Free Printable LEAP Review

1.

What is the equation of a circle with radius 4 and center (0, 8)?

a)

x² + (y-8)² = 16

b)

(x-8)² + y² = 4

c)

x² + (y-8)² = 4

d)

x² + (y+8)² = 16

2.

In the equation (x-4)²+(y-3)²=25, the radius is

a)

4

b)

3

c)

5

d)

25

3.

What is the radius of the given circle:
x²+y²-10x+8y-23=0?

a)

4

b)

2

c)

8

4.

Determine the center and radius: x²+ y²+ 14x - 2y = -1

a)

center= (-7,2) radius= 3

b)

center= (-7,1) radius= 7

c)

center= (-4,1) radius= 5

5.

Angle 1 = 27^oFind the measure of angle 4

a)

27^o

b)

153^o

c)

63^o

d)

90^o

6.

Solve for y.

a)

y = 20

b)

y = 120

c)

y = 60

d)

y = 10

7.

What is the measure of ∠ABC?

a)

25°

b)

75°

c)

108°

d)

150°

8.

In the figure below, the three lines are parallel and cut by the transversal, t. Which of the following is NOT a pair of same side interior angles?

a)

2 and 5

b)

8 and 9

c)

4 and 11

d)

8 and 11

9.

Which is the correct reason for statements 2 and 4 in the proof?

a)

Corresponding Angles

b)

Substitution

c)

Definition of Congruent Angles

d)

Vertical Angles are congruent.

10.

Given the points A(-1,2) and B(7,14), find the coordinates of the point P on directed line segment AB that partitions AB into a ratio 1:3.

a)

(1,5)

b)

(3,7)

c)

(4,4)

d)

(5,8)

11.

Given the points A(-2,4) and B(7,-2), find the coordinates of the point P on directed line segment AB that partitions AB in a the ratio 1:2.

a)

(3,1)

b)

(4,3)

c)

(1,2)

d)

(0,1)

12.

Find the point that is 2/5 of the distance from C to D.

a)

(-1, 2)

b)

(0, 0)

c)

(1, -2)

d)

(-2, 4)

13.

Find missing side

a)

5

b)

7

c)

9

d)

11

14.

Solve for X.

a)

2 ft

b)

3 ft

c)

4 ft

d)

6 ft

15.

Find y.

a)

144

b)

18

c)

72

d)

12

16.

What is the area of a triangle with base of 4 and height of 6 ?

a)

15

b)

24

c)

6

d)

12

17.

Angles 1 and 3 are...

a)

verical angles

b)

corresponding angles

c)

perpendicular

18.

What is the value of x?

a)

118

b)

180

c)

62

d)

117

19.

1/3Bh is the volume formula for

a)

triangular prism

b)

cone

c)

sphere

d)

rectangular prism

20.

What 3 are properties of a rhombus?

a)

all sides are congruent

b)

all angles are right angles

c)

the diagonals bisect the angles

d)

opposite angles are congruent

21.

What is the area of the trapezoid?

a)

110 square inches

b)

60 square inches

c)

120 square inches

d)

100 square inches

22.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

23.

Find the midpoint of the segment with the endpoints:(4, 12) and (-6, 14)

a)

(-1, 13)

b)

(13, 1)

c)

(13, -1)

d)

(5, 13)

24.

Find the slope of the line that passes through the points (2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

25.

What is the perimeter of an Olympic-size swimming pool?

a)

150 m

b)

125 m

c)

135 m

d)

165 m

26.

Find the volume of this shape

a)

1520.53

b)

276.46

c)

552.93

d)

6082.12

27.

Select the 2D object that can be rotated to form the 3D object shown.

a)

b)

c)

d)

28.

What shape will the vertical cross-section of a cube be?

a)

Square

b)

Triangle

c)

Trapezoid

d)

Circle

29.

The right triangle as shows is rotated $360\degree$ about the $y-axis$ in three dimensions. What is the 3-Dimensional solid resulting from the rotation?

a)

cone

b)

cylinder

c)

pyramid

d)

prism

30.

Solve for the misssing distance

a)

18.9 meters

b)

19.5 meters

c)

47.2 meters

d)

27.5 meters

31.

Kevin leans a 16 foot ladder l 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

32.

Elizabeth is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63.6 ft

b)

1.59 ft

c)

74.2 ft

d)

86.9 ft

33.

Find the measure of the indicated angle.

a)

9.39

b)

55.2

c)

20.2

d)

19.4

34.

What is the correct equation?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

35.

Find the length of side y.

a)

22.32 cm

b)

36.5 cm

c)

76.34 cm

d)

87.76 cm

36.

Find side AB?

a)

20 m

b)

5 m

c)

11.54 m

d)

8.66 m

37.

You are attacking an enemy castle. Your strategy is to go over the castle wall. You are 1500 meters away from the bottom of the wall. You measure the angle of elevation to the top of the wall at 3^o. How tall is the enemy castle wall?

a)

78.6 meters

b)

1498.0 meters

c)

78.5 meters

d)

75.3 meters

38.

When do you use partitioning formula?

a)

to find the distance of a line segment

b)

to find only the midpoint of a line segment

c)

to find a point that divides a line segment into a specific ratio

d)

to shorten a line

39.

What do we call the blue line?

a)

Chord

b)

Circumference

c)

Radius

d)

Arc

40.

What do we call the red line?

a)

Chord

b)

Arc

c)

Diameter

d)

Segment

41.

Which segment is a radius?

a)

LM

b)

DC

c)

BD

d)

ML

42.

What is m∠ACB?

a)

67.5°

b)

90°

c)

22.5°

d)

45°

43.

What is m∠LMO?
(Segment LO is a diameter of Circle P)

a)

30°

b)

45°

c)

80°

d)

90°

44.

a)

A

b)

B

c)

C

d)

D

45.

Find the measure of arc AB.

a)

17 degrees

b)

34 degrees

c)

68 degrees

d)

146 degrees

46.

Find a and b.

a)

a=74 degrees
b=93 degrees

b)

a=93 degrees
b=74 degrees

c)

a=87 degrees
b=106 degrees

d)

a=106 degrees
b=87 degrees

47.

In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree.

a)

90

b)

60

c)

55

d)

113

48.

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

49.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

50.

Which representation of a transformation on a coordinate grid preserves congruence?
I. Rotation
II. Reflection
III. Dilation
IV. Translation

a)

I, II, and IV

b)

I and II only

c)

I, II, and III

d)

IV only

51.

A transformation is applied to create a new figure. Which transformation does not preserve congruence?

a)

A reflection across the x-axis

b)

A translation 4 units up

c)

A dilation by a scale factor of 5

d)

A rotation 90° counter clockwise

52.

Which representation of a transformation on a coordinate grid does not preserve congruence?

a)

(x,y)--> (¹/₇x,¹/₇y)

b)

(x,y)--> (x + 7, y + 7)

c)

(x,y)--> (x,-y)

d)

(x,y)--> (y,-x)

53.

A dilation is given by the transformation (x, y) → (2/3x, 2/3y). Will this produce an enlargement or reduction?

a)

Enlargement

b)

Reduction

54.

A dilation is given by the transformation (x, y) → (3/2x, 3/2y). Will this produce an enlargement or reduction?

a)

Enlargement

b)

Reduction

55.

If you were to dilate line AB using point C as the center of dilation, which of the below would best describe the newly created image? (You may assume that the scale factor is not 1.)

a)

A line segment

b)

A ray

c)

A line that is parallel to line AB

d)

A line that is in the same place as line AB

56.

Solve for X.

Hint: set up a proportion

a)

2 ft

b)

3 ft

c)

4 ft

d)

6 ft

57.

a)

4 ft

b)

15 ft

c)

18 ft

d)

2 ft

58.

Determine whether the triangles are similar(name the postulate or theorem you used).

a)

SSS similar

b)

AA similar

c)

SAS similar

59.

2 triangles are similar if _____________.

a)

their angles are congruent.

b)

their sides are congruent.

c)

their areas are equal.

d)

their perimeters are equal.

60.

The measures of the angles in a triangle are 53⁰,78⁰, and 49⁰. A similar triangle is created by using a dilation with a scale factor of 2. What are the measures of the angles of this triangle?

a)

53⁰,78⁰, and 49⁰

b)

There is not enough information to answer this question.

c)

106⁰,156⁰, and 98⁰

d)

26.5⁰,39⁰, and 24.5⁰

61.

What are the 2 missing pieces of information?

a)

Transitive Property, SAS(Side-Angle-Side)

b)

Reflexive Property, SAS(Side-Angle-Side)

c)

Transitive Property, SSS(Side-Side-Side)

d)

Reflexive Property, SSS(Side-Side-Side)

62.

Donovan dilates SW about point P using a scale factor of 7.5. The image of S'W' is created. Which statements about P, SW, and S'W' must be true? (Select 2)

a)

If P is on SW, then SW is parallel to S'W'

b)

If P is on SW, then SW is perpendicular to S'W'

c)

If P is on SW, then SW is on the same line as S'W'

d)

If P is not on SW, then SW is parallel to S'W'

e)

If P is not on SW, then SW is perpendicular to S'W'

63.

The __________ is the ratio of a length of the new figure to the corresponding length on the original figure.

a)

reduction

b)

enlargement

c)

scale factor

d)

center of dilation

64.

Similar figures have the same ______ but different ______.

a)

measure; shapes

b)

sizes; shapes

c)

value; measures

d)

shape; sizes

65.

A turn is also called a ___________.

a)

Translation

b)

Reflection

c)

Rotation

d)

Transformation

66.

Write a rule for the translation.

a)

(x -1, y + 2)

b)

(x -2, y + 1)

c)

(x +2, y - 1)

d)

(x +1, y - 2)

67.

Identify the transformation from ABC to A'B'C'.

a)

90^o clockwise rotation

b)

90^o counter clockwise rotation

c)

Reflection across the y-axis

d)

Reflection across the x-axis

68.

Identify the transformation.

a)

Reflection across y-axis

b)

90 Rotation counter clockwise

c)

Translation 5 units left, 1 unit up.

d)

Translation 5 units right, 1 unit down

69.

Point (-5,2) is reflected over the y axis. Where is the new point located?

a)

(5,2)

b)

(-5,-2)

c)

(-5,2)

d)

(5,-2)

70.

How many degrees was the figure rotated?

a)

90 degrees counterclockwise

b)

180 degrees

c)

90 degrees clockwise

71.

Choose the correct scale factor:

a)

2

b)

3

c)

1/3

d)

1/2

72.

A triangle is dilated by a scale factor of ⅓ to produce a new triangle. Which of the following best describes the relationship between the perimeter of the original triangle compared to the perimeter of the new triangle?

a)

The perimeter of the new triangle is ⅓ that of the original triangle

b)

The perimeter of the new triangle is 3 times that of the original triangle.

c)

The perimeter of the new triangle is 1/9 that of the original triangle.

d)

The perimeter of the new triangle is 9 times that of the original triangle

73.

A segment that is 15 units long is dilated about the origin using scale factor j.

- the resulting image is 25 units long.

- the image is then dilated about the origin using scale factor r.

- the resulting image is 10 units long.

What are the values of j and r?

a)

$j\ =\ \frac{5}{3}$

b)

$k\ =\frac{2}{5}$

c)

$j\ =\ \frac{3}{5}$

d)

$k\ =\ \frac{2}{3}$

e)

$j\ =\ \frac{2}{5}$

74.

REVIEW: What is the slope of the line: $y=\frac{2}{3}x+4$

a)

$\frac{2}{3}$

b)

$-\frac{2}{3}$

c)

$\frac{3}{2}$

d)

$4$

e)

$-4$

75.

Which two lines are parallel?

a)

$y=\frac{3}{7}x-25$

b)

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

c)

$y=\frac{7}{3}x-25$

d)

$y=3x+13$

e)

$y=7x+9$

76.

Which two lines are parallel?

a)

$y=-\frac{1}{4}x-25$

b)

$y=\frac{1}{4}x+2$

c)

$y=-4x-25$

d)

$y=4x+13$

e)

$y=\frac{1}{4}x+9$

77.

Which two lines are perpendicular?

a)

$y=\frac{3}{7}x-25$

b)

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

c)

$y=-\frac{7}{3}x-25$

d)

$y=3x+13$

e)

$y=7x+9$

78.

Which is the equation of the line that is parallel to the graph of y = 5x + 7 and has a y-intercept at (0, -2)?

a)

y = 5x - 2

b)

y = -2x + 7

c)

y = 5(x - 2)

d)

y = -1/5x - 2

79.

Which of the following lines is PARALLEL to the graph of y = -6x + 3 and goes through the point (-1,4)?

a)

y=1/6x +25/6

b)

y = 1/6x + 4

c)

y = -6x - 2

d)

y = -6x + 4

80.

Which of the following represents the equation of the line passing through (-4, 5) PERPENDICULAR to the line y = -1/2x + 5/2?

a)

y = 2x + 13

b)

y = 2x + 5

c)

y = -1/2x + 3

d)

y = -1/4x + 11/2

81.

Two lines that are parallel will have ...

a)

Slope that is opposite reciprocals

b)

No slope

c)

Slope that is the same

d)

none of the above

82.

Two lines that are perpendicular lines have ...

a)

Slope that is opposite reciprocals

b)

No Slope

c)

Slope that is the same

d)

none of the above

83.

These two lines will intersect. Select the best answer

a)

True, it is not shown in the picture

b)

Maybe, you need to see more of the picture

c)

False, parallel lines never meet or intersect

d)

False, it was given that these are parallel lines, thus they will never meet by the parallel line postulate

84.

Angle "a" equals 60°. Is this statement true and why?

a)

False: it is equal to 70°, it is an isosceles triangle

b)

False: it is equal to 50°, it is an isosceles triangle

c)

True, the sum of the angles must equal 180°

d)

False, the sum of the angles must equal 360°

85.

Which of the following is an example of the transitive property?

a)

If x = 5 and x = y, then y = 5.

b)

If x = y then y = x

c)

x = x

d)

If 2x + 4 = 2, then x = -1

86.

Given: B is the midpoint of AC. What should you conclude?

a)

AB + BC = AC

b)

AB = BC

c)

A is the segment bisector of BC

d)

ABC is a straight angle

87.

Name the property of equality or congruence that justifies going from the first statement to the second statement.

a)

Reflexive Property of Equality

b)

Symmetric Property of Equality

c)

Symmetric Property of Congruence

d)

Reflexive Property of Congruence

88.

What is the missing statement in the proof?

a)

Addition property

b)

Segment Addition Postulate

c)

Substitution property

d)

Transitive property

89.

Give the reason for statement #1

a)

Given

b)

Reflexive Property

c)

Symmetric Property

d)

Definition of perpendicular

90.

If the sum of two angles is 180^o the angles are supplementary

a)

False

b)

True

91.

Angles 3 and 5 are congruent because they are (a) .

92.

If parallel lines are cut by a transversal, alternate interior angles are congruent.

a)

True

b)

False

93.

If angle 1 is congruent to angle 2, select all that are true

a)

Both angles are 90^o

b)

The angles are complimentary

c)

The angles are supplementary

d)

The angles form a linear Pair

94.

If two angles form a (a) , they are supplementary

95.

Corresponding angles are supplementary if two parallel lines are cut by a transversal

a)

True

b)

False

96.

Solve for x.

a)

7

b)

-4

c)

8

d)

9

97.

Which of the following are rigid motions

a)

Translation

b)

Reflection

c)

Dilation

d)

Rotation

98.

Adjacent Angles sum to 180

a)

always

b)

sometimes

c)

never

99.

Rigid motions preserve congruency. (shape, size, perimeter, area, side length, and angle measure)

a)

True

b)

False

100.

What are supplementary angles?

a)

Angles that add up to 180°

b)

Angles that add up to 90°

c)

Angles that are equal to each other

d)

Angles that are opposite of each other when lines intersect

101.

True of false: These angles are supplementary angles.

a)

True

b)

False

102.

Vertical angles are always

a)

acute

b)

total 180 degrees

c)

congruent (equal measures)

d)

adjacent angles

103.

A city has a population of 8792 people. The area of the city is approximately 6.5 square miles. Approximately, how many people per square mile live in the city?

a)

57148

b)

208

c)

1353

d)

135

104.

a)

A

b)

B

c)

C

d)

D

105.

a)

A

b)

B

c)

C

d)

D

106.

a)

A

b)

B

c)

C

d)

D

107.

a)

A

b)

B

c)

C

d)

D

108.

a)

A

b)

B

c)

C

d)

D

109.

a)

A

b)

B

c)

C

d)

D

110.

a)

A

b)

B

c)

C

d)

D

111.

When copying line segment AB using a straight edge and a compass, the compass should be used to:

a)

Draw an arc above point A

b)

Measure the length of segment AB

c)

Draw an arc between point A and point B

d)

Measure half the length of line segment AB

112.

Name the construction.

a)

Angle bisector

b)

Perpendicular line to a point not on a line

c)

Perpendicular line to a point on the line

d)

Perpendicular bisector of a line segment

113.

Name the construction.

a)

Angle bisector

b)

Perpendicular line to a point not on a line

c)

Angle median

d)

Perpendicular bisector of a line segment

114.

Select the best answer choice.

a)

F

b)

G

c)

H

d)

J

115.

What is this?

a)

Compass

b)

Circle creator

c)

Pencil swingy-thing

d)

Arc maker

116.

Eric was attempting to construct a perpendicular bisector to the segment AB with a compass and straight edge. Which of the below statements explains what Eric may have done wrong?

a)

Eric should have started by putting the compass needle point at the midpoint of the segment AB.

b)

On the second step, Eric should have placed the compass needle point where the first arc intersected the segment AB.

c)

Erick just needed to open the compass more to create arcs that have a radius of more than half the length of the segment AB.

d)

Erick didn’t do anything wrong he just needs to connect the opposite endpoints of each arc to finish the construction.

117.

What is being constructed?

a)

A congruent segment

b)

Parallel Lines

c)

Perpendicular Bisector

d)

Angle Bisector

118.

What does this symbol mean?

≅

a)

not equal

b)

congruent

c)

equal

d)

half

119.

Select the best answer choice.

a)

A

b)

B

c)

C

d)

D

LEAP Review

Total questions: 119

Worksheet time: 5hrs 50mins

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