Unit 4: Functions Involving Parameters, Vectors & Matrices
Precalculus · Unit 4 · Paper 2

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 22 terms and is the same for everyone, so a teacher can assign “Unit 4, Paper 2” 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 35 min 32 points0/17 attempted
1

Matrix as a transformation

2

Matrix multiplication

3

Eliminating the parameter

4

Determinant of a 2×2 matrix

5

Position, velocity and displacement vectors

6

Vector projection qualitatively

7

Parameterizing a line

8

Linear transformation composition

9

Matrix representing a rotation

10

Unit vector

11

Orientation of a parametric curve

12

Dot product

Short answer 1. Define or explain: Transition matrix

3 pts

Short answer 2. Define or explain: Parametrically defined circles and ellipses

3 pts

Short answer 3. Define or explain: Singular matrix

3 pts

Short answer 4. Define or explain: Solving systems with matrices

3 pts

Free response

8 pts

A drone’s position in the plane is given parametrically by x(t) = 2t and y(t) = 16t − 4t², where distances are in meters and t is in seconds, for 0 ≤ t ≤ 4. (a) Eliminate the parameter to express the drone’s path as y in terms of x. (b) Find the position vector of the drone at t = 1 and at t = 3, and compute the average rate of change vector over [1, 3]. (c) Determine the time at which the drone reaches its maximum height and state that height.