Free Printable Core Sem 2 Review Part 2(4C, 5, Vectors, Conics)

1.

In triangle XYZ:

X=56°; Y= 42°; z = 9

Find the measure of side y.

a)

6.081

b)

7.535

c)

11.310

d)

6.822

2.

Which would you use to solve for A?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Exponents

3.

a=2; b=7; c=8

Find angle C.

a)

95.636°

b)

110.106°

c)

113.132°

d)

39.286°

4.

A=50°; b=11; c=7

Solve for a.

Round to 3 decimal places

(a)

5.

8.Solve for x

a)

3.85

b)

4.25

c)

3.35

d)

5.65

6.

Simplify

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

7.

Simplify

a)

-1

b)

sin θ

c)

csc θ

d)

1

8.

sin²θ=

a)

1 - cos²θ

b)

1 - sin²θ

c)

sec²θ - 1

d)

csc²θ - 1

9.

cot²θ=

a)

sec²θ - 1

b)

1 - cos²θ

c)

csc²θ - 1

d)

1 - sin²θ

10.

$1-\sin^2\theta=$

a)

$\cos^2\theta$

b)

$\tan^2\theta$

c)

$\sec^2\theta$

d)

$\cot^2\theta$

11.

$\frac{\cos^2\theta}{\cos\theta}=$

a)

$\cos\theta$

b)

$\sec\theta$

c)

$\sin\theta$

d)

$\csc\theta$

12.

Find the magnitude of vector AB if A is (-3, 1) and

B is (3, 9).

Hint: Use Head Minus Tail Rule, then calculate the magnitude

a)

8

b)

2√7

c)

10

d)

5√2

13.

A vector has a magnitude of 140 and an angle of 22°. What is its component form?

a)

$<129.806,52.445>$

b)

$<52.445,129.806>$

c)

$<16.853,14.141>$

d)

$<14.141,16.853>$

14.

What is the center of the hyperbola?

a)

(0, 4)

b)

(4, 0)

c)

(-4, 0)

d)

(0, -4)

15.

Is the hyperbola vertical or horizontal?

a)

Vertical

b)

Horizontal

16.

Write the equation for this hyperbola.

a)

$\frac{x^2}{9}-\frac{y^2}{25}=1$

b)

$\frac{x^2}{25}-\frac{y^2}{9}=1$

c)

$\frac{y^2}{9}-\frac{x^2}{25}=1$

d)

$\frac{y^2}{25}-\frac{x^2}{9}=1$

17.

Write the equation for this hyperbola.

a)

$\frac{x^2}{25}-\frac{y^2}{16}=1$

b)

$\frac{x^2}{16}-\frac{y^2}{25}=1$

c)

$\frac{y^2}{16}-\frac{x^2}{25}=1$

d)

$\frac{y^2}{25}-\frac{x^2}{16}=1$

18.

What is the center of the given equation?

a)

(h, k) = (4, 3)

b)

(h, k) = (-4, -3)

c)

(h, k) = (-4, 3)

d)

(h, k) = (4, -3)

19.

25x² + 5y² + 6x + 4y +2 = 0

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

20.

Classify the conic section.

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

21.

a)

Vertical Ellipse

b)

Vertical Hyperbola

c)

Horizontal Ellipse

d)

Horizontal Hyperbola

22.

What is the direction angle for the vector shown?

(a)

23.

Calculate the direction angle to 3 decimal places for the vector <5,7>.

(a)

24.

Calculate the direction angle to 3 decimal places for the vector <5,-1>.

a)

371.310°

b)

348.690°

c)

281.310°

d)

11.310°

e)

168.690°

25.

Which is an ellipse with a major axis of 12 and a minor axis of 6?

a)

$\frac{x^2}{36}+\frac{y^2}{144}=1$

b)

$\frac{x^2}{9}+\frac{y^2}{36}=1$

c)

$\frac{x^2}{6}+\frac{y^2}{12}=1$

d)

$\frac{x^2}{144}+\frac{y^2}{576}=1$

26.

My calculator says that the sin315° = -.7071067812.

Which is the equivalent exact answer?

a)

$-\frac{1}{\sqrt[]{2}}$

b)

$-\frac{\sqrt[]{3}}{2}$

c)

$-\frac{1}{\sqrt[]{3}}$

d)

$-\sqrt[]{2}$

27.

Graph (2,30°)

A

B

C

D

E

F

G

H

I

28.

Graph (-2,30°)

A

B

C

D

E

F

G

H

I

29.

Graph (-3,150°)

A

B

C

D

E

F

G

H

I

30.

Graph (-3,-120°)

A

B

C

D

E

F

G

H

I

J

Core Sem 2 Review Part 2(4C, 5, Vectors, Conics)

Total questions: 30

Worksheet time: 42mins

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