Free Printable Diagnostic Test Spring 2025

1.

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

2.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

3.

Factor:
v² + 3v - 88

a)

(v + 11)(v - 8)

b)

(v + 22)(v - 4)

c)

(v + 8)(v - 11)

d)

(v - 22)(v + 4)

4.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

5.

Which of the following is equivalent to:
$2x^2-13x-70$

a)

$\left(2x-7\right)\left(x+10\right)$

b)

$\left(7x+5\right)\left(x+2\right)$

c)

$\left(2x+7\right)\left(x-10\right)$

d)

$2\left(x-7\right)\left(x+10\right)$

6.

Factor Completely:
x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

7.

Find the slope-intercept equation

a)

y = 4x + 6

b)

y = -4x - 6

c)

y = 1/4x - 6

d)

y = -1/4x + 6

8.

Find the graph of the standard form equation: 2x - 5y = -20

a)

b)

c)

d)

9.

a)

y = 2x + 3

b)

y = -2x + 3

c)

y = -2x + 11

d)

y = -2x - 11

10.

a)

y = 1/2 x

b)

y = -1/2 x

c)

y = 2x - 10

d)

y = -2x + 6

11.

What is the slope of this line?

a)

m = 0

b)

m = undefined

c)

m = 3

d)

m = ¹/₃

12.

What is the slope of this line?

a)

m = 0

b)

m = undefined

c)

m = 5

d)

m = ¹/5

13.

What is the solution to the system of equations below?

2x+y=7

3x+2y=16

a)

(2,5)

b)

(2,11)

c)

(-2,-11)

d)

(-2,11)

14.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

15.

√36x³y⁴

a)

6y²x√x

b)

3y²√2x

c)

3y√x

d)

6x√3y

16.

√45x⁴y⁷

a)

3x²y³√5

b)

9x²y³√5y

c)

3x²y³√5y

d)

3x⁴y⁷

17.

a)

x = 49

b)

x = 53

c)

x = 45

d)

x = 18

18.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

19.

Simplify

a)

√5

b)

-3√6

c)

√6

d)

6

20.

Simplify

2√27+3√3

a)

15√30

b)

5√3

c)

9√3

d)

9√8

21.

Given the following table of values, construct the function that represents the sequence.

a)

y = 3(4)^x

b)

y = 3x + 4

c)

y = 4(3)^x

d)

y = 4x + 3

22.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

23.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

24.

The table shows the price of a cup of yogurt with up to 5 toppings. What is the rate of change in price with respect to the number of toppings?

a)

$0.89 per topping

b)

$2.99 per topping

c)

$3.88 per topping

d)

$1.24 per topping

25.

What is the equation of the graph?

a)

y = -5

b)

y = 5

c)

x = -5

d)

x = 5

26.

Identify the x-intercept of the graph.

a)

(-4, 0)

b)

(0, -2)

c)

(0, -4)

d)

(-2, 0)

27.

What is another name for the x-intercepts of a quadratic?

a)

y-intercept

b)

Zeros

c)

x-axis

d)

They don't have another name

28.

What is the solution?

a)

No solution

b)

(0, 2)

c)

(0, -4)

d)

(3, -3)

29.

What is the graph of the function

y=5\cdot2^x

a)

b)

c)

d)

30.

What was the maximum height of the water?

a)

0 feet

b)

2 feet

c)

10 feet

d)

3.85 feet

31.

-7(w-4)+3w - 27

a)

10w + 21

b)

-4w + 1

c)

3w + 5

d)

2w - 5

32.

Simplify:

1y - 2x - 3y + 4x

a)

-2y + 2x

b)

-2y - 2x

c)

-4y - 6x

d)

2y - 2x

33.

Solve 2x - 3 = 1

a)

3

b)

2

c)

1

d)

-2

34.

Solve:

5x + 4 = 5x − 3

a)

x = 4

b)

x = -3

c)

infinitely many solutions

d)

no solutions

35.

Solve:

3(x − 2) = 3x − 6

a)

x = 6

b)

x = -6

c)

infinitely many solutions

d)

no solutions

36.

What is the Range of this function?

a)

1 ≤ f(x) ≤ 7

b)

1 ≤ x ≤ 7

c)

-3 ≤ f(x) ≤ 3

d)

-3 ≤ x ≤ 3

37.

What is the Domain of this function?

a)

All Real Numbers

b)

-1 ≤ x ≤ 1

c)

-1 ≤ f(x) ≤ 1

d)

1 ≥ x

38.

What would be the best first step to solving the equation in one step?

a)

multiply both sides by 3

b)

multiply both sides by -3

c)

divide both sides by -3

d)

add 3 to each side

39.

-5(x-6)=15

a)

x=-2

b)

x=-3

c)

x=-9

d)

x=3

40.

What is the RANGE of this graph?

a)

y < -3

b)

y ≤ -3

c)

y > 1

d)

y ≥ 1

41.

What is the range of the table?

a)

{-4, 0, 1, 3}

b)

{-2, 0, 2, 3}

c)

{-4, -2, 0, 1, 2, 3}

d)

{ (0, 0), (2, -4), (3, 3), (-2, 1) }

42.

What is the domain of the relation shown in the table?

a)

{12}

b)

{6, 18}

c)

{3, 9, 15, 16}

d)

{13}

43.

Discrete or Continuous?

a)

Discrete

b)

Continuous

44.

Is the graph pictured discrete or continuous?

a)

Discrete

b)

Continuous

45.

The following ordered pairs represent a relation.
{(1,3) , (5,15) , (2,6), (4,12) , (3,9)}
What are the range values from least to greatest!

a)

{1, 5, 2, 4, 3}

b)

{3, 15, 6, 12, 9}

c)

{3}

d)

{3, 6, 9, 12, 15}

46.

The table of values are shown. What is the range of the relation? From least to greatest.

a)

(-4,-8,-3)

b)

(-3,2,6)

c)

(-8,-4,4)

d)

(6,2,-3)

47.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

48.

Does the graph represent a function?

a)

Yes, because the vertical line test shows there are no repeating input values

b)

No, because the vertical line test shows there are repeating input values

49.

Does this table represent a function?

a)

Yes

b)

No

50.

For the function f(x) = -3(x-1) find f(0).

a)

0

b)

-3

c)

3

d)

-1

51.

The function h(t) represents the height in inches of a plant after t weeks. What does the notation h(4) = 5 mean?

a)

After 5 week the plant is 4 inches tall

b)

The plant grows at a rate of 5/4 inch per week

c)

After 4 weeks the plant is 5 inches tall

d)

The plant grows at a rate of 1 inch per week

52.

Find the slope of the line.

a)

-5/4

b)

5/4

c)

-4/5

d)

4/5

53.

What is the slope of the line with the equation
$y\ =\ -\frac{3}{2}x\ +\ 4$

a)

$-\frac{3}{2}$

b)

$\frac{3}{2}$

c)

$4$

d)

$-4$

54.

Are these two lines parallel, perpendicular or neither?

y = 7/3x - 5

y = 7/3x + 2

a)

Parallel

b)

Perpendicular

c)

Neither

55.

Write the equation of a line PERPENDICULAR to y = -1/3x + 5 and passes through the point (6,4)

a)

$y=-\frac{1}{3}x+14$

b)

$y=3x+22$

c)

$y=-\frac{1}{3}x-10$

d)

$y=3x-14$

56.

Determine the slope and y-intercept. y = 3/2x + 3

a)

slope: 5 y-intercept: (0,3)

b)

slope: 3/2 y-intercept: (0,3)

c)

slope: 4 y-intercept: (0,3/2)

d)

slope: 1/5 y-intercept: (0,5)

57.

Write equation of a line in point slope form that passes through (3,8) and has a slope of 5?

a)

y-8=5(x-3)

b)

y=5x+8

c)

y-3=5(x-8)

d)

y-y₁₌ m(x-x₁₎

58.

If x₁ is 3 and x₂ is 2, how would use the numbers in the slope formula?

a)

2*3

b)

3+2

c)

3-2

d)

2-3

59.

Find the slope of the line.

a)

-2

b)

2

c)

-1

d)

1

60.

Find the slope of the line that passes through:
(-4, 7) and (-6, -4)

a)

2/11

b)

13/2

c)

3/10

d)

11/2

61.

What is the x-intercept shown on the graph?

a)

(4, -2)

b)

(0, -2)

c)

(4, 0)

d)

(0, 4)

62.

What is the y-intercept shown on the graph?

a)

(0, -2)

b)

(4, -2)

c)

(4, 0)

d)

(0, 4)

63.

Given the list of ordered pairs, what is the x-intercept?
(8,10), (3, -4), (0, 8), (4, -3), (9, 0)

a)

(8,10)

b)

8, 3, 0, 4, 9

c)

(0,8)

d)

(9,0)

64.

Write the equation of the line.

a)

y = -2/3x + 4

b)

y = 2/3x + 4

c)

y = 3/2x + 4

d)

y = -3/2x + 4

65.

Write the slope-intercept form of the equation of each line.

a)

y=-x+4

b)

$y=-4x-1$

c)

$y=5x+4$

d)

$y=4x-1$

66.

What is the equation of this line?

a)

0

b)

undefined

c)

y = -2

d)

x = -2

67.

Graph. y = -4

a)

a

b)

b

c)

c

d)

d

68.

Vertical or horizontal?
Slope of 0

a)

vertical

b)

horizontal

c)

neither

69.

What is the solution to this system?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

70.

Simplify by combining like terms:
5a + 2b - 3a + 4

a)

8a + 2b + 4

b)

2a + 2b + 4

c)

8ab

d)

4ab + 4

71.

n -10 +9n -3=

a)

-3

b)

9n-3

c)

n

d)

10n -13

72.

Combine like terms
3x + 2x + 3y - 7y

a)

5x + 10y

b)

5x + 4y

c)

5x - 4y

d)

5x -10y

73.

Simplify the expression:
n -10 +9n -3

a)

-3

b)

9n-3

c)

n

d)

10n -13

74.

Solve for n:
2m - n = 8

a)

n = 2m - 8

b)

n = -2m - 8

c)

n = 2m + 8

d)

n = -2m + 8

75.

Solve:
C = 2πr, for r

a)

C/(2π) = r

b)

C + 2π = r

c)

C - 2π = r

d)

2πC = r

Diagnostic Test Spring 2025

Total questions: 75

Worksheet time: 4hrs 40mins

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