SAT Math practice

If 3x + 7 = 22, what is x?

Subtract 7 from both sides to get 3x = 15, then divide by 3.

What is the slope of the line through (0, 2) and (4, 10)?

Slope = (10 − 2) / (4 − 0) = 8 / 4 = 2.

What are the solutions of x² − 4x + 3 = 0?

It factors as (x − 1)(x − 3) = 0.

A jacket costs $80. It is discounted by 25%, then a 10% tax is added to the discounted price. What is the final price?

$80 × 0.75 = $60, and $60 × 1.10 = $66.

If x + y = 10 and x − y = 4, what is x?

Add the two equations: 2x = 14, so x = 7.

What is the area of a circle with radius 3?

Area = πr² = π × 3² = 9π.

A right triangle has legs of 6 and 8. How long is the hypotenuse?

By Pythagoras, √(6² + 8²) = √100 = 10.

Which expression equals (x + 3)²?

(x + 3)(x + 3) = x² + 3x + 3x + 9.

The mean of five numbers is 12. Four of them add up to 46. What is the fifth number?

The five numbers add up to 5 × 12 = 60, and 60 − 46 = 14.

If 2ˣ = 32, what is x?

2 × 2 × 2 × 2 × 2 = 32, so x = 5.

y varies directly with x, and y = 12 when x = 4. What is y when x = 10?

y = kx with k = 12 / 4 = 3, so y = 3 × 10 = 30.

Two fair coins are tossed. What is the probability that both land heads?

Each coin has a 1/2 chance, and 1/2 × 1/2 = 1/4.

What is sin 30°?

In a 30-60-90 triangle the side opposite 30° is half the hypotenuse.

Which values of x satisfy |x − 3| = 5?

x − 3 = 5 gives 8, and x − 3 = −5 gives −2.