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AP Pre-Calculus MCQs

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AP Pre-Calculus practice questions by unit

Fiveable has 9,930 AP Pre-Calculus multiple-choice practice questions across 4 units. Practice one unit or topic at a time.

  • Unit 1 – Polynomial and Rational Functions: 2,593 multiple-choice questions
  • Unit 2 – Exponential and Logarithmic Functions: 2,810 multiple-choice questions
  • Unit 3 – Trigonometric and Polar Functions: 2,334 multiple-choice questions
  • Unit 4 – Functions Involving Parameters, Vectors, and Matrices: 2,193 multiple-choice questions

Sample AP Pre-Calculus practice question

The equation x+1=−2(y−5)2x + 1 = -2(y - 5)^2 represents a parabola. Which statement correctly describes the vertex, opening direction, and the mathematical reasoning?

Vertex is (−1,5)(-1, 5) opening leftward because the equation is in the form x−h=a(y−k)2x - h = a(y - k)^2 with a=−2<0a = -2 < 0.

Correct answer

Vertex is (1,−5)(1, -5) opening rightward because the negative coefficient indicates rightward orientation.

Vertex is (−1,5)(-1, 5) opening downward because the squared term is (y−5)2(y - 5)^2.

Vertex is (−1,5)(-1, 5) opening leftward, but the parabola is actually a circle because the equation involves a squared term.

Explanation

The equation matches the standard form for a horizontal parabola x−h=a(y−k)2x - h = a(y - k)^2. The vertex is (h,k)=(−1,5)(h, k) = (-1, 5), and since a=−2<0a = -2 < 0, the parabola opens leftward (in the negative xx direction).

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