Unit 4: Functions Involving Parameters, Vectors & Matrices
Precalculus · Unit 4 · Paper 3

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 3” 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

Resultant vector

2

Singular matrix

3

Solving systems with matrices

4

Unit vector

5

Identity and inverse matrices

6

Orientation of a parametric curve

7

Vector components and magnitude

8

Position, velocity and displacement vectors

9

Vector addition and scalar multiplication

10

Vector projection qualitatively

11

Eliminating the parameter

12

Domain restrictions from a parameter

Short answer 1. Define or explain: Determinant of a 2×2 matrix

3 pts

Short answer 2. Define or explain: Linear transformation composition

3 pts

Short answer 3. Define or explain: Dot product

3 pts

Short answer 4. Define or explain: Transition matrix

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.