Free Printable Benchmark Crash Course Review

1.

What is the radius of a circle with the following equation?

x² + y² - 8x + 10y - 8 = 0

a)

7

b)

14

c)

49

d)

24.5

2.

Which interval is decreasing? (2 answers)

a)

0.5 < x < 2

b)

x > -2

c)

4 < x < 6

d)

x > 8

3.

If the function $f(x)=\frac{x+10}{7}$ represents the number of ants in a hole after x hours. What is the inverse and what does it represent?

a)

$f^{-1}(x)=7x+10$

where f^-1(20) tells you the hours passed if 20 ants are in the hole

b)

$f^{-1}(x)=7x-10$

where f^-1(20) tells you the hours passed if 20 ants are in the hole

c)

$f^{-1}(x)=7\left(x-10\right)$

where f^-1(20) tells you the number of ants after 20 hours

d)

$f^{-1}\left(x\right)=7\left(x+10\right)$

where f^-1(20) tells you the number of ants after 20 hours

4.

What is the equation of the following table?

a)

$y=\frac{1}{2}\left(3\right)^x$

b)

$y=2x+3$

c)

$y=3\left(2\right)^x$

d)

y = 1/2x = 3

5.

How many non real solutions does the polynomial f(x)= 3x⁴- 10x³ +5x² - 1 have?

(a)

6.

How many complex zeroes does the following polynomial have? (Hint: think total)
y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

(a)

7.

If this polynomial were used in a word problem, what would be considered the initial amount of the given polynomial?

a)

18

b)

−8

c)

4

d)

3

8.

Reese is solving the equation $\frac{6^x}{3}=90$ . What would be the first step to solving this equation?

a)

Subtract 3 on both sides

b)

Convert to log form in order to solve

c)

Multiply by 3 on both sides

d)

Divide by 3 on both sides

9.

The graph of a function is shown. Which interval is decreasing and negative?

a)

(3 , infinity)

b)

(-1, 0)

c)

(-5, -4)

d)

(0,2)

10.

For what value(s) of x does f(x) = g(x) (choose all that apply!)

f(x) = x² + 3x - 5

g(x) = x + 3

a)

-3

b)

2

c)

-1

d)

-4

11.

Rewrite in exponential form:

log₉x=2

a)

9^x=2

b)

2^x=9

c)

2⁹=x

d)

9²=x

12.

Subtract
$\frac{x-5}{3x+4}-\frac{3x-5}{3x+4}$

a)

$\frac{-2x-10}{3x+4}$

b)

$\frac{-2x}{3x+4}$

c)

$-2x$

d)

$-2x-10$

13.

Add
$\frac{3x-2}{x+2}+\frac{2x}{4x-1}$

a)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}$

b)

$\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)}$

c)

$\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}$

d)

$\frac{14x^2-7x-2}{\left(x+2\right)\left(4x-1\right)}$

14.

The table represents some points on the graph of an exponential function. Which point is the y intercept?

a)

(-2, 12.5)

b)

(0, 18)

c)

(-6, 0)

d)

(3, 28.2)

15.

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

a)

-2, 3 (multiplicity 2), 4

b)

-2 (multiplicity 2), 3, 4

c)

2, -3 (multiplicity 2), -4

d)

2 (multiplicity 2), -3, -4

16.

The function below can be used to determine the salary of a painter per week after a certain amount of hours (x).

How much would the painter make after 60 hours?

a)

$1020

b)

$900

c)

$840

d)

He works for free!

17.

An ice cream package is cone shaped. It has a diameter of 11 cm and a height of 17 cm. Find the volume of the ice cream package.

a)

1,615.6 cubic cm

b)

905.8 cubic cm

c)

885.7 cubic cm

d)

538.5 cubic cm

e)

2154.1 cubic cm

18.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

(x+10)(x+8)/ 6x+60

19.

Solve the equation. Round your answer to the nearest ten-thousandth. $14^{3x}=63.7$

a)

1.3669

b)

0.6014

c)

1.3847

d)

0.5247

20.

What is the remainder when $4x^3-5x^2+10\ \div x-2$

(a)

21.

What is the equation of the graph below?

a)

f(x) = I x + 2 I

b)

f(x) = I x + 2 I +2

c)

f(x) = I x − 2 I +2

d)

f(x) = I x − 2 I

22.

a)

horizontal shift to the right 4 and vertical shift down 2

b)

horizontal shift to the left 4 and vertical shift down 2

c)

horizontal shift to the right 4 and vertical shift up 2

d)

horizontal shift to the left 4 and vertical shift up 2

23.

Solve

a)

A

b)

B

c)

C

d)

D

24.

A solid cone was placed in the center of a rectangular fish tank as shown. Which is closest to the maximum amount of water that the fish tank can hold?

a)

1286 in³

b)

1455 in³

c)

1476 in³

d)

1569 in³

25.

A city has a population density of 31 people per square mile. If the city has an area of 2050 square miles, how many total people live in this city?

(Just type the number!)

(a)

26.

f(x) = x² + 4x - 3
g(x)= 4x² - 2x - 5
Find f(x) - g(x)?

a)

-3x² + 6x + 2

b)

-3x² + 2x - 8

c)

5x² + 6x - 8

d)

-3x²- 2x - 4

27.

Solve

a)

x = 0 , 4

b)

x = 1 , 3

c)

x = -4 , 0

d)

x = 5 , 2

28.

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

a)

Center (4,3)
Radius = 5 units

b)

Center (4,3)
Radius = 25 units

c)

Center (-4,-3)
Radius = 25 units

d)

Center (-4,-3)
Radius = 5 units

29.

What is the value of $\angle JKL$ ?

a)

? = 210

b)

? = 105

c)

? = 75

d)

? = 30

30.

The figure is a parallelogram.
Solve for x.

(a)

31.

The following expression represents annual growth.

$y=3\left(1.25\right)^t$

What is the monthly growth rate as a decimal? (Round to the hundredths place)

(a)

32.

A radioactive element grows at a rate of 6% annually. There are 50 grams of the substance present. When will the substance reach 150 grams? (Round to the nearest years)

(a)

33.

Rotating this rectangle around line AB creates a ____________.

a)

rectangle

b)

rectangular prism

c)

cylinder

d)

cone

34.

Match the graph with the correct equation.

a)

b)

c)

d)

35.

What type of center is point M?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

36.

If Pacman's mouth, when open, is 70° and the radius of his mouth is 8mm, what is the area of the rest of Pacman's body to the nearest mm?

(a)

37.

If minor arc AC = 96° and major arc AC = 264° , what is the measure of ∠ ABC?

a)

53°

b)

64°

c)

72°

d)

84°

38.

If $f\left(x\right)=4x+20$

$g\left(x\right)=5^x$

$h\left(x\right)=3x^2$

For x > 15 which function would have the greater values?

a)

The value of h(x) would be greater than f(x) & g(x)

b)

The value of g(x) would be greater than f(x) & h(x)

c)

The value of f(x) would be greater than g(x) & h(x)

d)

You cannot compare different functions this way

39.

What is reason #6?

a)

SSS Triangle Congruence Postulate

b)

AAS Triangle Congruence Theorem

c)

ASA Triangle Congruence Theorem

d)

SAS Triangle Congruence Theorem

Benchmark Crash Course Review

Total questions: 39

Worksheet time: 1hrs 18mins

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