AP Exam Prep · AP Precalculus

AP Precalculus Unit 4 Practice Test: Parameters, Vectors and Matrices

Unit 4 is part of the AP Precalculus course, but it is not tested on the AP Exam. Many schools teach it for class tests and to prepare for calculus. It covers parametric functions and motion, implicitly defined functions and conic sections, vectors, and matrices as functions and models.

Exam weighting:
Not on the AP Exam
Questions:
18 multiple choice
Time:
about 45 minutes
Cost:
Free, no sign-up

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Question 1 of 18 · 0 answered

Question 1

Topic 4.1 · Apply it

A curve is defined by x(t) = t2 − 1 and y(t) = 2t + 3. Which point is on the curve when t = 2?

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What AP Precalc Unit 4 covers

Unit 4, Functions Involving Parameters, Vectors, and Matrices, is part of the course but is not tested on the AP Exam and usually takes ~30 class periods. These are the topics in the current course framework, and every question in the test above is tagged with one of them.

  1. 4.1Parametric Functions
  2. 4.2Parametric Functions Modeling Planar Motion
  3. 4.3Parametric Functions and Rates of Change
  4. 4.4Parametrically Defined Circles and Lines
  5. 4.5Implicitly Defined Functions
  6. 4.6Conic Sections
  7. 4.7Parametrization of Implicitly Defined Functions
  8. 4.8Vectors
  9. 4.9Vector-Valued Functions
  10. 4.10Matrices
  11. 4.11The Inverse and Determinant of a Matrix
  12. 4.12Linear Transformations and Matrices
  13. 4.13Matrices as Functions
  14. 4.14Matrices Modeling Contexts

Unit 4 key ideas

Parametric functions trace motion

x = x(t), y = y(t) gives a point's position at time t. The average rate of change of x or of y over a t-interval tells you how fast each coordinate changes; x = h + r cos t, y = k + r sin t traces a circle with centre (h, k) and radius r.

Conic sections from equations

x²/a² + y²/b² = 1 is an ellipse, x²/a² − y²/b² = 1 a hyperbola and y = ax² a parabola. Completing the square reveals the centre or vertex.

Vectors have magnitude and direction

For v = ⟨a, b⟩, |v| = √(a² + b²). Add vectors component by component; the dot product u · v = u₁v₁ + u₂v₂ is zero exactly when the vectors are perpendicular.

Matrices transform and model

A 2×2 matrix maps vectors to vectors. Its determinant ad − bc scales area, and the matrix has an inverse only when the determinant is not zero. Transition matrices model how a population moves between states each step.

Common Unit 4 mistakes

  • Multiplying matrices entry by entry instead of row by column.
  • Forgetting that a parametric graph can retrace or reverse direction as t increases.
  • Treating a determinant of 0 as 'no answer' rather than 'not invertible'.

How to study this unit

  • Check with your teacher whether your class covers Unit 4: it matters for class grades, not for the AP score.
  • For matrix multiplication, write the row-by-column products out in full before simplifying.

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More AP Precalculus practice tests

← Unit 3: Trigonometric and Polar FunctionsAll AP Precalculus units →

About these questions

StudyCoach wrote these questions for this test. Each one is mapped to a topic in the College Board's current AP Precalculus course framework. Every answer key was also checked by a separate AI review, and any disagreement was rechecked by hand. They have not yet been reviewed by an AP Precalculus teacher. If you think an answer is wrong, email support@studycoach.io.

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