Unit 4: Functions Involving Parameters, Vectors & Matrices
Precalculus · Unit 4 · Paper 1

Functions Involving Parameters, Vectors & Matrices unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 52 terms and is the same for everyone, so a teacher can assign “Unit 4, Paper 1” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 33 min 30 points0/17 attempted
1

Implicitly defined relation

2

Parametrization is not the path

3

Dot product is a scalar

4

Dot product from magnitudes

5

Resultant vector

6

Steady state is independent of the start

7

Zero determinant and solution count

8

Parametric equations

9

Parametrizing a circle clockwise

10

Matrix multiplication is not commutative

11

Dot product

12

Eliminating the parameter

Short answer 1. Define or explain: Parameterizing a line

3 pts

Short answer 2. Define or explain: Matrix multiplication

3 pts

Short answer 3. Define or explain: Magnitude from a self dot product

3 pts

Short answer 4. Define or explain: Which side to multiply by an inverse

3 pts

Free response

6 pts

NO CALCULATOR IS ALLOWED FOR THIS QUESTION. Consider the matrix A and the vector v given by A = [ 2 1 ] v = ⟨4, −3⟩ [ 1 3 ]

A. Determine whether A has an inverse. If it does, find A⁻¹.

B. Use a matrix method to solve the system of equations 2x + y = 8 and x + 3y = 9, and verify your solution.

C. Find the magnitude of v and the measure of its direction angle. Then find the vector that results from applying to v the transformation represented by the matrix [[0, −1], [1, 0]], and describe geometrically what that transformation does.