Free Printable MOCK UP BRAINQUEST 3

1.

Factor completely. −2y−8+6u

a)

2(y −2 + 3u)

b)

2(y − 4 + 3u)

c)

2(y − 4 + 3u)

d)

−2(y + 4 −3u)

2.

Write the equation for the line.

a)

y= -1x+3

b)

y= 4x+3

c)

y=1/4x+3

d)

y= -4x+3

3.

Find the slope of the line.

a)

-2

b)

2

c)

-1

d)

1

4.

What is the equation of the line that passes through these points?

a)

y = 3x + 2

b)

y = 2x + 3

c)

y = -2x + 3

d)

y = 2x - 3

5.

What is the equation for this graph?

a)

y=3x

b)

y=x+3

c)

y=x-3

d)

y=-3x

6.

What is the equation for this graph?

a)

y=1x+4

b)

y=4x+1

c)

y=2x+4

d)

y=-2x+4

7.

Write the equation for the line in slope-intercept form.

a)

y= -1x+3

b)

y= 4x+3

c)

y= ¼x+3

d)

y= -4x+3

8.

Which equation matches the graph?

a)

y = 2x + 2

b)

y = 1/4x + 2

c)

y = 1x + 4

d)

y = 4x + 2

9.

Write the equation of the line.

a)

y= ⅗x+1

b)

y= ⅗x-1

c)

y= (5/3)x+1

d)

y= (-3/5)x-1

10.

Write the equation of the line.

a)

y= -1x-3

b)

y= -3x-1

c)

y=(-1/3)x-1

d)

y= -3x-3

11.

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

a)

A

b)

B

c)

C

d)

D

12.

Find the domain

a)

(-4,5)

b)

(-4,-1) u [-2,3) u [3,5]

c)

[-4,5)

d)

(-4,-1] u [-2,3) u [3,5)

13.

What is the range of the function?

a)

$\left\{y:\ -1\le y<+\infty\right\}$

b)

$\left\{y\ :\ 1.5\le y<+∞\right\}$

c)

$\left\{y:−1<y<1\right\}$

d)

$\left\{y:−1\le y\le1.5\right\}$

14.

What is the Range?

a)

All real numbers

b)

y > 3

c)

y ≥ 3

d)

3 ≤ y ≤ 8

15.

What is the Domain?

a)

All real numbers

b)

x = 4

c)

x > 3

d)

x ≥ 3

16.

Find the Domain.

a)

$\left(-\infty,\infty\right)$

b)

$(0,∞)$

c)

$(3,+∞)$

d)

$[0,+∞)$

17.

What is the domain of the graph?

a)

$\left\{x\ :\ x\ =all\ real\ numbers\right\}$

b)

$\left\{x\ :\ x\ e\ R,\ \infty\ \le x\le\infty\right\}$

c)

$\left\{y\ :\ y\ e\ R,\ -15\ \le y\le9\right\}$

d)

$\left\{y\ :\ y\ e\ R,\ -3\ \le y\le3\right\}$

18.

What is the domain of the function?

a)

{x| x = all real numbers}

b)

{x| -2 ≤ x ≤ 4}

c)

{x| -2 < x < 4}

d)

{x| -6 ≤ x ≤ 3}

19.

What is the range of the graph?

a)

$\left\{x\ :\ x\ e\ R,\ -15\ \le x\le9\right\}$

b)

$\left\{x\ :\ x\ e\ R,\ -3\ \le x\le3\right\}$

c)

$\left\{y\ :\ y\ e\ R,\ -15\ \le y\le9\right\}$

d)

$\left\{y\ :\ y\ e\ R,\ -3\ \le y\le3\right\}$

20.

What is the DOMAIN of this graph?

a)

$\left\{x|x\ e\ R,-4\le x\le3\right\}$

b)

$\left\{x|x\ e\ R,\ 4<x<3\right\}$

c)

$\left\{x|x\ e\ R,\ -1\le x\le4\right\}$

d)

$\left\{x|x\ e\ R,\ -1<x<4\right\}$

21.

What is the domain?

a)

{-2, -1, 0, 1, 8}

b)

{-2, -1, 0, 1, 3, 5, 7, 8, 9}

c)

{3, 5, 7 , 9, 0}

d)

{-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

22.

What is the domain of the graph?

a)

[-3, 3]

b)

(-3, 3)

c)

(3, -3]

d)

(2, 10]

23.

Identify all of the functions

a)

b)

c)

d)

e)

24.

Which mapping diagram is not a function?

a)

b)

c)

d)

25.

What is the hypothesis of the statement, "If 3 or more points lie on the same line, then the points are collinear." ?

a)

If 3 or more points lie on the same line.

b)

Three or more points lie on the same line.

c)

The points are collinear.

d)

Then the points are collinear.

26.

What is the conclusion of the statement, "If 3 or more points lie on the same line, then the points are collinear." ?

a)

If 3 or more points lie on the same line.

b)

Three or more points lie on the same line.

c)

Then the points are collinear.

d)

The points are collinear.

27.

An educated guess that may be a true or false statement is called ______________.

a)

counterexample

b)

conditional statement

c)

conjecture

d)

conjunction

28.

Which best describes the hypothesis of the statement "If tomorrow is Monday, then today is Sunday." ?

a)

Tomorrow is Monday.

b)

If tomorrow is Monday.

c)

Then today is Sunday.

d)

Today is Sunday.

29.

Which best describes the conclusion of the statement "The sum of the interior angles of any triangle is

180\degree

" ?

a)

The interior angles of a triangle are added.

b)

The sum of the interior angles of any triangle.

c)

The sum is $180\degree.$

d)

The interior angles is $180\degree.$

30.

All of the given statements are true except ___________.

a)

The area of a square is the square is its side.

b)

A triangle can have at least 1 acute angle.

c)

A square is a regular polygon.

d)

A rectangle has four $90\degree$ angles.

31.

"The set of integers consist of negative and positive numbers." is an example of a false conjecture. Which of the following is a counterexample to the given conjecture?

a)

$-1$

b)

$0$

c)

$1$

d)

$\frac{1}{2}$

32.

The sum of two consecutive numbers is always an odd number.

a)

TRUE

b)

FALSE

33.

If $2x-3=13,$ then $x=8$ .

a)

TRUE

b)

FALSE

34.

Transform the given statement into its equivalent If-then statement.
$A\ number\ with\ only\ two\ factors\ is\ prime.\$

a)

If a number with only two factors, then is prime.

b)

If a number has two or more factors, then it is a prime.

c)

If a number two is a factor, then it is a prime number.

d)

If a number has only two factors, then it is a prime number.

35.

What do you call the part of a conditional statement that follows “if” when written in if-then form?

a)

conclusion

b)

converse

c)

hypothesis

d)

inverse

36.

What do you call the part of a conditional statement that follows “then” when written in if-then form?

a)

conclusion

b)

converse

c)

hypothesis

d)

inverse

37.

If you do your homework, then you will receive snacks.

What do you call the underlined portion in this conditional statement?

a)

abstract

b)

conclusion

c)

generalization

d)

hypothesis

38.

If you drink milk, then you will grow.

What do you call the underlined portion in this conditional statement?

a)

conclusion

b)

converse

c)

hypothesis

d)

inverse

39.

If two lines form right angles, then the lines are perpendicular.

What do you think is the hypothesis of the given conditional statement?

a)

the lines are perpendicular

b)

if two lines form right angles

c)

two lines form right angles

d)

then the lines are perpendicular

40.

Cheese contains calcium.

What do you think is the conclusion of the given sentence?

a)

it is cheese

b)

if it is cheese

c)

then it contains calcium

d)

it contains calcium

41.

Equilateral triangles are equiangular.

What do you think is the conclusion of the given sentence?

a)

if a triangle is equilateral

b)

it is equiangular

c)

a triangle is equilateral

d)

then it is equiangular

42.

If the degree measure of an angle is between 90 and 180 degrees, then the angle is obtuse.

What is the hypothesis of the given conditional statement?

a)

the degree measure of an angle is between 90 and 180 degrees

b)

the angle is obtuse

c)

then the angle is obtuse

d)

If the degree measure of an angle is between 90 and 180 degrees

43.

If a whole number has two as a factor, then it is even.

What is the conclusion of the given conditional statement?

a)

 then it is even

b)

If a whole number has two as a factor

c)

a whole number has two as a factor

d)

it is even

44.

A point in the first quadrant has two positive coordinates.

What is the hypothesis of the given sentence?

a)

if a point is in the first quadrant

b)

then it has two positive coordinates

c)

a point is in the first quadrant

d)

it has two positive coordinates

45.

What is the converse statement of "If a number is divisible by 3, then it is divisible by 9."?

a)

If a number is divisible by 3, then it is divisible by 9.

b)

If a number is divisible by 9, then it is divisible by 3.

c)

If a number is not divisible by 3, then it is not divisible by 9.

d)

If a number is not divisible by 9, then it is divisible by 3.

46.

What is the inverse statement of "If a number is divisible by 3, then it is divisible by 9."?

a)

If a number is divisible by 3, then it is divisible by 9.

b)

If a number is divisible by 9, then it is divisible by 3.

c)

If a number is not divisible by 3, then it is not divisible by 9.

d)

If a number is not divisible by 9, then it is divisible by 3.

47.

What is the contrapositive statement of "If a number is divisible by 9, then it is divisible by 3."?

a)

If a number is divisible by 3, then it is divisible by 9.

b)

If a number is divisible by 9, then it is divisible by 3.

c)

If a number is not divisible by 3, then it is not divisible by 9.

d)

If a number is not divisible by 9, then it is divisible by 3.

48.

If a polygon is a quadrilateral, then it is a square.

a)

TRUE

b)

FALSE

49.

What statement is shown in the illustration?

a)

Conditional

b)

Contrapositive

c)

Converse

d)

Inverse

50.

It means that the two statements have the same truth values for every possible interpretation.

a)

Logically Equal Statements

b)

Logically Equivalent Statements

c)

Logical Equal Statements

d)

Logical Equivalent Statements

51.

Which statement is logically equivalent to the conditional statement?

a)

converse

b)

inverse

c)

contrapositive

d)

reverse

52.

Which two statements should both be true to have a biconditional statement?

a)

conditional and converse

b)

conditional and inverse

c)

conditional and contrapositive

d)

converse and inverse

53.

What is the converse of a contrapositive statement?

a)

conditional

b)

converse

c)

inverse

d)

contrapositive

54.

What is the inverse of the converse of the contrapositive of an inverse statement?

a)

conditional

b)

converse

c)

inverse

d)

contrapositive

55.

The type of reasoning where a person makes conclusions based on observations and patterns is called...

a)

Inductive reasoning

b)

Deductive reasoning

c)

Conjecture

d)

Experiments

56.

What are the missing numbers in this pattern?
23, 33, ___, 53, ___, 73

a)

32, 62

b)

42, 63

c)

43, 63

d)

42, 62

57.

Where would the next red square be?

a)

bottom left

b)

top right

c)

top left

d)

bottom right

58.

a)

1

b)

15

c)

20

d)

12

59.

What is the rule for this pattern?
1st term:32
2nd term:36
3rd term:40

a)

4x+28

b)

4x+32

c)

x+4

d)

4x

60.

Using the statements:
If it is Friday, then I will get paid.
It is Friday.
Write the conclusion.

a)

It is not Friday

b)

It is Friday

c)

I will not get paid

d)

I will get paid

61.

(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3) ???????
What belongs in line 3?

a)

Figure A is a polygon.

b)

Figure A is a circle.

c)

Figure A is a square.

d)

invalid; nothing belongs in line 3

62.

What can be concluded from the following statements?
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.

a)

If Tom goes fishing then he catches a fish.

b)

If Tom brings his pole then he goes fishing

c)

If Tom catches a fish then he brought his pole.

d)

If Tom brings his pole then he catches a fish.

63.

If it rains, then practice is cancelled that day.

It rains on Thursday. What can you conclude?

a)

Practice is cancelled on Thursday.

b)

The grass gets too wet on Thursday.

c)

No conclusion.

d)

The team lifts weights instead on Thursday.

64.

Answer these questions by figuring out which of the four figures belongs on the spot of the question mark.
Latin Square Rules
1. A row or column never contains the same figure/number twice.
2. Every row and column contain the same figures/numbers.

a)

a

b)

b

c)

c

d)

d

65.

What is a direct proof?

a)

A proof that always involves the multiplication of two values.

b)

A proof that can only use number properties to show that a certain

statement is false.

c)

A proof that assumes a statement's hypothesis is true and uses a series of

logical deductions to conclude that the statement's conclusion is true.

d)

A proof that assumes that the statement being proven is false and then

attempts to find a contradiction to that assumption proving the original

statement to be true.

66.

Given ∠𝐴 ≅ ∠𝐵 and ∠𝐵 ≅ ∠𝐶. Prove ∠𝐴 ≅ ∠𝐶. What is the reason for the statement

𝑚∠𝐴 = 𝑚∠𝐶 in Step 3 of the proof?

a)

Addition Property of Equality

b)

Distributive Property of Equality

c)

Subtraction Property of Equality

d)

Transitive Property of Equality

67.

Given ∠𝐴 is an angle. Prove ∠𝐴 ≅ ∠𝐴. What is the reason for the statement 𝑚∠𝐴 ≅

𝑚∠𝐴 in Step 2 of the proof?

a)

Distributive Property of Equality

b)

Reflexive Property of Equality

c)

Symmetric Property of Equality

d)

Transitive Property of Equality

68.

What does an indirect proof rely on?

a)

a contradiction

b)

a function

c)

a product

d)

a sum

69.

What is the reason for the statement 2(3𝑚) − 2(5) = 8 in Step 2?

a)

Indirect proofs look for a contradiction to their original assumption, and

direct proofs do not.

b)

Direct proofs use other theorems, rules, and definitions in their proofs, and

indirect proofs do not.

c)

Indirect proof usually starts with the statement 'assume not' or 'assume the

opposite', and direct proofs do not.

d)

Direct proofs involve assuming a hypothesis is true, and indirect proofs

involve assuming a conjecture is false.

70.

Which statement is true using Addition Property of Equality in Step 4?

a)

6𝑚 − 10 − 8 = 8 − 8

b)

6𝑚 − 10 + 8 = 8 + 8

c)

6𝑚 − 10 + 10 = 8 + 10

d)

6𝑚 − 10 − 10 = 8 − 10

71.

Which of the following is NOT a difference between direct and indirect proofs?

a)

Indirect proofs look for a contradiction to their original assumption, and

direct proofs do not.

b)

Direct proofs use other theorems, rules, and definitions in their proofs, and

indirect proofs do not.

c)

Indirect proof usually starts with the statement 'assume not' or 'assume the

opposite', and direct proofs do not.

d)

Direct proofs involve assuming a hypothesis is true, and indirect proofs

involve assuming a conjecture is false.

72.

Which statement is correct for Step 1 of the proof?

a)

b)

c)

d)

73.

What is the reason for the statement 𝐴𝐵 = 𝐸𝐹 in Step 3 of the proof?

a)

Addition Property of Equality

b)

Distributive Property of Equality

c)

Subtraction Property of Equality

d)

Transitive Property of Equality

74.

What assumption would you make from the statement that, "There can be only one 90° angle in a triangle" using indirect proof?

a)

All the angles in a triangle add up to 90°.

b)

All the angles in a triangle add up to 180°.

c)

There can be more than one 90° angle in a triangle.

d)

There can be more than one 180° angle in a triangle.

75.

What assumption would you make from the statement that “If 3𝑥 + 7 > 13, then

𝑥 > 2" using indirect proof?

a)

𝑥 ≤ 2

b)

𝑥 < 2

c)

𝑥 ≥ 2

d)

𝑥 = 2

76.

What is the first step of an indirect proof?

a)

Write the given.

b)

Contradict the given.

c)

Assume the negation of the given.

d)

Assume the negation of what you are trying to prove.

77.

If you were proving that a given line 𝑙, is perpendicular to another line 𝑗, using

indirect proof, what would your initial assumption be?

a)

Assume that line 𝑙 is not perpendicular to line 𝑗.

b)

Assume that line 𝑙 is perpendicular to line 𝑗.

c)

Assume that line 𝑙 and line 𝑗 are parallel.

d)

None of these are correct.

78.

What is the “reason” for the "statement" 𝐵𝐶 = 𝐵𝐶 in Step 3 of the proof?

a)

Commutative Property

b)

Reflexive Property

c)

Symmetric Property

d)

Transitive Property

79.

What is the “reason” from the "statement" 𝐴𝐵 + 𝐵𝐶 = 𝐴𝐶, 𝐵𝐶 + 𝐶𝐷 = 𝐵𝐷 in Step 5 of the proof?

a)

Angle Addition Postulate

b)

Segment Addition Postulate

c)

Commutative Property of Equality

d)

Distributive Property of Equality

80.

Which statement is true using Subtraction Property of Equality in Step 3?

a)

3𝑦 + 4 − 10 = 10 − 10

b)

3𝑦 + 4 − 4 = 10 − 4

c)

3𝑦 + 4 + 10 = 10 + 10

d)

3𝑦 + 4 + 4 = 10 + 4

81.

What is the reason for the statement 𝑦 = 2 in Step 4 of the proof?

a)

Addition Property of Equality

b)

Multiplication Property of Equality

c)

Subtraction Property of Equality

d)

Substitution Property

82.

What assumption would you make from the statement that ⊿𝐴𝐵𝐶 ≅ ⊿𝐷𝐸𝐹 using

indirect proof?

a)

⊿𝐴𝐵𝐶 ≠ ⊿𝐷𝐸𝐹

b)

⊿𝐴𝐵𝐶 ≇ ⊿𝐷𝐸𝐹

c)

⊿𝐴𝐵𝐶 ≤ ⊿𝐷𝐸𝐹

d)

⊿𝐴𝐵𝐶 ≥ ⊿𝐷𝐸𝐹

83.

Which statement is true using Multiplication Property of Equality in Step 2?

a)

$\frac{1}{2}AC$

b)

𝐴𝐵 = 2𝐴𝐶

c)

2𝐴𝐵 = 𝐴𝐶

d)

2𝐴𝐵 = 2𝐴𝐶

84.

What is the reason for the statement 𝐴𝐵 + 𝐵𝐶 = 𝐴𝐶 in Step 4?

a)

Line Addition Postulate

b)

Segment Addition Postulate

c)

Congruent Segment Addition

d)

Line Segment Addition

85.

Which of the following best describes a mathematical system? I. Axioms, Postulates and Theorems II. Undefined Terms III. Defined Terms IV. Shapes

a)

I only

b)

II only

c)

I, II, and III

d)

I, II, III, and IV

86.

What are the undefined Terms in Geometry?

a)

Point, Line, and Plane

b)

Axiom, postulate, and theorem

c)

Bisector, betweenness, and midpoint

d)

Parallel, perpendicular, and intersecting lines

87.

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

a)

Angle

b)

Line segment

c)

Midpoint

d)

Ray

88.

Which of the following is accepted to be true without proof?

a)

Axiom

b)

Definition

c)

Postulate

d)

Theorem

89.

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

a)

Axiom

b)

Definition

c)

Postulate

d)

Theorem

90.

Which of the following does not describe a mathematical system?

a)

Intersecting lines

b)

Postulate and Axioms

c)

Theorems

d)

Undefined, and defined terms

91.

What undefined term that has infinite length but with no width ang thickness?

a)

Angle

b)

Line

c)

Plane

d)

Point

92.

What does the edge of the box represents?

a)

Line

b)

Plane

c)

Point

d)

Polygon

93.

Which mathematical system does not require a definition but it is used as basis in defining other terms?

a)

Defined terms

b)

Postulate

c)

Theorem

d)

Undefined terms

94.

a)

line RS

b)

line ST

c)

line RT

d)

line RP

95.

1. Which of the following is NOT part of an axiomatic system?

a)

A. Inequality

b)

B. Postulate

c)

C. Theorems

d)

D. Undefined Terms

96.

2. The following are undefined terms EXCEPT:

a)

A. Line

b)

B. Plane

c)

C. Point

d)

D. Ray

97.

3. Which of the following is undefined term?

a)

A. Angle

b)

B. Point

c)

C. Parallel Lines

d)

D. Ray

98.

Which of the following does not represent a plane?

a)

board

b)

edge of a notebook

c)

surface of the table

d)

screen of an iPad

99.

In every line, there are at least how many distinct points?

a)

5

b)

4

c)

3

d)

2

100.

Which of the following represents a line?

a)

dot

b)

table cover

c)

envelop

d)

yarn

101.

Which of the following represents a point?

a)

tip of a pen

b)

pen

c)

peso bill

d)

edge of the ruler

102.

In every plane, there are at least how many noncollinear points?

a)

5

b)

4

c)

3

d)

2

103.

What is the intersection of a plane and a line perpendicular to the plane?

a)

line

b)

plane

c)

point

d)

space

104.

Which of the following best describes a line?

a)

Usually represented by a dot

b)

A flat surface

c)

Can be extended in both directions

d)

Has width and thickness

105.

The top of a table represents what geometric term?

a)

point

b)

plane

c)

line segment

d)

line

106.

What does a rope represent?

a)

point

b)

line

c)

plane

d)

space

107.

Which of the following does not represent a point?

a)

dot

b)

edge of a notebook

c)

intersection of two lines

d)

tip of a pen

108.

Collinear points Collinear points are points that lie on the same plane.

a)

True

b)

False

109.

Coplanar points are points that lie on the same line.

a)

True

b)

False

110.

Parallel Lines are lines in plane that do not intersect.

a)

True

b)

False

111.

Perpendicular are lines that intersect and form right angles.

a)

True

b)

False

112.

Midpoint is a point on a line segment that divides it into two equal parts.

a)

True

b)

False

113.

An angle is the figure formed by two rays with a common point.

a)

True

b)

False

114.

An acute angle is an angle whose measure is 90°.

a)

True

b)

False

115.

Vertical angles are two angles in which the sides of one angle are opposite rays to the sides of the other angles.

a)

True

b)

False

116.

If two angles have a common vertex and a common side, then they are called adjacent angles.

a)

True

b)

False

117.

If two angles have their noncommon sides forming a straight angles or opposite rays, then they are called linear pair.

a)

True

b)

False

118.

If the sum of the measures of two angles are 180°, then they are said to be complementary angles.

a)

True

b)

False

119.

If the sum of the measures of two angles is 90°, then they are said to be supplementary angles.

a)

True

b)

False

120.

An angle bisector is a ray that divides an angle into two congruent angles.

a)

True

b)

False

121.

Segment bisector is a point, a line or a segment that divides the segment into two congruent parts.

a)

True

b)

False

MOCK UP BRAINQUEST 3

Total questions: 121

Worksheet time: 2hrs 1mins

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