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AP Precalculus Unit 4: Functions Involving Parameters, Vectors, and Matrices

12 questions

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Unit 4: Functions Involving Parameters, Vectors, and Matrices

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Question 1

A projectile is launched with initial velocity $v_{0} = ⟨ 20, 30 ⟩$ m/s. Ignoring gravity, what is its position vector at $t = 4$ seconds, starting from the origin?

⟨ 24, 34 ⟩

mB.

⟨ 80, 120 ⟩

mC.

⟨ 20, 30 ⟩

mD.

⟨ 5, 7.5 ⟩

Question 2

The parametric curve $x (t) = cos (t)$ , $y (t) = sin (2 t)$ has what behavior at $t = 0$ ?

A.Passes through

(1, 0)

moving in the

- y

direction.B.Passes through

(1, 0)

moving in the

+ y

direction.C.Passes through

(0, 0)

moving in the

+ x

direction.D.Passes through

(1, 0)

stationary.

Question 3

Compute $u + v$ where $u = ⟨ 2, - 1 ⟩$ and $v = ⟨ - 3, 4 ⟩$ .

⟨ - 1, 3 ⟩

⟨ 5, - 5 ⟩

⟨ - 6, - 4 ⟩

⟨ 1, 5 ⟩

Question 4

Compute the dot product of $u = ⟨ 2, 3 ⟩$ and $v = ⟨ 4, - 1 ⟩$ .

5

11

⟨ 8, - 3 ⟩

2

Question 5

Find the magnitude of the vector $v = ⟨ 3, 4 ⟩$ .

3

4

5

7

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Question 6

Find the inverse of the matrix $A = [2111]$ .

[1 - 1 - 1 2]

[- 1 1 1 - 2]

[2 - 1 - 1 1]

[1121]

Question 7

Solve the system using matrix methods: $2 x + y = 5$ and $x - y = 1$ .

x = 1

y = 2

x = 2

y = 1

x = 3

y = - 1

x = 0

y = 5

Question 8

Eliminate the parameter from $x = t + 1$ , $y = t^{2}$ to express $y$ as a function of $x$ .

y = x^{2}

y = (x - 1)^{2}

y = (x + 1)^{2}

y = x^{2} - 1

Question 9

If $A = [2003]$ acts on a vector by left multiplication, what is $A ⟨ 1, 4 ⟩^{T}$ ?

⟨ 2, 4 ⟩^{T}

⟨ 2, 12 ⟩^{T}

⟨ 1, 12 ⟩^{T}

⟨ 5, 7 ⟩^{T}

Question 10

What is the unit vector in the direction of $w = ⟨ 6, - 8 ⟩$ ?

⟨ 6, - 8 ⟩

⟨ \frac{3}{5}, - \frac{4}{5} ⟩

⟨ \frac{6}{10}, \frac{- 8}{10} ⟩ \cdot 2

⟨ \frac{1}{6}, - \frac{1}{8} ⟩

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Question 11

A particle moves along the parametric curve $x (t) = t + 1$ , $y (t) = 2 t - 3$ . What is the position at $t = 2$ ?

(2, - 3)

(3, 1)

(2, 1)

(1, 2)

Question 12

A parametric curve is given by $x (t) = 2 cos (t)$ , $y (t) = 2 sin (t)$ for $t \in [0, 2 π)$ . Which curve does it trace?

A.A circle of radius

1

centered at the origin.B.A circle of radius

2

centered at the origin.C.An ellipse with semi-axes

2

and

1

.D.A line of slope

1

through the origin.

AP Precalculus Unit 4: Functions Involving Parameters, Vectors, and Matrices — Free with Answer Explanations | Test Practice Hub