Free Printable CPC diagnostic test level1

1.

According to exponent rules, when we raise a power to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

2.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

3.

Simplify the following:
(x³)⁶

a)

x⁹

b)

x¹⁸

c)

x⁶

d)

x³

4.

What is the value of:
(2³)³

a)

1

b)

4

c)

64

d)

512

5.

3.) Simplify
(45x⁶y²) / (5x⁴y⁹)

a)

(9x²)/y⁷

b)

40x²y⁷

c)

9x²y⁷

d)

9x¹⁰y¹¹

6.

Reduce: √52

a)

26

b)

2√13

c)

13√2

d)

4√13

7.

Reduce: √200

a)

10√2

b)

2√10

c)

100

d)

20

8.

2√5 + 4√5 =

a)

6√10

b)

8√10

c)

8√5

d)

6√5

9.

2√3(√6 - √3)

a)

6√2 - 6

b)

3√2 + 3

c)

6 - √3

d)

√3 - √2

10.

Given the polynomial below, how many roots will it have?
$y=x^2-25$

a)

2

b)

1

c)

3

d)

0

11.

Given the polynomial below, how many roots will it have?
$y=x^3+5x^2-9x-2$

a)

2

b)

1

c)

3

d)

0

12.

Given the polynomial below, how many roots will it have?
$y=-2x^5+4x^2-x$

a)

2

b)

3

c)

5

d)

1

13.

Which of the following is the graph of $y=\left(x-2\right)^3-4$

a)

b)

c)

d)

14.

The graph of $y=x^3$ is graphed in blue. Which of the following equations could be equation of the function graphed in red?

a)

$y=-5\left(x+2\right)^3-1$

b)

$y=5\left(x+2\right)^3-1$

c)

$y=-\frac{1}{5}\left(x+2\right)^3-1$

d)

$y=\frac{1}{5}\left(x+2\right)^3-1$

15.

Which of the following is the graph of

y = -0.5(x)^1/3 ?

a)

b)

c)

d)

16.

What is the inverse of -5(x + 6)³ -1?

Remember that the x and y switch. Also think about where you will divide out the -5 in the solving process.

a)

-(0.2(x + 1))^1/3-6

b)

-(5(x +1))^1/3-6

c)

-5(x + 1)^1/3-6

d)

-0.2(x + 1 )^1/3-6

17.

Given the function y = x²+ 2x - 16; what is the value of y when x = -2

a)

y = -16

b)

y = -24

c)

y = 0

d)

y = 8

18.

Simplify:
[25-(13+4)+4] ÷ 3

a)

6

b)

2

c)

3

d)

4

19.

2x + 5(y - 1) when x=8 and y=5

a)

20

b)

31

c)

36

d)

-4

20.

7[12 − (6 − 2) ÷ 4]

a)

7

b)

77

c)

14

d)

0

21.

What slope is parallel to:
m = 3/4

a)

4/3

b)

3/4

c)

-3/4

d)

-4/3

22.

What is the y- intercept of the graph of y = -5x + 6

a)

5

b)

-5

c)

6

d)

-6

23.

Which equation represents the following graph?

a)

y = 3x + 2

b)

y = -2x + 3

c)

y = 2x + 3

d)

y = -3x + 2

24.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

25.

What do w, x, y and z equal in this matrix subtraction?

a)

w = 13, x = 4, y = 7, z = 23

b)

w = 13, x = -4, y = 11, z = 23

c)

w = 13, x = 4, y = 11, z = 23

d)

w = 13, x = 4, y = 11, z = 17

26.

In Matrix R (pictured) what element is a₂₃?

a)

8

b)

9.01

c)

6

d)

1

27.

What is the entry at f₄₂?

a)

23

b)

-81

c)

-44

d)

99

e)

-56

28.

Find the n^th term for the following quadratic sequence...

7, 13, 23, 37, 55...

a)

2n² + 5

b)

2n² + 5n

c)

n² + 5

d)

n² - 5

29.

Find the n^th term for the following quadratic sequence...

6, 11, 18, 27, 38...

a)

n² + 2n + 3

b)

2n² + n + 3

c)

n² - 2n - 3

d)

2n² - 2n + 3

30.

Find the common difference: -34, -29, -24, -19, ...

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

31.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

32.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

33.

Write the explicit formula for the geometric sequence.

a)

a_n = 10(2)^n-1

b)

a_n = 2(10)^n-1

c)

a_n = 10(2)ⁿ

d)

a_n = 2(10)ⁿ

34.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

35.

? = (a) degrees

36.

In the figure, PA and PB are tangents to a circle with centre O. If $\angle AOB=120\degree$ then what is $\angle OPA$

a)

$30\degree$

b)

$80\degree$

c)

$90\degree$

d)

$25\degree$

37.

Simplify.

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

38.

Please select the correct solution cot²x + 1 =

a)

sec²x - 1

b)

1

c)

sec²x

d)

csc²x

39.

If $\sin\theta=\frac{4}{5}$ and $\cos\theta=\frac{3}{5}$ find $\tan2\theta$ .

a)

$-\frac{7}{24}$

b)

$\frac{24}{7}$

c)

$\frac{7}{24}$

d)

$-\frac{24}{7}$

40.

sin^-1(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

CPC diagnostic test level1

Total questions: 40

Worksheet time: 3hrs 46mins

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