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 1 Paper 2 Paper 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 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 33 min 30 points0/17 attempted

Perpendicular vector in two dimensions

Parameterizing a line

Vector addition and scalar multiplication

Eliminating the parameter can enlarge the curve

What a transition matrix assumes

Work as a dot product

Matrix as a transformation

Identifying a conic from its equation

Sign of a dot product

Parametrically defined circles and ellipses

Steady state is independent of the start

Resultant vector

Short answer 1. Define or explain: Matrix equation for a system

3 pts

Short answer 2. Define or explain: Dot product

3 pts

Short answer 3. Define or explain: Which side to multiply by an inverse

3 pts

Short answer 4. Define or explain: Splitting an implicit curve into functions

3 pts

Free response

6 pts

NO CALCULATOR IS ALLOWED FOR THIS QUESTION. A particle moves in the xy-plane so that its position at time t is given by the parametric equations x(t) = t² − 4 y(t) = 2t − 1 for −3 ≤ t ≤ 3.

A. Eliminate the parameter to write an equation relating x and y, and identify the resulting curve, including its vertex and the direction in which it opens.

B. Find the particle’s position at t = −3, t = 0, and t = 3, and describe the direction of the particle’s motion along the curve as t increases.

C. Find all values of t for which the particle lies on the y-axis, and give the corresponding points.