = 5

Hard polynomials

100

Factor completely: x² - x - 6

(x - 3)(x + 2)

200

Factor: x³ - 8

(x - 2)(x² + 2x + 4)

300

Divide: (x³ + 2x² - x - 2) ÷ (x + 1)

x² + x - 2

400

If x³ - 6x² + 11x - 6 = 0, find one real root.

x = either 1, 2 or 3

500

Find all real roots of: x³ - 2x² - 5x + 6 = 0

x = -1, 1, 6  

Trigonometry

100

What is cos(0°)?

1

200

What is the sine of a 45° angle in simplest radical form?

√2 / 2

300

In a right triangle, if adjacent = 4 and hypotenuse = 5, find cos(θ).

4/5

400

What is the exact value of tan(60°)?

√3

500

If sin(θ) = 3/5 and θ is in the first quadrant, find cos(θ).

4/5

Advanced Math

100

Solve for x: 4x+7=19

3

200

(x^2 - 4) / (x - 2)

x + 2(Note: Factor numerator as (x - 2)(x + 2))

300

Solve the system;

x + y = 10  

x - y = 2

x = 6, y = 4

400

Simplify the expression: sqrt(72) + sqrt(8)

6√2 + 2√2 = 8√2

500

A quadratic equation has roots 5 and -2. Write the equation in standard form.

x^2 - 3x - 10 = 0