Free Printable Geometry A Final Exam Review

1.

Simplify and write the resulting polynomial in standard form. Then classify (name) by degree and number of terms: $35 + 30x^3 - 30x^2 + 25x - 25x^2 - 42x$ .

a)

$30x^3 - 55x^2 + 17x + 35$ , cubic polynomial (4 terms)

b)

$30x^3 - 55x^2 - 17x$ , cubic trinomial

c)

$30x^3 - 5x^2 - 17x + 35$ , cubic polynomial (4 terms)

d)

$30x^3 - 55x^2 - 17x + 35$ cubic polynomial (4 terms)

2.

Simplify and write the resulting polynomial in standard form. Then classify (name) by degree and number of terms: $-x^3 + 2x - 4x^2 + 7 + 3x^3 + 4x - 2x^3$ .

a)

$-4x^2 + 6x + 7$ , quadratic trinomial

b)

$-4x^2 + 6x + 7$ , quadratic binomial

c)

$-x^3 - 4x^2 + 6x + 7$ , cubic polynomial (4 terms)

d)

$4x^2 + 6x + 7$ , quadratic trinomial

3.

Add or subtract the given polynomials. Write the resulting polynomial in standard form. Then classify (name) by degree and number of terms: $(5x^2 - 8x - 3) + (2x + 7 - 6x^2)$ .

a)

$-x^2 - 6x + 4$ , quadratic trinomial

b)

$x^2 - 6x + 4$ , quadratic trinomial

c)

$-x^2 + 6x - 4$ , quadratic trinomial

d)

$-x^2 - 6x - 4$ , quadratic trinomial

4.

Add or subtract the given polynomials. Write the resulting polynomial in standard form. Then classify (name) by degree and number of terms: $(2x^2 - 8x + 2) + (5 + x^2)$ .

a)

$3x^2 - 8x + 7$ , quadratic trinomial

b)

$x^2 - 8x + 7$ , quadratic trinomial

c)

$3x^2 + 8x + 7$ , quadratic trinomial

d)

$3x^2 - 8x - 7$ , quadratic trinomial

5.

Add or subtract the given polynomials. Write the resulting polynomial in standard form. Then classify (name) by degree and number of terms: $(7x^2 + 3x + 5) - (3x^2 + x + 1)$ .

a)

$4x^2 + 2x + 4$ , quadratic trinomial

b)

$4x^2 + 4x + 2$ , quadratic trinomial

c)

$10x^2 + 2x + 4$ , quadratic trinomial

d)

$4x^2 - 2x + 4$ , quadratic trinomial

6.

Add or subtract the given polynomials. Write the resulting polynomial in standard form. Then classify (name) by degree and number of terms: $(4x^2 + 2x + 9) - (6x^2 + 7x + 8)$ .

a)

$-2x^2 - 5x + 1$ , quadratic trinomial

b)

$2x^2 - 5x + 1$ , quadratic trinomial

c)

$-2x^2 + 5x + 1$ , quadratic trinomial

d)

$-2x^2 - 5x - 1$ , quadratic trinomial

7.

Find the perimeter of the given polynomials. Triangle ABC has sides labeled $2x + 3$ , $2x + 3$ , and $4x + 10$ . Find the perimeter.

a)

$8x + 16$

b)

$8x + 10$

c)

$6x + 16$

d)

$4x + 13$

8.

Find the perimeter of the Rectangle with side lengths of $(x + 3)$ and $(3x + 8)$ . Label the rectangle and find the perimeter.

a)

$8x + 22$

b)

$4x + 11$

c)

$6x + 14$

d)

$8x + 11$

9.

The perimeter of the triangle is $(32c + 32)$ . How tall is the triangle’s side length AC?

a)

$16c + 9$

b)

$20c + 9$

c)

$16c + 29$

d)

$12c + 9$

10.

A square has a side length of $3z - 2$ . Find the perimeter of the square.

a)

$12z - 8$

b)

$9z - 6$

c)

$6z - 4$

d)

$3z - 2$

11.

Multiply the given polynomials. Write the result in standard form: $5x(6x - 5)$ .

a)

$30x^2 - 25x$

b)

$30x - 25x^2$

c)

$11x^2$

d)

$30x^2 + 25x$

12.

Multiply the given polynomials. Write the result in standard form: $7(4x^2 + 3x + 5)$ .

a)

$28x^2 + 21x + 35$

b)

$28x^2 + 3x + 5$

c)

$28x^3 + 21x + 35$

d)

$4x^2 + 3x + 35$

13.

Multiply the given polynomials. Write the result in standard form: $(7x - 6)(5x + 2)$ .

a)

$35x^2 - 16x - 12$

b)

$35x^2 + 16x - 12$

c)

$12x^2 - 16x + 35$

d)

$35x^2 - 16x + 12$

14.

Multiply the given polynomials. Write the result in standard form: $(3x + 2)(7x^2 + 9x + 4)$ .

a)

$21x^3 + 41x^2 + 30x + 8$

b)

$21x^3 + 27x^2 + 12x + 8$

c)

$21x^2 + 41x^2 + 30x + 8$

d)

$21x^3 + 41x + 30x^2 + 8$

15.

Find the area of this rectangle. $A = (b)(h)$ . The rectangle has base $x - 3$ and height $x + 2$ .

a)

$x^2 - x - 6$

b)

$x^2 + x - 6$

c)

$x^2 - 5$

d)

$x^2 - x + 6$

16.

Find the area of the given shapes. A rectangle has side lengths of $(x - 5)$ and $(8x - 8)$ . Label the rectangle below and find the area of the rectangle. $A = (b)(h)$ .

a)

$8x^2 - 48x + 40$

b)

$8x^2 - 13x - 40$

c)

$8x^2 - 40$

d)

$8x^2 - 48x - 40$

17.

Find the area of the right triangle shown. $A = \tfrac{1}{2}bh$ . The legs are labeled $(5x + 3)$ and $(6x + 2)$ .

a)

$15x^2+14x+3$

b)

$30x^2+28x+6$

c)

$15x^2+5x+9x+3$

d)

$15x^2$

18.

Find the area of the triangle shown. $A = \tfrac{1}{2}bh$ . The base is labeled $(6x + 8)$ and the height is labeled $(x + 6)$ .

a)

$3x^2$

b)

$6x^2+44x+48$

c)

$3x^2+22x+24$

d)

$3x^2+4x+18x+24$

19.

Identify the relationship between ∠a and ∠b

a)

alternate exterior angles

b)

alternate interior angles

c)

vertical angles

d)

linear pair

20.

Identify the relationship between ∠a and ∠b

a)

alternate exterior angles

b)

alternate interior angles

c)

vertical angles

d)

linear pair

21.

$\overrightarrow{MN}\ bi\sec ts\ \overline{PQ}$ Find the value of x.

a)

1

b)

2

c)

3

d)

4

22.

Line $\overline{LM}$ bisects $\overline{PQ}$ . Find the value of x.

a)

7.5

b)

9

c)

6

d)

12

23.

M is the midpoint of PQ. If PM = 6x + 7 and MQ = 9x − 8, find the length of PQ.

a)

64

b)

70

c)

74

d)

80

24.

M is the midpoint of LN. Which set of values is correct for x, LM, and MN?

a)

x = 12, LM = 111, MN = 111

b)

x = 9, LM = 78, MN = 78

c)

x = 6, LM = 45, MN = 57

d)

x = 15, LM = 144, MN = 120

25.

Find BC if B is between A and C, AC = 25, and AB = 11.

a)

12

b)

14

c)

15

d)

36

26.

Find WX if X is between W and Y, XY = 20, and WY = 50.

a)

25

b)

30

c)

20

d)

35

27.

$\overrightarrow{AB}$ bisects $\angle CAD$ . Find the value of x.

a)

4

b)

8

c)

33

d)

5

28.

BD bisects ∠ABC. In the diagram, m∠ABD = 34° and m∠DBC = (x − 7)°. Find the value of x.

a)

27

b)

34

c)

41

d)

48

29.

Find the value of x. The two adjacent angles form a straight line and are labeled (4x + 8)° and (6x + 2)°.

a)

14

b)

16

c)

17

d)

18

30.

$m\angle HGF=16x+4$ , $m\angle EGF=110\degree$ , and $m\angle HGE=3x+11$

Find x.

a)

33

b)

9

c)

5

d)

24

31.

Name the relationship between $\angle1\ and\ \angle3$ in the diagram shown.

a)

Same side interior angles

b)

vertical angles

c)

corresponding angles

d)

alternate exterior angles

32.

Name the relationship between $\angle3\ and\ \angle7$ in the diagram shown.

a)

Same side interior angles

b)

vertical angles

c)

corresponding angles

d)

alternate exterior angles

33.

Name the relationship between $\angle4\ and\ \angle6$ in the diagram shown.

a)

Same side interior angles

b)

alternate interior angles

c)

corresponding angles

d)

alternate exterior angles

34.

Name the relationship between $\angle4\ and\ \angle5$ in the diagram shown.

a)

Same side interior angles

b)

alternate interior angles

c)

corresponding angles

d)

alternate exterior angles

35.

Name the relationship between $\angle1\ and\ \angle7$ in the diagram shown.

a)

Same side interior angles

b)

vertical angles

c)

corresponding angles

d)

alternate exterior angles

36.

Find the value of x.

a)

10

b)

5

c)

25

d)

20

37.

Find the value of x.

a)

9

b)

7

c)

2

d)

3

38.

Find the missing (?) angle.

a)

$119\degree$

b)

$61\degree$

c)

$122\degree$

d)

$78\degree$

39.

Find the missing (?) angle.

a)

$128\degree$

b)

$38\degree$

c)

$52\degree$

d)

$98\degree$

40.

Solve for x.

Then find the measure of the angle indicated by the arrow.

a)

60°

b)

65°

c)

70°

d)

75°

41.

Solve for x. Then find the measure of the angle indicated by the arrow.

a)

$100\degree$

b)

$80\degree$

c)

$70\degree$

d)

$110\degree$

42.

Find the value of x.

a)

4

b)

5

c)

3

d)

6

43.

Find the value of x.

a)

4

b)

5

c)

6

d)

3

44.

Complete the two-column proof by matching the correct reasons to the statements.

a)

$\angle EBG\cong\angle BCD$

1.

Corresponding Angles Theorem

b)

$m\angle EBG=m\angle BCD$

2.

Definition of Congruent

c)

$\angle BCD\ and\ \angle DCF$ are supplementary

3.

Linear Pair Theorem

d)

$m\angle BCD+m\angle DCF=180\degree$

4.

Definition of Supplementary

e)

$m\angle EBG+m\angle DCF=180\degree$

5.

Substitution Property

45.

Complete the two-column proof by matching the correct reasons to the statements.

a)

$j\ \parallel\ k$

1.

Given

b)

$\angle2\cong\angle10$

2.

Corresponding Angles Theorem

c)

$\angle10\cong\angle12$

3.

Corresponding Angles Theorem

d)

$\angle2\cong\angle12$

4.

Transitive Property

46.

Complete the proof by matching the correct information for each blank.

a)

LMNO is a square

1.

Given

b)

$m\angle LON=90\degree$

2.

A square has 4 right angles

c)

5x - 75 = 90

3.

Substitution property

d)

5x = 165

4.

Addition Property

e)

x = 33

5.

Division Property

47.

Using the quadrilateral properties chart, choose all statements that are always true for a rectangle.

a)

Opposite sides are parallel.

b)

Opposite sides are congruent.

c)

All four angles are congruent.

d)

Diagonals bisect each other.

e)

Diagonals are congruent.

48.

Using the quadrilateral properties chart, choose all statements that are always true for a rhombus.

a)

Opposite sides are parallel.

b)

All four sides are congruent.

c)

Diagonals bisect opposite angles.

d)

Diagonals are perpendicular.

e)

All four angles are congruent.

49.

Using the quadrilateral properties chart, choose all statements that are always true for a square.

a)

All four sides are congruent.

b)

All four angles are congruent.

c)

Diagonals are congruent.

d)

Diagonals are perpendicular.

e)

Opposite sides are not parallel.

50.

Using the quadrilateral properties chart, choose all statements that are always true for a parallelogram.

a)

Opposite angles are congruent

b)

Diagonals bisect each other.

c)

Diagonals are congruent.

d)

Consecutive angles are supplementary.

e)

Opposite sides are parallel and congruent.

51.

Solve for x.

a)

1

b)

2

c)

3

d)

4

52.

Solve for x.

a)

1

b)

2

c)

85

d)

95

53.

Solve for x.

a)

1

b)

9

c)

2

d)

5

54.

In parallelogram STRQ, the diagonals intersect at Z. If RT = 12 and ZT = x − 2, find x.

a)

6

b)

8

c)

10

d)

12

55.

ABCD is a parallelogram. Which side is congruent to AB?

a)

BC

b)

CD

c)

AD

d)

AC

56.

ABCD is a parallelogram. Which side is congruent to BC?

a)

AB

b)

CD

c)

AD

d)

BD

57.

ABCD is a parallelogram. Which segment is congruent to AE?

a)

BE

b)

CE

c)

DE

d)

AB

58.

In parallelogram ABCD, which angle is congruent to ∠ABC?

a)

∠BAD

b)

∠CDA

c)

∠BCD

d)

∠BEA

59.

In parallelogram ABCD, which angle is congruent to ∠BEA?

a)

∠CED

b)

∠BEC

c)

∠AED

d)

∠ABC

60.

In parallelogram ABCD, what is the value of m∠BAD + m∠CDA?

a)

$90^{\circ}$

b)

$120^{\circ}$

c)

$180^{\circ}$

d)

$360^{\circ}$

61.

In parallelogram FGHI, solve x, y, and z.

a)

x = 38, y = 75, z = 75

b)

x = 38, y = 75, z = 67

c)

x = 38, y = 67, z = 75

d)

x = 38, y = 75, z = 105

62.

ABCD is a rectangle. Find x.

a)

7

b)

14

c)

21

d)

28

63.

ABCD is a rectangle. Find y.

a)

7

b)

5

c)

10

d)

12

64.

In the rectangle from the diagram, find BD.

a)

60

b)

120

c)

30

d)

150

65.

ABCD is a rhombus. Solve for x.

a)

18

b)

36

c)

81

d)

162

66.

ABCD is a rhombus. Solve for y.

a)

18

b)

36

c)

81

d)

162

67.

ABCD is a rhombus. What is m $\angle$ BEC?

a)

180

b)

90

c)

45

d)

15

68.

ABCD is a rhombus. What is m $\angle$ CEA?

a)

180

b)

90

c)

45

d)

15

69.

FGHI is a square. What is m $\angle$ FIJ?

a)

180

b)

90

c)

45

d)

30

70.

FGHI is a square. What is m $\angle$ JHG?

a)

180

b)

90

c)

45

d)

30

71.

FGHI is a square. What is m $\angle$ FJG?

a)

180

b)

90

c)

45

d)

30

72.

FGHI is a square. If GJ = 4 cm, what is JI?

a)

4

b)

8

c)

2

d)

12

73.

FGHI is a square. If GJ = 4 cm, what is FJ?

a)

4

b)

8

c)

2

d)

12

74.

FGHI is a square. If GJ = 4 cm, what is FH?

a)

4

b)

8

c)

2

d)

12

75.

Quadrilateral ABCD has the following ordered pairs: A: (-3, 1) B: (4, 2) C: (9, -3) D: (2, -4). Using the distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ , find the length of $\text{AB}$ .

a)

$\sqrt{26}$

b)

$5\sqrt{2}$

c)

$\sqrt{50}$

d)

$7$

76.

Quadrilateral ABCD has the following ordered pairs: A: (-3, 1) B: (4, 2) C: (9, -3) D: (2, -4). Using the slope formula $m=\dfrac{y_2-y_1}{x_2-x_1}$ , find the slope of $\overline{\text{BC}}$ .

a)

$-1$

b)

$1$

c)

$\dfrac{5}{4}$

d)

$-\dfrac{4}{5}$

77.

Quadrilateral ABCD has the following ordered pairs: A: (-3, 1) B: (4, 2) C: (9, -3) D: (2, -4). Using the midpoint formula $\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$ , find the midpoint of $\overline{\text{CD}}$ .

a)

$\left(\dfrac{11}{2},-\dfrac{7}{2}\right)$

b)

$\left(\dfrac{7}{2},-\dfrac{11}{2}\right)$

c)

$(6,-2)$

d)

$(3,-1)$

78.

Quadrilateral ABCD has the following ordered pairs: A: (-3, 1) B: (4, 2) C: (9, -3) D: (2, -4). Using the distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ , find the length of diagonal $\text{AC}$ .

a)

$4\sqrt{10}$

b)

$\sqrt{136}$

c)

$\sqrt{160}$

d)

$8\sqrt{5}$

79.

Quadrilateral ABCD has the following ordered pairs: A: (-3, 1) B: (4, 2) C: (9, -3) D: (2, -4). Using the slope formula $m=\dfrac{y_2-y_1}{x_2-x_1}$ , find the slope of diagonal $\overline{\text{BD}}$ .

a)

$-3$

b)

$\dfrac{1}{3}$

c)

$3$

d)

$-\dfrac{3}{2}$

80.

Quadrilateral ABCD has the following ordered pairs: A: (-3, 1) B: (4, 2) C: (9, -3) D: (2, -4). Using the midpoint formula $\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$ , find the midpoint of $\overline{\text{AC}}$ .

a)

$(0,-1)$

b)

$(3,-1)$

c)

$(3,1)$

d)

$(0,1)$

81.

Solve for the missing angle (?) in the triangle shown.

a)

$55^\circ$

b)

$65^\circ$

c)

$75^\circ$

d)

$85^\circ$

82.

What is the value of x?

a)

$3$

b)

25

c)

50

d)

$4$

83.

Solve for x. Then find the measure of Angle A.

a)

x = 8, m<A = 35

b)

x = 8, m<A = 70

c)

x = 5, m<A = 26

d)

x = 5, m<A = 43

84.

Solve for x.

a)

4

b)

5

c)

6

d)

7

85.

Solve for y.

a)

4

b)

5

c)

6

d)

7

86.

Solve for z.

a)

4

b)

5

c)

6

d)

7

87.

Given $\triangle ABC \cong \triangle XYZ$ . Which side is congruent to $\overline{\text{CA}}$ ?

a)

$\overline{\text{ZX}}$

b)

$\overline{\text{XY}}$

c)

$\overline{\text{YZ}}$

d)

$\overline{\text{XZ}}$

88.

Given $\triangle ABC \cong \triangle XYZ$ . Which angle is congruent to $\angle Y$ ?

a)

$\angle A$

b)

$\angle B$

c)

$\angle C$

d)

$\angle X$

89.

What criterion would prove $\triangle ABC \cong \triangle ADC$ ?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

e)

HL

90.

Given $\overline{NY}\ \cong\ \overline{ZY}$ , what additional information is needed to prove $\triangle LNY\cong\triangle XZY$ by SAS? (which pair of sides or angles?)

a)

$\overline{YL}\ \cong\ \overline{YX}$

b)

$\overline{NL}\ \cong\ \overline{ZX}$

c)

$\angle L\ \cong\ \angle X$

d)

$\angle N\ \cong\ \angle Z$

91.

Mark the triangles using the given information.

$\angle D\ \cong\ \angle M;\ \overline{DC}\ \cong\ \overline{MN};\ \overline{BD}\ \cong\ \overline{XM}$

How are the triangles congruent?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

92.

The triangles shown are congruent by what criterion?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

e)

HL

93.

The triangles shown are congruent by what criterion?

a)

Not congruent

b)

SAS

c)

ASA

d)

AAS

e)

HL

94.

The triangles shown are congruent by what criterion?

a)

Not congruent

b)

SAS

c)

ASA

d)

AAS

e)

HL

95.

The triangles shown are congruent by what criterion?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

e)

HL

96.

What is the image of the point (−9, 0) after a reflection over the x-axis?

a)

(−9, 0)

b)

(9, 0)

c)

(0, 9)

d)

(0, -9)

97.

What is the image of the point (−8, 2) after a reflection over the y-axis?

a)

(−8, −2)

b)

(8, 2)

c)

(−8, 2)

d)

(8, −2)

98.

What is the image of the point (0, −8) after a reflection over the line y = x?

a)

(−8, 0)

b)

(8, 0)

c)

(0, 8)

d)

(0, −8)

99.

What is the image of the point (−2, 5) after a translation right 3 units and up 4 units?

a)

(1, 9)

b)

(−5, 9)

c)

(1, 1)

d)

(−5, 1)

100.

What is the image of the point (0, −5) after a translation left 5 units and down 2 units?

a)

(5, −3)

b)

(−5, −7)

c)

(−5, −3)

d)

(5, −7)

101.

What is the image of the point (6, 8) after a translation right 5 units and down 3 units?

a)

(1, 11)

b)

(11, 5)

c)

(11, −5)

d)

(−1, 5)

102.

What is the image of the point (−8, 0) after a rotation of 180° clockwise about the origin?

a)

(−8, 0)

b)

(0, −8)

c)

(8, 0)

d)

(0, 8)

103.

What is the image of the point (−1, 2) after a rotation of 270° counterclockwise about the origin?

a)

(−2, −1)

b)

(2, 1)

c)

(−1, −2)

d)

(1, −2)

104.

The point N is plotted on a coordinate grid. When a point is reflected over the x-axis, which coordinate changes sign?

a)

x-coordinate

b)

y-coordinate

105.

When the figure is reflected over the line y = -4 as shown in the picture, what are coordinates of the point whose original coordinates were (-3, -5)?

a)

(-3, -4)

b)

(-3, -3)

c)

(-4, -3)

d)

(-5, -3)

106.

If the star-shaped figure does have rotational symmetry, what is the smallest possible rotation that maps the figure onto itself?

a)

90°

b)

120°

c)

180°

d)

45°

107.

Which transformation would take Shape A to Shape B?

a)

A reflection over the y-axis

b)

A reflection over the x-axis

c)

A clockwise rotation of 90° about the origin

d)

A clockwise rotation of 270° about the origin

108.

Which transformation would take Figure R onto Figure S?

a)

A translation right 6 and down 7

b)

A translation left 6 and up 7.

c)

A translation right 7 and down 6.

d)

A translation left 7 and up 6.

109.

Figure V is the result of a transformation on Figure U. Which transformation would accomplish this?

a)

A rotation 180° clockwise about the origin

b)

A reflection over the y-axis

c)

A reflection over the x-axis

d)

A translation 2 units up

110.

Which transformation would take Shape A to Shape B?

a)

A counterclockwise rotation of 90° about the origin

b)

A reflection over the line y = −x

c)

A reflection over the line y = x

d)

A counterclockwise rotation of 180° about the origin

111.

Figure J is the result of a transformation on Figure I. Which transformation would accomplish this?

a)

A reflection over the x-axis

b)

A translation 4 units to the left and 8 units up

c)

A rotation 180° clockwise about the origin

d)

A rotation 90° counterclockwise about the origin

112.

Figure L is the result of a transformation on Figure K. Which transformation would accomplish this?

a)

A translation 4 units to the left and 4 units down

b)

A rotation 180° clockwise about the origin

c)

A rotation 90° clockwise about the origin

d)

A rotation 90° counterclockwise about the origin

113.

Figure T is the result of a transformation on Figure S. Which transformation would accomplish this?

a)

A rotation 90° clockwise about the origin

b)

A reflection over the y-axis

c)

A reflection over the x-axis

d)

A rotation 90° counterclockwise about the origin

Geometry A Final Exam Review

Total questions: 113

Worksheet time: 9hrs 15mins

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