Free Printable Diagnostic Quiz 1

1.

What is the GCF? 5x²+20x

a)

5

b)

x

c)

5x

d)

20x

2.

Classify by number of terms:
7x³ – 8x² + 9

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

3.

Simplify
4a(5a²- a + 4)

a)

20a³- 4a²+ 16a

b)

20a²- 5a + 8a

c)

20a²+ 4a²+ 16a

d)

20a³+3a² + 16a

4.

Simplify
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

5.

Simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

a)

4b⁴ - 2b³ + 7

b)

5b⁴ - 2b³ + 4

c)

b⁴ - 2b³ + 7

d)

5b⁴ - 2b³ + 7

6.

Simplify the following:
(3ab²)³

a)

27a³b⁶

b)

3ab⁶

c)

3a³b⁶

d)

27ab²

7.

(-2)³⋅(-2)⁶

a)

(-2)⁹

b)

(-2)¹⁸

c)

(-2)⁻³

d)

(-2)

8.

Simplify:
b⁴ x b⁻³ ÷ b⁻²

a)

b³

b)

b⁻³

c)

b⁵

d)

b⁻¹

9.

3.) Simplify
(45x⁶y²) / (5x⁴y⁹)

a)

(9x²)/y⁷

b)

40x²y⁷

c)

9x²y⁷

d)

9x¹⁰y¹¹

10.

Given a rectangle and 2 circles, find the area of the shaded region if the circles both have a radius of 5 inches.

a)

50 - 25π in²

b)

100 - 50π in²

c)

200 - 50π in_²

d)

200 - 25π in²

11.

Find the area of the shaded region.

a)

144π - 288 cm²

b)

72π - 144 cm²

c)

144π - 72 cm²

d)

144π - 360 cm²

12.

Find the perimeter

a)

25cm

b)

35cm

c)

50cm

d)

100cm

13.

Find the area:

a)

84 m²

b)

168 m²

c)

112 m²

d)

56 m²

14.

Write the equation for the line.

a)

y= -1x+3

b)

y= 4x+3

c)

y=1/4x+3

d)

y= -4x+3

15.

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)

16.

Find the slope of the line that passes through
(10, 1) and (5, 2)

a)

1/5

b)

-1/5

c)

5

d)

-5

17.

Find the slope of the line.

a)

-2

b)

2

c)

-1

d)

1

18.

Find the slope of the line.

a)

Undefined

b)

0

c)

1

d)

-1

19.

Write the equation of the line.

a)

y = -1/3x - 2

b)

y = 1/3x - 2

c)

y = 3x - 2

d)

y = -3x - 2

20.

Find the slope from the table.

a)

1/4

b)

-1/4

c)

-4/1

d)

4/1

21.

a)

y = 4/5x + 3

b)

y = -5/4x + 3

c)

y = 5/4x + 4

d)

y = -4/5x + 3

22.

Write the equation in slope-intercept form (solve for y):
-3y + 5x = 12

a)

y = -4 + 5x

b)

y = -4 + 5/3x

c)

y = 4 - 5/3x

d)

y = 12 + 5x

23.

Which equation represents slope intercept form?

a)

y - 1 = 2(x + 3)

b)

5y=x+5

c)

y=2x+5

d)

4y+2x=8

24.

y = 3x +2
y = 3x - 3
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

d)

The same line

25.

y = -2/3x + 2
y = 3/2x + 9
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

26.

Determine the slope and y-intercept from the following equation: 4x + y = -10

a)

slope: 4 y-intercept: (0,10)

b)

slope: -4 y-intercept: (0,-10)

c)

slope: -4 y-intercept: (0,10)

d)

slope: 4 y-intercept: (0,-10)

27.

Find the measure of angle x.

a)

138

b)

96

c)

93

d)

87

28.

Find the missing angle in the following figure.

a)

A

b)

B

c)

C

d)

D

29.

Simplify

$3x^2-3x\left(x-1\right)-x\left(3-x\right)\$

a)

$6x+x^2$

b)

$x^2$

c)

$x$

d)

$-6x+x^2$

30.

Factorise fully 6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

31.

Multiply out the brackets: $\left(4x+3\right)\left(x-1\right)$

a)

$4x^2-x-3$

b)

$4x+3x-x$

c)

$4x^2+7x+3$

d)

$4x^2-3$

32.

Expand (x+5)²

a)

x²+25

b)

x²-25

c)

x²+10x+25

d)

x²-10x+25

33.

Which equation below could represent the data in the table?

a)

$y\ =\ x-3$

b)

$y=x+3$

c)

$y=2x+3$

d)

$y=3x+1$

34.

Find the expansion for the following.

$\left(x+2\right)^2$

a)

$x^2+2x+2$

b)

$x^2+2x+4$

c)

$x^2+4x+4$

d)

$x^2+4$

35.

Find the value of $x$ for the following equation.

$\frac{2x-4}{3}=6$

a)

15

b)

3

c)

14

d)

11

36.

Choose the correct formula for basic trigonometry ratio.

a)

$Sin\ \theta=\frac{Hypotenuse}{Opposite}$

$Cos\ \theta=\frac{Hypotenuse}{Adjacent}$ $Tan\ \theta=\frac{Adjacent}{Opposite}$

b)

$Sin\ \theta=\frac{Opposite}{Hypotenuse}$

$Cos\ \theta=\frac{Adjacent}{Hypotenuse}$ $Tan\ \theta=\frac{Opposite}{Adjacent}$

c)

$Sin\ \theta=\frac{Adjacent}{Hypotenuse}$

$Cos\ \theta=\frac{Opposite}{Hypotenuse}$ $Tan\ \theta=\frac{Hypotenuse}{Adjacent}$

37.

Which equation below matches the graph shown to the right?

a)

$y=-2x-2$

b)

$y=x-2$

c)

$y=-x-2$

d)

$y=2x-2$

38.

Fully Factorize.

$x^2+8x+15$

(a)

39.

$\cos\left(\theta\right)=?$

a)

$\frac{3}{5}$

b)

$\frac{4}{5}$

c)

$\frac{3}{4}$

d)

$\frac{4}{3}$

40.

What is the value of x?

a)

17.30

b)

11.33

c)

0.06

d)

23.82

41.

A 16 foot ladder leans against a building. If the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach?

a)

39.6

b)

6.0

c)

14.8

d)

13.6

42.

Which rule would you use to find angle PAB?

a)

Sine rule

b)

Cosine rule

c)

SOHCAHTOA

d)

Area of a triangle

43.

Find the perimeter of the rectangle

a)

2x - 2

b)

6x - 15

c)

4x - 4

d)

6x - 15

44.

What is the equation of a line that is parallel to $y=\frac{2}{3}x+5$ and goes through $\left(6,-7\right)$ ?

a)

$y=\frac{2}{3}x-7$

b)

$y=\frac{2}{3}x-11$

c)

$y=\frac{2}{3}x-3$

d)

$y=\frac{2}{3}x-9$

45.

What is the equation of the line that goes through the points (2, 9) and (3, 1) ?

a)

y= 8x - 5

b)

y= -8x + 25

c)

y= (1/8)x - 2

d)

y= (-1/8)x + 1

46.

Evaluate the following: $\frac{2^9\times2^{-3}}{2^5}$

(a)

47.

At a school disco there are always about 25% more girls than boys. If at one disco there were 60 boys, how many girls were there?

(a)

48.

Factorise the expression:

x² - 121

a)

(x - 11)²

b)

(x - 12)(x + 10)

c)

(x + 11)(x - 11)

d)

(x - 10)(x + 12)

49.

Factorise the expression:

x² - 6x - 27

a)

(x - 9)(x - 3)

b)

(x - 9)(x + 3)

c)

(x - 3)(x + 9)

d)

(x + 3)(x + 9)

50.

$\frac{y-5}{3}=\frac{y-3}{5}$

a)

16

b)

8

c)

2

d)

1

51.

Solve 3(t – 3) = 5(2t + 1)

a)

9

b)

-3

c)

14

d)

-2

52.

Find perimeter

a)

15

b)

30

c)

22

d)

26

53.

Simplify : $\left(3x^2-8x\right)+\left(4x^2+y\right)$

a)

$7x^2$

b)

$7x^2-8x+y$

c)

$-x^2+y$

d)

$-x^2+x+y$

54.

Simplify: (3k-5)(2k+7)

a)

6k²+11k-35

b)

6k²+31k+35

c)

6k²-11k-35

d)

6k²-31k+35

55.

Determine whether the ordered pair (4, 55) is a solution to the equation y = 13x

a)

(4, 55) is not a solution.

b)

(4, 55) is a solution.

56.

Does the parabola open up or down?

a)

Open Up

b)

Open Down

57.

Is the vertex a maximum or minimum?

a)

Max

b)

Min

58.

What is the starting value?

a)

-64

b)

4

c)

-12

d)

-48

59.

Solve for x.

a)

6 $\sqrt[]{3}$

b)

$\sqrt[]{253}$ or 15.9

c)

6 $\sqrt[]{2}$

d)

10.4

60.

Solve for x.

a)

53.19

b)

8.5

c)

7.3

d)

8.5 $\sqrt[]{2}$

61.

Solve the proportion.

a)

k=5

b)

k=3.3333333

c)

k=60

d)

k=90

62.

Solve the proportion.

a)

-3

b)

-1.5

c)

2.1

d)

9

63.

If you are given the two sides that are not the hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

64.

a)

A

b)

B

c)

C

d)

D

65.

What is cos B?

a)

9/41

b)

40/41

c)

9/40

d)

40/9

66.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

67.

Are these similar triangles? Explain.

a)

Yes, because it looks like it

b)

Yes, because

36 + 72 + 33 = 180

c)

No, because

36 + 72 + 33 $\ne$ 180

d)

No, because they are facing the opposite way

68.

a)

b)

c)

d)

Diagnostic Quiz 1

Total questions: 68

Worksheet time: 2hrs 7mins

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