Beginning-of-Year Diagnostic Test - Classroom … Lessons...Beginning-of-Year Diagnostic Test 25. A...

Name _______________________________________ Date __________________ Class __________________

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5

Beginning-of-Year Diagnostic Test

Use the figure for 1–2.

1. What is the length of ?XY

A 2 3 units C 10 units

B 2 7 units D 14 units

2. What is the midpoint of ?XY

A (1, 1) C (3, 4)

B (2, 2) D ( 2, 2 )

3. In the figure, m 70.KJM

What is the value of x?

A 31 C 41

B 39 D 109

4. Line segment AB with endpoints A(3, 2)

and B(1, 5) is reflected over the x-axis.

What are the coordinates of A' and B'?

A A'(3, 2), B'(1, 5)

B A'(3, 2), B'(1, 5)

C A'(2, 3), B'(5, 1)

D A'(3, 2), B'(1, 5)

5. What is the coordinate notation for the

rule that maps DEF to ?DEF

A (x, y) (x, y)

B (x, y) (x, y)

C (x, y) (y, x)

D (x, y) (y, x)

6. If (x, y) (x 3, y 2), where does

A(4, 6) get mapped to?

A A'(1, 4) C A'(1, 4)

B A'(1, 4) D A'(1, 4)


7. How many lines of symmetry does the

figure have?

A 0 C 2

B 1 D 3

8. What are the angles of rotation less than

360 for the figure?

A 180

B 120, 240

C 90, 180, 270

D 60, 120, 180, 240, 300

Name _______________________________________ Date __________________ Class __________________


6


For 9–10, use the figures and the

congruence statement .RST XYZ

9. Which side is congruent to ?RT

A ST C YZ

B XY D XZ

10. What is mY?

A 32 C 65

B 33 D 115

11. What transformation or transformations

can you use to show that quadrilaterals

JKLM and J′K′L′M′ are congruent?

A translation 5 units up

B translation 5 units down

C reflection across the x-axis and

translation 1 unit up

D reflection across the x-axis and

translation 1 unit down

12. In the figure, m2 68. What is m5?

A 22 C 112

B 68 D 122


13. What is the value of x?

A 35 C 105

B 55 D 125

14. What is the value of y?

A 35 C 105

B 55 D 125

15. Which line is parallel to y 3x 4?

A y 3x 1 C 1 43 3

y x

B y 3x 4 D 1

43

y x

16. What is the equation of a line

whose y-intercept is 6 and that is

perpendicular to 2x y 3?

A y 2x 6 C 1

62

y x

B y 2x 6 D 1

62

y x

Name _______________________________________ Date __________________ Class __________________


7


17. Which angles are complementary?

A 4 C 1 and 6

B 2 and 3 D 5 and 6

18. In the figure below, .PQR STU

Which statement must be true?

A QR TU C PR TU

B QR SU D QP ST

19. What theorem shows ?DEF JKL

A SSS C ASA

B SAS D AAS

20. What information is needed to show that

ABC XYZ by SAS congruence?

A A X C AB XY

B B Y D AC XZ

21. What information is needed to show that

ABC XYZ by AAS congruence?

A A X C AB XY

B B Y D AC XZ

22. Which congruence statement correctly

shows that the triangles are congruent?

A DEF FGH

B DEF FHG

C DEF HGF

D DEF GHF

23. What is the value of x in the figure?

A 42 C 132

B 48 D 138

24. An equilateral triangle has a perimeter of

12 centimeters. What is the side length of

the triangle?

A 3 cm C 6 cm

B 4 cm D 36 cm

Name _______________________________________ Date __________________ Class __________________


8


25. A triangle has side lengths of 7 cm,

10 cm, and 7 cm. Which description best

describes the triangle?

A right C isosceles

B scalene D equilateral

26. Two sides of a triangle measure 8 meters

and 12 meters. What is a possible side

length for the third side?

A 4 m C 20 m

B 10 m D 24 m

27. Which statement is true about the

measures of the angles in ?DEF

A mF mE C mD mE

B mE mF D mD mF

28. A median is a segment that connects the

vertex of a triangle to the midpoint of the

opposite side. What are the coordinates

of the intersection of the three medians of

the triangle?

A (1, 1) C (0, 1)

B (1, 2) D (0, 2)

29. In the figure, MN is the midsegment of

.JKL If KN 7 cm, what is KL?

A 3.5 cm C 14 cm

B 7 cm D 21 cm

30. In the figure, ,LP ,MP and NP are

perpendicular bisectors. Which statement

is not true?

A PH PK C PK PJ

B HM MJ D PL PM

31. In the figure, BD bisects ABC. What is

the value of x?

A 3 C 6

B 5 D 11

Name _______________________________________ Date __________________ Class __________________


9


32. Which statement about a parallelogram is

false?

A Diagonals are congruent.

B Diagonals bisect each other.

C Opposite sides are congruent.

D Opposite angles are congruent.

33. A rectangle is shown. If GI 18 cm, what

is GJ?

A 8 cm C 18 cm

B 9 cm D 36 cm

34. PQRS is a parallelogram. What are the

coordinates for the missing vertex S?

A (0, 2) C (1, 2)

B (0, 3) D (4, 2)

35. A parallelogram has vertices

D(1, 1), E(2, 4), F(5, 1), G(2, 2). Which

description best describes the figure?

A rectangle C square

B trapezoid D kite

36. KLMN is a rectangle. What are the

missing coordinates of M?

A (a, a) C (a, b)

B (b, b) D (b, a)

Use the following information for 37–38.

The figure is symmetric about the x-axis.

37. Which description best describes the

figure?

A right triangle

B scalene triangle

C isosceles triangle

D equilateral triangle

38. What is the area of the figure?

A 12 units2 C 36 units2

B 18 units2 D 42 units2

39. What is the perimeter of the figure to the

nearest tenth?

A 12.7 units C 19.4 units

B 18 units D 20.1 units

Name _______________________________________ Date __________________ Class __________________


10


40. What is the scale factor of the dilation?

A 14

C 2

B 12

D 4

41. A figure has vertex A(3, 6). The figure is

dilated by a scale factor of 4. The

resulting image is dilated by a scale

factor of 1.

3 What are the coordinates of

vertex A' of the final image?

A (1, 2) C (4, 8)

B (3, 6) D (12, 24)

42. In this figure, .JKL XYZ Which

statement is not true?

A JK LJXY ZX

C LJ KLZX YZ

B KL LJYZ ZX

D KL KJYX YZ

43. Which sequence of transformations maps

ABC to ?RTS

A a translation 4 units right, then a

translation 3 units up

B a translation 3 units right, then a

dilation by a scale factor of 2

C a translation 7 units right, then a

dilation by a scale factor of 2 about S

D a translation 7 units left, then a

dilation by a scale factor of 12

about S

44. In the figure, .CAB EAD What

is AB?

A 9 cm C 15 cm

B 12 cm D 18 cm

45. What is the distance across the river?

A 20 m C 57.6 m

B 30 m D 80 m

Name _______________________________________ Date __________________ Class __________________


11


46. Rectangles ABCD and EFGH are similar.

Rectangle ABCD has a length of 6 feet

and a perimeter of 20 feet. Rectangle

EFGH has a length of 18 feet. What is the

perimeter of EFGH ?

A 30 feet C 120 feet

B 60 feet D 216 feet

47. What are the coordinates of point C, such

that 1

?4

AC AB

A (2, 2) C (2, 0)

B (0, 1) D (2, 1)

Use triangle XYZ for 48–49.

48. What is sin X?

A 512

C 1213

B 513

D 1312

49. What is cos X?

A 512

C 1213

B 513

D 1312

50. What is the measure of X to the nearest

tenth of a degree?

A 28.1 C 57.8

B 32.2 D 61.9

51. If BC 4, what is AC?

A 2 C 4 3

B 2 3 D 8

52. What is XZ?

A 11.3 C 27.2

B 21.2 D 51.1

53. What is BC?

A 4.3 C 19.7

B 15.7 D 25.5

Name _______________________________________ Date __________________ Class __________________


12



In the circle, m 80AB

54. What is mADB?

A 20 C 80

B 40 D 160

55. What is m ?ADB

A 80 C 160

B 100 D 280

56. In the circle, mACB 98. What is

mAXB?

A 49 C 92

B 82 D 98

57. In the circle, QS and TR intersect at

point P. What is PR?

A 5 C 11

B 9 D 16

Use the circle with center P for 58–59.

58. Find the exact arc length of .QR

A 3

cm C 6 cm

B 3 cm D 18 cm

59. Convert the central angle to radians.

A 3

C 23

B 6

D 32

60. What is the area of the sector formed by

QPR to the nearest tenth of a square

centimeter?

A 4.7 cm2 C 42.4 cm2

B 9.4 cm2 D 84.8 cm2

61. Write an equation of a circle with center

(3, 2) and radius 4.

A 22( 3) 2 16x y

B 22( 3) 2 4x y

C 22( 3) 2 16x y

D 22( 3) 2 4x y

62. Write an equation of a parabola with

focus (0, 2) and directrix y 2.

A 218

y x

B 212

y x

C 22 2y x

D 28 2y x

Name _______________________________________ Date __________________ Class __________________


13


63. What is the volume of the prism?

A 120 ft3 C 248 ft3

B 240 ft3 D 480 ft3

64. A rectangular prism has a length of 7 feet

and a width of 5 feet. The volume of the

prism is 280 cubic feet. What is the height

of the prism?

A 8 ft C 40 ft

B 9.3 ft D 56 ft


A cylindrical tank has a diameter of

12 meters and a height of 5 meters.

65. What is the volume of the tank?

A 414.7 m3 C 942.5 m3

B 565.5 m3 D 2261.9 m3

66. What is the surface area of the tank?

A 414.7 m3 C 565.5 m3

B 534.1 m3 D 1281.8 m3

67. What is the volume of the cone?

A 576.0 in3 C 2303.8 in3

B 1073.4 in3 D 6911.5 in3

68. A right circular cone has a slant length of

9 inches and a radius of 4 inches.

What is the surface area of the cone

to the nearest tenth?

A 150.8 in2 C 367.6 in2

B 163.4 in2 D 452.4 in2

69. What is the surface area of a sphere with

a radius of 12 inches?

A 452.4 in3 C 1809.6 in3

B 603.2 in3 D 7238.2 in3

70. A square pyramid with a base area of 16

square feet and a cube with a side length

of 4 feet have equal volumes. What is the

height of the pyramid?

A 4 ft C 32 ft

B 12 ft D 64 ft

71. The trash can shown below is made of

a cylinder and a hemisphere. What is the

volume of the trash can to the nearest

tenth?

A 586.4 in3 C 1172.9 in3

B 1038.8 in3 D 4691.4 in3

72. A solid wooden rectangular prism has

dimensions 3 cm, 2cm, and 5 cm. If it

weighs 22.35 grams, what is the density

of the wood it is made of?

A 0.75 g/cm3 C 1.34 g/cm3

B 0.89 g/cm3 D 2.24 g/cm3

73. A cylinder must have a volume of at least

150 m3 and a radius of 10 m. What is the

minimum possible height of the cylinder?

A 0.2 m C 1.5 m

B 0.5 m D 2.4 m

Name _______________________________________ Date __________________ Class __________________


14


74. A paper bag has 10 tiles numbered 1–

10. You randomly choose 3 tiles. What is

the probability that you choose 1, 2, 3 in

that order?

A 310

C 1

720

B 1

120 D

11000

75. There are 12 students on the academic

team. The team advisor randomly

chooses 4 students for the next

competition. What is the probability that

Marcus, Adam, Brittany, and Luisa are

chosen in any order?

A 13

C 1

11,880

B 1

495 D

120,736

76. A jar contains 8 red marbles, 6 yellow

marbles, 4 blue marbles, and 6 green

marbles. One marble is taken from the

jar and not replaced. Then a second

marble is taken from the jar. What is the

probability of choosing a red marble

followed by a blue marble?

A 12

C 132

B 118

D 469

77. A spinner has 4 equal sections

numbered 1–4. A number cube with 6

sides is numbered 1–6. What is the

probability of spinning a 2 and rolling a

4?

A 15

C 512

B 112

D 124

Use the table for 78–79.

Has Pet No Pet Total

Has Sibling 7 7 14

No Sibling 3 5 8

Total 10 12 22

78. Ms. Roberts surveyed the students in her

class about whether they had a sibling or

a pet. The results are shown in the table.

What is the probability that a student has

a sibling if he or she also has a pet?

A 12

C 722

B 710

D 1022

79. What is the probability that a student has

a pet if he or she does not have a

sibling?

A 38

C 318

B 310

D 322

80. A contest allows anyone to enter as

many times as they would like and at the

end of the contest, a winner is randomly

chosen from all the entries. Suppose 450

people enter the contest. If Sabine

entered 3 times and Joe entered 5 times,

then what is the probability Joe or

Sabine will win the contest?

A 0.002 C 0.018

B 0.007 D 0.033

81. A company stores 75% of items in

warehouse A and the rest in warehouse

B. A report found that 1% of items in A

and 2% of items in B are defective. An

item is randomly selected and found to

be defective. What is the probability it

came from A?

A 0.01 C 0.33

B 0.05 D 0.60

Name _______________________________________ Date __________________ Class __________________


203

Answer Key


1. C Correct

Substitute the coordinates of the

endpoints into the Distance Formula

to find the length of the line segment.

TEST PREP DOCTOR: Students

who answered A, B, or D should

review the Distance Formula and

operations with integers.

2. A Correct

Substitute the coordinates of the

endpoints into the Midpoint Formula

to find the coordinates of the

midpoint.


who answered B, C, or D did not use

the Midpoint Formula correctly.

Students should review how the

Midpoint Formula differs from the

Distance Formula.

3. A Correct

In the figure, mKJM mKJL

mLJM. Subtract 39 from 70 to find

the value of x.


who answered B think the two

smaller angles are congruent.

Students who answered C made a

calculation error. Students who

answered D added the given angle

measurements.

4. B Correct

A reflection across the x-axis maps

a point according to the rule ( , ) ( , ).x y x y


who answered A, C, or D used an

incorrect rule for a reflection.

Students should review what rules to

use for a reflection depending on the

line of reflection.

5. D Correct

Compare the coordinates of the

vertices of the preimage and the

image. The coordinates of D(1, 2) to

D(2, 1) follows the rule ( , ) ( , ).x y y x


who answered A, B, or C used an

incorrect rule for a rotation. Students

should review what rules to use for a

rotation depending on angle and

direction of the rotation.

6. B Correct

Based on the rule, this is a translation

three units right and 2 units down.

Add three to the x-coordinate and

subtract 2 from the y-coordinate.


who answered A, C, or D should

review rules for translations and

operations with integers.

7. D Correct

There is a line of symmetry through

each vertex of the triangle.


who answered A, B, or C need to

review lines of reflection.

8. B Correct

The angle of rotation is the smallest

angle that maps a figure onto itself.

Identify the fraction of a circle that

the rotation describes, and multiply

it by 360


who answered A, C, or D need to

review angles of rotation.


204

9. D Correct

The congruence statement indicates

that .RT XZ


who answered A, B, or C should

review congruence statements and

corresponding parts of congruent

triangles.

10. B Correct


that Y S.


who answered A, C, or D review

congruence statements and


triangles.

11. C Correct

The orientation of the image is

reversed, so there is a reflection

across the x-axis. The figure is then

translated up 1 unit.


who answered A or B did not

consider that the orientation of the

image is reversed. Students who

answered D reversed the preimage

and the image.

12. C Correct

2 and 4 are corresponding angles,

so they are congruent. 4 and 5

form a linear pair, so they are

supplementary. Therefore, 2 and

5 are supplementary.


who answered A, B, or D need to

review the angle relationships formed

by parallel lines cut by a transversal.

13. B Correct

The angle that measures x is vertical

to the angle that measures 55, so

the angles are congruent.


who answered A, C, or D need to


by intersecting lines and understand

that vertical angles are congruent.

14. D Correct

The angle that measures x forms a

linear pair with the angle that

measures 55, so the angles are

supplementary.




by intersecting lines and understand

that the sum of the angles that form a

linear pair is 180.

15. A Correct

The y 3x 4 has a slope of 3.

A line that is parallel to this line will

also have a slope of 3.


who answered B, C, or D need to

review that parallel lines have the

same slope.

16. C Correct

The 2x y 3 can be written in slope-intercept form as 2 3,y x

which has a slope of 2. A line that is

perpendicular to this line will have a

slope of 12

since 1

2 1.2



review that the product of the slopes

of perpendicular lines is equal to 1.


205

17. D Correct

The sum of the measures of

complementary angles is 90.

4, 5, and 6 form a linear pair.

Since 4 is a right angle, the sum of

the measures of 5 and 6 is 90.


who answered A need to understand

that complementary angles refer to a

pair of angles. Students who answered

B should review the definition of

complementary angles. Students who

answered C should be reminded that

they can only use information that is

given in a problem and should not

rely on how a figure is drawn.

18. A Correct


that the corresponding sides are

,PQ ST ,QR TU .PR SU


who answered B, C, or D should



triangles.

19. B Correct

The triangles have two sides and the

included angle congruent, so the

SAS Theorem can be used to show

that the triangles are congruent.



review the criteria required for

triangle congruence.

20. D Correct

To use SAS, two sides and the

included angle of one triangle need to

be congruent to two sides and the

included angle of another triangle.

C is the included angle for sides

BC and CA and Z is the included

angle for sides YZ and .ZX



review the criteria required for

triangle congruence.

21. A Correct

To use AAS, two angles and the non-

included angle of one triangle need to

be congruent to two angles and the

non-included angle of another

triangle. BC is the non-included side

for A and C and YZ is the non-

included side for X and Z.


who answered B should review the

difference between an included side

and a non-included side. Students

who answered C or D should review

the criteria required for triangle

congruence.

22. D Correct

In the figure, F F, so the

triangles are congruent by SAS. Use

the corresponding parts to write the

congruence statement.





triangles.

23. D Correct

The angle that measures x is an

exterior angle. The measure of an

exterior angle is equal to the sum of

its remote interior angles. The remote

interior angles measure 90 and 48.


who answered A used the Triangle

Sum Theorem to find the missing

interior angle. Students who

answered B determined that x was

congruent to the given angle, 48.

Students who answered C

determined that x was supplementary

to the given angle, 48. Students

should review the relationships

between the interior and exterior

angles of a triangle.


206

24. B Correct

An equilateral triangle has three

congruent sides. To find the side

length, divide the perimeter by 3.


who answered A or C may have

made a calculation error. Students

who answered D multiplied the

perimeter by 3 instead of dividing

by 3. Students should review the

properties of equilateral triangles.

25. C Correct

The triangle has two congruent sides,

so it is isosceles.


who answered A, B, or D should

review how to classify a triangle by

its sides.

26. B Correct

The Triangle Inequality Theorem

states that any two sides of a triangle

are greater than the third side.

Therefore, the length of the third side

of the triangle must be greater than

12 8 4 and less than 12 8 20.


who answered A or C need to be

reminded that two sides of a triangle

must be greater than, not greater

than or equal to, the third side.

Students who answered D should

review the Triangle Inequality

Theorem.

27. A Correct

In a triangle, the larger angle is

opposite the longer side.



review side-angle relationships in

triangles.

28. A Correct

Draw each median of the triangle and

find the point of intersection. The

medians lie on the lines x 1,

y 1, and y 2x 2.



review how to find the medians of

a triangle.

29. C Correct

The midsegment connects the

midpoints of two sides of the triangle,

so KN KL.


who answered A may have used

KL 7, and found KN. Students who

answered B found NL, but did not

follow through with finding the KL.

Students who answered D need

to review the properties of a

midsegment of a triangle.

30. D Correct

Each perpendicular bisector

intersects a side of the triangle at its

midpoint. Point P is the intersection

of the three perpendicular bisectors,

so it is equidistant to H, J, and K.


who answered A need to review the

definition of a perpendicular bisector

and understand that it intersects a

line segment at its midpoint. Students

who answered B or C need to

understand that that the point of

concurrency of the three

perpendicular bisectors of a triangle

is equidistant from the vertices of the

triangle.

31. B Correct

Since point D is on the bisector of the

angle, it is equidistant from the sides

of the angle. So, AD DC. To find

the value of x, solve the equation

2x 6 16.


who answered D solved the equation

incorrectly. Students who answered

A or C need to review the properties

of angle bisectors.


207

32. A Correct

The diagonals of a parallelogram are

not congruent unless it is a rectangle.



review properties of parallelograms.

33. B Correct

The diagonals of a rectangle bisect

each other and are congruent.


who answered C or D may have

misread the given information.

Students who answered D should

review properties of rectangles and

understand that the diagonals bisect

each other.

34. A Correct

PS must be parallel and congruent

to .QR


who answered B may have misread

the graph since the height of the

parallelogram is 3 units. Students

who answered C or D should review

properties of parallelograms and

understand how to determine the

length and slope of a line segment on

the coordinate plane using the

Distance Formula and Slope

Formula.

35. C Correct

One way to solve the problem is to

graph the vertices. The diagonals of

the parallelogram are perpendicular

and congruent, so the parallelogram

is a square.


who answered A did not choose the

best description for the figure.

Students who answered B or D

should review properties of

quadrilaterals and understand how to

determine the length and slope of a

line segment on the coordinate plane

using the Distance Formula and

Slope Formula.

36. C Correct

Opposite sides of a rectangle are

congruent and all four angles are

right angles. The rectangle has

length a and width b, so the

x-coordinate is a and the

y-coordinate is b.


who answered D reversed the x-

and y-coordinates. Students who

answered A or B should review how

to position a figure on the coordinate

plane and assign coordinates to each

vertex.

37. C Correct

Use the Distance Formula to find

each length: DE 45, EF 45, and FD 6. Since the triangle has

two congruent sides, the triangle is

isosceles.



review how to use the Distance

Formula to find the length of a line

segment on the coordinate plane.

Students may also need to review

how to classify a triangle by its sides.

38. B Correct

Use the formula A 12

bh. The base

of the triangle is 6 units and the

height is 6 units.


who answered A added the length of

the base and height of the triangle,

and students who answered B did

not multiply the product of the base

and height by 1.

2 These students

should review the formula for the

area of a triangle. Students who

answered D need to review how to

use the Distance Formula to find the

length of a line segment on the

coordinate plane.


208

39. C Correct

Use the Distance Formula to find

each length: DE 45, EF 45, and FD 6. Add the sides to find the

perimeter.


who answered A only added 2 sides

of the triangle. Students who

answered B used a side length of 6

units for each side and students who

answered D used a side length of

45 for each side. Review how to

use the Distance Formula to find the

length of a line segment on the

coordinate plane.

40. B Correct

Compare the coordinates of the

image to the preimage. The dilation

follows the rule 1 1

( , ) , .2 2

x y x y


who answered A may have misread

the coordinates of the vertices of the

triangles. Students who answered C

made an error in determining which

figure is the preimage and which

figure is the image. Students who

answered D need to review how to

find a scale factor of a dilation on the

coordinate plane.

41. C Correct

Perform the dilation ( , ) (4 , 4 )x y x y

followed by the dilation The dilation


( , ) , .3 3

x y x y

Both dilations can be combined into a

single transformation. The dilation


( , ) , .3 3

x y x y


who answered A or D only performed

one of the dilations. Students who

answered B need to review how to

perform dilations using coordinates.

42. D Correct

The similarity statement and angle arcs indicate that ,J X

,K Y L Z and,

.JK KL LJXY YZ ZX



review how to set up proportions

using the corresponding sides of

similar triangles.

43. C Correct

First map point C to point S by a

translation 7 units right. Then dilate

the figure by a scale factor of 2.

TEST PREP DOCTOR: Students who answered A may have confused the side lengths of the triangles with the change in coordinates for a translation. Students who answered B did not translate the vertices of the preimage to the corresponding vertices of the image. Students who answered D mapped RTS to ABC.

44. C Correct

Since ~ ,CAB EAD .ED ADCB AB

Solve the proportion 4 6

.10 AB


who answered A found the length of

.DB Students who answered B or D

should review how to set up a

proportion for corresponding sides of

similar figures, and understand that a

line parallel to one side of a triangle

that intersects the other two sides,

divides the triangle proportionally.


209

45. A Correct

Use similar triangles to set up and

solve the proportion 48 24

.40 JK


who answered B, C, or D did not

write a correct proportion for the

diagram. Review how to solve

indirect measurement problems using

similar triangles.

46. B Correct

Use the given length and perimeter to

find the width of rectangle ABCD.

The dimensions of rectangle ABCD

are 6 by 4. Use corresponding parts

of similar figures to find the width of

rectangle EFGH. The dimensions of

rectangle EFGH are 18 by 12. Use

these dimensions to calculate the

perimeter of EFGH.


who answered A found the correct

length and width of EFGH, but only

added the two sides to find the

perimeter. Students who answered C

found the width of ABCD to be

20 6 14 and did not divide by 2 to

find the correct length and width of

ABCD. Students who answered D

found the area of EFGH. Review

how to make a plan to solve word

problems with more than one step.

47. A Correct

Look at the rise and run between the endpoints of the line segment. The rise is

4 units and the run is 8 units. Find 14

of

each distance: 1•4 1

4 (rise) and

1•8 2

4 (run). So, the coordinates of

point C will be 1 unit up and 2 units right from point A.

TEST PREP DOCTOR: Students who answered B or C found the coordinates

of point C to be 12

AB and 34

AB,

respectively. Students who answered D did not find a point on the line. Review how to find the coordinates of a point that is a fractional distance from one end of a line segment.

48. B Correct

Use the sine ratio, sin .YZ

XXY

TEST PREP DOCTOR: Students who answered A, C, or D should review the definitions of trigonometric ratios.

49. C Correct

Use the cosine ratio, cos .XZ

XXY

TEST PREP DOCTOR: Students who answered A, B, or D should review the definitions of trigonometric ratios.

50. A Correct

Since 8

tan ,15

X use the inverse

tangent ratio, mX 1 8tan .

15

TEST PREP DOCTOR: Students who answered B, C, or D should review the definitions of trigonometric ratios and inverse trigonometric ratios.

51. C Correct

In a 30-60-90 triangle, the hypotenuse is twice as long as the

shorter leg and the longer leg is 3

times as long as the shorter leg.

TEST PREP DOCTOR: Students who answered A, B, or D should review the

properties of 30-60-90 right triangles.


210

52. B Correct

Since XZ is opposite Y and XY is

the hypotenuse of the right triangle,

you can solve the equation

sin6224x

, where x represents the

length of .XZ


who answered A or D used cos 62

in their calculations. Students who

answered C did not set up the

equation correctly. Review how to

use trigonometric ratios and inverse

trigonometric ratios to solve right

triangles.

53. A Correct

Using the Law of Sines,

sin(78 ) sin(50 )20 BC

. Cross multiplying,

20sin(50 )15.7.

sin(78 )BC

TEST PREP DOCTOR: Students who answered A attempted to use right angle trigonometry. Students who answered D used the Law of Sines but did not math angles with opposite sides. Students who answered C should review solving triangles in general.

54. B Correct

The measure of an inscribed angle is

equal to half the measure of its

intercepted arc. So,

1m m .

2ADB AB


who answered D may have reversed

the measures of the inscribed angle

and the arc. Students who answered

C may have confused the properties

of inscribed angles with the

properties of central angles. Students

who answered A should review the

properties of inscribed angles.

55. D Correct

In the figure, ADB is a major arc and

AB is a minor arc. So,

m 360 .ADB AB



review the properties of minor arcs,

major arcs, and arc addition.

56. B Correct

A circumscribed angle of a circle and

its associated central angle are

supplementary. So,

m m 180.AXB ACB



review the properties of tangents,

circumscribed angles, and central

angles.

57. B Correct

If two chords intersect inside a circle,

then the products of the lengths of

the segments of the chords are

equal. So, QP PS TP PR.



review how segments in circles are

related.

58. B Correct

The arc length, s, of an arc with

measure m and radius r is given by

the formula 2 .360m

s r

TEST PREP DOCTOR: Students who

answered C used the diameter in their

calculations. Students who answered D

found the circumference of the circle.

Students who answered A should

review how to find arc length using the

measure of a central angle and the

radius of a circle. Students should also

understand the proportional relationship

between arc length and the

circumference of a circle.


211

59. A Correct

To convert to a radian measure, let m

represent the degree measure of an

angle and evaluate the expression

•2 .360m


who answered B, C, or D reduced

60360

incorrectly or did not multiply by

2. Students should review how to

convert degrees to radians and

radians to degrees.

60. C Correct

The area A of a sector with a central

angle of m of a circle with radius r is

2.360m

A r


who answered A did not square the

radius. Students who answered D

reduced 60360

incorrectly. Students

who answered D should review how

to find the area of a sector using the

measure of a central angle and the

radius of a circle. Students should

also understand the proportional

relationship between the area of a

sector of a circle and the area of the

circle.

61. C Correct

The equation of a circle with center

(h, k) and radius r is 2 2 2( ) ( ) .x h y k r


who answered A did not subtract the

coordinates of the center of the circle.

Students who answered D did not

square the radius. Students who

answered B did not subtract the

coordinates and did not square the

radius. Review how to write an

equation of a circle using the

coordinates of the center and the

length of the radius.

62. A Correct

The general form of a parabola of this

type is 214

y xp

and p 2.

Therefore 2 21 1.

4(2) 8y x x



review how to find the equation of

a parabola given the focus and

directrix.

63. B Correct

The formula for the volume of a prism

is V Bh. The base is a triangle, so

1•6•8

2B and h 10.


who answered A or D did not use the

correct formula to find the area of the

triangular base. Students who

answered C need to review the

formula for the volume of a triangular

prism.

64. A Correct

The formula for the volume of a prism

is V Bh. The volume and base area

are given, so divide the volume by

the base area to find the height of the

prism.


who answered B made a calculation

error in finding the base area.

Students who answered C or D

did not divide the volume by both

dimensions of the base. Review

the formula for the volume of a

rectangular prism and how to

solve for a variable.

65. B Correct

The formula for the volume of a

cylinder is V r2h. Substitute r 6

and h 5 into the formula to find the

volume of the tank.


who answered A found the surface

area. Students who answered C


212

switched the values for the diameter

and the height. Students who

answered D used the value for the

diameter in their calculations. Review

the formula for the volume of a

cylinder and remind students to find

the value of the radius when they are

given the diameter.

66. A Correct

The formula for the surface area of a

cylinder is S 2rh 2r 2. Substitute

r 6 and h 5 into the formula to find

the surface area of the tank.


who answered B switched the values

for the diameter and the height.

Students who answered D used the

value for the diameter in their

calculations. Students who answered

C should review the formula for the

volume of a cylinder.

67. C Correct

The formula for the volume of a cone

is V 13r 2h. Substitute r 10 and

h 22 into the formula.


who answered D did not multiply by

13

. Students who answered A or B

should review the formula for the

volume of a cone.

68. B Correct


cone is S r r 2. Substitute

r 4 and 9 into the formula.


who answered A used the given

values in the formula for the volume

of a cone. Students who answered C

switched the values for the radius

and slant height. Students who

answered D should review the

formula for the surface area of

a cone.

69. C Correct


sphere is S 4 r 2. Substitute r 12

into the formula.


who answered A used 12

r in their


B found the 13

surface area of a

sphere. Students who answered D

found the volume of a sphere.

Review the formula for the surface

area of a sphere.

70. B Correct

One way to solve this problem is to

recognize that the pyramid and the

cube have the same base area.

Since a pyramid is 13

the volume of a

cube with the same base area, the

height of the pyramid must be 3 times

the height of the cube.


who answered A did not consider

that the volume of a pyramid is 13

times the product of the base area

and the height. Students who

answered C or D should review the

formulas for the volume of a pyramid

and the volume of a cube and

understand the relationship between

the volumes of these figures.

71. B Correct

Use 2V r h for the volume of a

cylinder and V 31 42 3

r

for the

volume of the hemisphere. Substitute

r 4 and h 18 into the appropriate

formulas.


who answered C used the volume of

a sphere instead of a hemisphere.

Students who answered D used the

value for the diameter in their



213

A should review the formulas for

cylinders, spheres, hemispheres, and

how to find the volume of composite

figures.

72. A Correct

The volume of the prism is 3 2 5

30 cm3. Using this and the given

mass in the density formula

massD

volume results in the value 0.75.


who answered B or D should review

the formula for volume of a prism.

Students who answered C should

review the formula for the density.

73. B Correct

The minimum height will occur when

the volume is at its minimum.

Therefore, 2150 10 h . Solving

this formula for h results in h 0.5.


who answered A used the correct

volume formula but did not replace

values correctly. Students who answered C did not include in their


D should review the volume formula

for a cylinder.

74. C Correct

Since order is important, the number

of possible outcomes is the

permutation of 10 objects taken 3 at

a time. So, the probability is 10 3

1.

P


who answered A found the simple

probability of choosing 1, 2, or 3 out

of 10 tiles. Students who answered B

used a combination instead of a

permutation. Students who answered

D found the probability of

independent events. Students should

review permutations and

combinations.

75. B Correct

Since order is not important, the

number of possible outcomes is the

combination of 12 objects taken 4 at

a time. So, the probability is 12 4

1.

C


who answered A found the simple

probability of choosing any 4 out of

12 students. Students who answered

C found the probability of dependent

events. Students who answered D

used a permutation instead of a

combination. Students should review

permutations and combinations.

76. D Correct

These are dependent events, so

and ( ) ( | )P A B P A PB A . There

are 24 marbles in the bag. Since the

first marble is not replaced, there are

23 marbles in the bag for the second

draw. The probability is 8 4

.24 23


who answered B found the

probability with replacement.

Students who answered A or C

should review probability of

dependent events.

77. D Correct

These are independent events, so

and P A B P A P B . The

probability of spinning a 2 is 14

and

the probability of rolling a 4 is 1.

6 So,

the probability of both events is 1 14 6

.


who answered C added the

probabilities of each event. Students

who answered A or B should review

probability of independent events.


214

78. B Correct

The formula for conditional probability

is ( )

( | ) .( )

P A BPB A

P A

Look at the

column for students who have a pet.

There are 10 students. Of those 10

students, 7 students also have a

sibling.


who answered A found the

probability that a student has a pet

given that the student has a sibling.

Students who answered C found the

probability of students who have both

a pet and a sibling. Students who

answered D found the probability that

a student has a pet. Students should

review conditional probability.

79. A Correct

The formula for conditional probability

is ( )

( | )( )

P A BPB A

P A

. Look at the

row for students who do not have

a sibling. There are 8 students. Of

those 8 students, 3 students have

a pet.


who answered B found the

probability that a student does not

have a sibling given that the student

has a pet. Students who answered C

or D should review conditional

probability.

80. C Correct

The two possibilities are disjoint so ( ) ( ) ( )P A B P A PB . The

probability Sabine wins is 3

450 and

the probability Joe wins is 5

.450



probability that a single entry would

win. Students who answered B found

the probability that Sabine would win.

Students who answered D multiplied

the probabilities for Sabine and Joe.

81. D Correct

Using Bayes Formula,

0.75(0.01)( | )

0.75(0.01) 0.25(0.02)0.60

P A def

.



probability that a randomly selected

item is defective. Students who

answered B used the percentages for

the opposite warehouses. Students

who answered C used 0.75 instead

of 0.25 in the denominator.

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