Free Printable Diagnostic Test in Mathematics 8

1.

x² - 9

a)

(x + 3)²

b)

(x + 3) (x - 3)

c)

x + 3(x - 3)

d)

(x - 3)²

2.

x² - 16

a)

(x + 4) (x - 4)

b)

(x + 4)²

c)

(x + 8) (x - 2)

d)

x + 4(x - 4)

3.

Solve the following using the FOIL method: $\left(a-5\right)\left(a+2\right)$

a)

$a^2−3a−10$

b)

$a^2+3a+10$

c)

$2a^2+7a−10$

d)

$2a^2+9a+7$

4.

Used the distributive (FOIL) method to solve $\left(6x-1\right)\left(x-2\right)$

a)

$6x^2+11x−2$

b)

$6x^2+11x−2$

c)

$6x^2-13x-3$

d)

$6x^2-13x+2$

5.

Using Distributive property: 3(2c - 5)

a)

6c - 15

b)

6c + 15

c)

6c + 15

d)

-6c - 15

6.

Using Distributive Property: 7a(3b - 2c + 4)

a)

10ab + 5ac + 11a

b)

21ab + 14ac + 28a

c)

10ab + 5ac + 28a

d)

21ab - 14ac + 28a

7.

Is this a perfect square trinomial?

x² + 16x + 64

a)

YES

b)

NO

8.

Is this a perfect square trinomial?

x² + 18x + 9

a)

YES

b)

NO

9.

Factor:

x² + 24x + 144

a)

(x + 12)²

b)

(x + 15)²

c)

(x + 9)²

d)

(x + 13)²

10.

Simplify the Rational Algebraic Expression $\frac{x+9}{x^2-81}$

a)

$\frac{(x-9)}{(x+9)}$

b)

$(x+9)$

c)

$\frac{1}{(x-9)}$

d)

$\frac{1}{(x+9)}$

11.

What are the undefined terms in Geometry?

a)

axiom/ postulate and theorem

b)

bisector, betweenness and midpoint

c)

intersecting and parallel lines

d)

point, line and plane

12.

It is a statement that is accepted without proof.

a)

axiom

b)

postulate

c)

proof

d)

theorem

13.

Which of the following is a statement formed by interchanging the hypothesis and conclusion of the original if-then statement?

a)

conditional

b)

contrapositive

c)

converse

d)

inverse

14.

It is a statement formed by negating the hypothesis and conclusion of the converse of an if-then statement.

a)

argument

b)

contrapositive

c)

converse

d)

inverse

15.

Complete the following: 1, 3, 9, 27, _____

a)

30

b)

51

c)

81

d)

90

16.

It is a type of reasoning that uses accepted facts to reason in a step-by-step manner until we arrive at a desired statement.

a)

abductive reasoning

b)

analogical reasoning

c)

deductive reasoning

d)

inductive reasoning

17.

It is a logical argument in which each statement you make is supported/ justified by given information, definitions, axioms, postulates, theorems and previously proven statements.

a)

axiom

b)

postulate

c)

proof

d)

theorem

18.

This type of reasoning uses specific examples to arrive at a general rule, generalization or conclusion.

a)

causal reasoning

b)

critical thinking

c)

deductive reasoning

d)

inductive reasoning

19.

What do you call the statement formed by negating the hypothesis and conclusion of a given if-then statement?

a)

collinear

b)

contrapositive

c)

converse

d)

inverse

20.

What do you call a statement that has become a rule because it has been proven to be TRUE?

a)

axiom

b)

postulate

c)

proof

d)

theorem

21.

Which of the following is a subset of a line with two endpoints?

a)

angle

b)

line segment

c)

midpoint

d)

ray

22.

It is represented by a dot. It has no length, width or thickness and occupies no space. All geometric figures are made up of a collection of these.

a)

line

b)

plane

c)

point

d)

none of these

23.

A straight mark with arrow heads. Have infinite length but no width and thickness.

a)

line

b)

plane

c)

point

d)

none of these

24.

The building blocks of geometry and do not have formal definition because they can only be described or illustrated.

a)

defined terms

b)

postulate/axiom

c)

theorem

d)

undefined terms

25.

A flat surface that extends infinitely in all directions. It has length and width but no thickness.

a)

line

b)

point

c)

plane

d)

none of these

26.

These are points that lie on the same line.

a)

collinear points

b)

coplanar points

c)

noncollinear points

d)

noncoplanar points

27.

Which congruence postulate tells us that if the two sides and an included angle of one triangle are congruent to the corresponding two sides and the included angle of another triangle, then the two triangles are congruent?

a)

ASA Congruence Postulate

b)

SAS Congruence Postulate

c)

SSS Congruence Postulate

d)

None of these

28.

Which congruence postulate tells us that if the two angles and an included side of one triangle are congruent to the corresponding two angles and the included side of another triangle, then the two triangles are congruent?

a)

ASA Congruence Postulate

b)

SAS Congruence Postulate

c)

SSS Congruence Postulate

d)

None of these

29.

Which congruence postulate tells us that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent?

a)

ASA Congruence Postulate

b)

SAS Congruence Postulate

c)

SSS Congruence Postulate

d)

None of these

30.

a)

ASA Congruence Postulate

b)

SAS Congruence Postulate

c)

SSS Congruence Postulate

d)

None of these

31.

a)

80⁰

b)

100⁰

c)

120⁰

d)

150⁰

32.

Which of the following is the equivalent converse statement of “If the weather is nice, then I will wash the helicopter.”?

a)

If I wash the helicopter, then the weather is nice.

b)

If the weather is not nice, then I wash the helicopter.

c)

If I don’t wash the helicopter, then the weather is not nice.

d)

If the weather is not nice, then I will not wash the helicopter.

33.

The triangles at right are congruent. Which of the following statements must be true?

a)

b)

c)

d)

34.

What undefined term in geometry is depicted by a taut wire?

a)

point

b)

line

c)

plane

d)

none of these

35.

$\frac{\sqrt[]{3x\ }\ -\ 5}{2x}$

a)

Rational Algebraic Expressions

b)

NOT

36.

$\frac{x^{2\ }-\ 3x\ +\ 5}{2x\ -\ 2x}$

a)

Rational Algebraic Expressions

b)

NOT

37.

What is a Rectangular Coordinate System?

a)

It is a coordinate system that is used for naming points in a plane.

b)

It is a coordinate system that is used for graphing linear functions.

c)

It is a coordinate system that is used to determine the location of a point by using a single number.

d)

It is a coordinate system that is composed of two perpendicular number lines that meet at a point of origin.

38.

How many quadrants does a Rectangular Coordinate System have?

a)

2

b)

4

c)

6

d)

8

39.

Which among these mathematicians was the Cartesian Plane named after?

a)

Euclid

b)

Pythagoras

c)

Rene Descartes

d)

Blaise Pascal

40.

What do you call the vertical number line in the Cartesian plane?

a)

y-axis

b)

x-axis

c)

origin

d)

quadrant

41.

For the coordinates of the point in quadrant IV, the x value and y value are always _____ and ______, respectively.

a)

negative, positive

b)

negative, negative

c)

positive, negative

d)

positive, positive

42.

In the quadrant l, the values of x and y are always ____, and _____, respectively.

a)

positive, positive

b)

positive, negative

c)

Negative, negative

d)

Negative, positive

43.

The point of intersection of the the horizontal and vertical number lines is called _____.

a)

y-axis

b)

x-axis

c)

origin

d)

quadrant

44.

The point (9, −1) is an example of______.

a)

fractions

b)

numbers

c)

labels

d)

ordered pair

45.

When plotting the point (−8,1), which describes the movement along the x-axis and y-axis in the correct order?

a)

8 units right then 1 unit up

b)

8 units down then 1 unit left

c)

8 units left then 1 unit up

d)

8 units up then 1 unit right

46.

What is the slope-intercept form of a linear equation?

a)

$y=mx\ +b$

b)

$y\ =ax^2+bx+c$

c)

$y\ =\ mx-b$

d)

$Ax+By\ +C\ =0$

47.

What does variable m represent in the slope-intercept form?

a)

Slope of the line

b)

Y-intercept of the line

c)

X-intercept of the line

d)

None of the above

48.

What is the slope of the line represented by the equation y = 4x + 2?

a)

4

b)

2

c)

-4

d)

-2

49.

What is the slope of a horizontal line?

a)

0

b)

1

c)

Undefined

d)

Infinity

50.

Which of the following equations represents a vertical line?

a)

y = 3x + 2

b)

y = -5

c)

x = 2

d)

y = -2x

Diagnostic Test in Mathematics 8

Total questions: 50

Worksheet time: 2hrs 40mins

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