SAT College Entrance Exam Sample Test

Try 5 free practice questions with instant feedback. See how ready you are.

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Sample Questions

Question 1

What is the vertex form of a quadratic equation, and what do each of its components represent?

Answer: y = a(x - h)² + k, where (h, k) is the vertex of the parabola and 'a' determines the direction and width of the opening.

Question 2

Using the quadratic formula, what are the solutions to ax² + bx + c = 0?

Answer: x = (−b ± √(b² − 4ac)) / 2a. Both the plus and minus cases must be considered to find all solutions.

Question 3

What does the discriminant (b² − 4ac) tell you about the solutions of a quadratic equation?

Answer: If positive, two real solutions; if zero, exactly one real solution (a repeated root); if negative, no real solutions (two complex solutions).

Question 4

How do you convert a quadratic from standard form ax² + bx + c to vertex form by completing the square?

Answer: Factor out 'a' from the first two terms, add and subtract (b/2a)² inside the parentheses, then rewrite as a(x − h)² + k.

Question 5

If a parabola has x-intercepts at x = p and x = q, what is its factored form?

Answer: y = a(x − p)(x − q), where 'a' is determined by another point on the parabola (such as the y-intercept).