Free Printable IM2H Cumulative Review

1.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

2.

If the discriminant is negative, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

2 Imaginary Solutions

3.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

4.

What is i¹²⁹?

a)

-i

b)

i

c)

1

d)

-1

5.

What is the equation of the graph below?

a)

f(x) = I x + 2 I

b)

f(x) = I x I + 2

c)

f(x) = I x I - 2

d)

f(x) = I x - 2 I

6.

What is f when x equals 4?

a)

-5

b)

0

c)

3

d)

6

7.

Match the graph with the correct equation.

a)

b)

c)

d)

8.

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 70 hour week?

a)

$1020

b)

$1140

c)

$840

d)

He works for free!

9.

Describe domain of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

10.

What is the equation for the graph

a)

y=\log_{10}\left(x\right)

b)

$y=\log_5\left(x\right)$

c)

$y=\log_2\left(x\right)$

d)

$y=\log_5\left(-x\right)$

11.

Write in exponential form

log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

12.

Write as one logarithm. Simplify, if possible.

log₃9 + log₃27

a)

log₃3

b)

log₃243

c)

log₃1/3

d)

not possible

13.

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

14.

Name the postulate, if possible, that makes the triangles congruent.

a)

SSS

b)

SAS

c)

ASA

d)

Not Possible

15.

What is the "reason" for step 5 of the proof?

a)

Angle Bisector Theorem

b)

Reflexive property

c)

CPCTC Theorem

d)

Proof

16.

Identify the missing statement or reason

a)

Definition of Angle Bisector

b)

Alternate Interior Angles Theorem

c)

Reflexive Property

d)

Definition of Midpoint

17.

Identify the missing statement or reason

a)

LN≅MJ

b)

JK≅NK

c)

MK≅LK

d)

∠JKM≅∠NKL

18.

Simplify:
(secx-1)(secx+1).
Hint: you will need to FOIL first

a)

tan²x

b)

sinx

c)

cot²x

d)

cosx

19.

Simplify: $\frac{1-\sin^2x}{\sec x}$

a)

$\sin^2x$

b)

$\cos^2x$

c)

$\sin^3x$

d)

$\cos^3x$

20.

Simplify: $\frac{\sin^2x+\cos^2x+\cot^2x}{1+\tan^2x}$

a)

$\cot^2x$

b)

$\tan^2x$

c)

$\csc^2x$

d)

$\sec^2x$

21.

Find the mistake

a)

tan 68 should be cos 68

b)

there is no mistake

c)

they should have divided

d)

x/14 should be 14/x

22.

Calculate the value of cosine without drawing any right-angled triangles or using Pythagoras theorem or a calculator. (use the Unit circle!!)
$\sin\theta=\frac{\sqrt{2}}{2},\ \cos\theta=??,\ \tan\theta=1$

a)

1/2

b)

√2/2

c)

√3/2

d)

1

23.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram and trigonometry to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

24.

What is the measure of angle A?

a)

34°

b)

180°

c)

112°

d)

79°

25.

What is x?

a)

15

b)

23

c)

2

d)

92

26.

a)

A

b)

B

c)

C

d)

D

27.

Find the measure of arc AB.

a)

17

b)

34

c)

68

d)

146

28.

What is the area of the shaded SECTOR? Round to the nearest hundredth.

a)

9.42 u²

b)

113.10 u²

c)

284.3 u²

d)

452.39 u²

29.

Find the area of the pentagon

a)

58.12

b)

47.02

c)

76.08

d)

38.04

30.

What is the focus of the following parabola?
(y + 5)²= -12 (x - 2)

a)

(2, - 5)

b)

( -5, 2)

c)

(1 , -5 )

d)

(-1, -5 )

31.

Put the ellipse in standard form

a)

A

b)

B

c)

C

d)

D

32.

Which direction does this parabola open?

a)

Up

b)

Down

c)

Left

d)

Right

33.

Which equation shows an ellipse?

a)

$y^2+x-3y-15=0$

b)

$2x^2-4y^2+18x+120y-159=0$

c)

$4x^2+4y^2-16y+81=0$

d)

$16x^2+11y^2+54x-61y-121=0$

34.

Determine the equation of the hyperbola.

a)

$\frac{x^2}{4}-y^2=1$

b)

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

c)

$\frac{x^2}{4}+y^2=1$

d)

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

35.

What is the probability that a student does play a sport given they do not play an instrument?

a)

.2

b)

.2222

c)

.10

d)

.5

36.

What is P(T given C)?

a)

45%

b)

29.6%

c)

40%

d)

33.3%

37.

What is the probability of flipping a coin

3 times and getting 3 heads?

a)

1/8

b)

1/4

c)

1/2

d)

3/4

IM2H Cumulative Review

Total questions: 37

Worksheet time: 9hrs 15mins

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