Honors Geometry Final Review Fall #1
Name :__________________________
1. Simplify the following expressions:
a. 6x – 7y – 2x + 13y
b. 3(x + 2) - 4x + (x – 3)
2. Solve for x.
a.
x 2  49  ( x  1) 2
x 7

4 3
b.
3. Find x given that the area of the rectangle to the right is 18 units2
4+x
3
4. Find Xx given that the perimeter of the rectangle to the right is 32 units
5. Reflect PQR across the y–axis and label the
image P QR . THEN, Rotate the image 90 degrees CCW
around the origin. Label the new image P Q R  .
P
Q
R
6. Reflect ABC over the line m. Label the image ABC  . Reflect ABC  over line n. Label the image ABC  . This
transformation can also be achieved by only one move. What is the mathematical name for the one transformation occurring between
ABC and ABC  ?
Name = ______________
7. A regular hexagon has rotational symmetry about its center. What is the minimum number of degrees of rotation necessary to
show rotational symmetry? Explain your reasoning using math vocabulary.
8.
For each figure, draw the transformation described.
a. Reflect ABCD across line l
D
A
l
C
b. Rotate PQR 90 clockwise (  )
about the origin.
P
B
Q
9.
Simplify.
a. 3(x + 2) – 4x
b. 4(3x – 5) – 3(7x – 2)
c. x(x + 3)
d. 3x + 4y – 9(x + 2)
R
a. ABC is translated so that A ends up
at A(4,  1) what is the coordinate of
10.
b.
C ?
Rotate PQR 180 clockwise ()
around point P.
A
Q
C
B
11.
P
R
There are 26 letters in the alphabet. What is the probability that a letter chosen at random is in the word Geometry?
b. Graph the equations on this grid.
12. a. Fill in the chart for each equation.
EQUATION SLOPE Y-INTERCEPT
y=
1
2
x–4
y = -x + 5
y – 2x = 7
13
A regular figure has rotational symmetry about its center so that every time it is rotated 90 it looks exactly the same. What is the
minimum number of sides this figure must have. What is that figure called? Justify your reasoning and draw a sketch of the shape.
14.
Where will the graph of the equation: y = 2x - 7 cross the y-axis? Explain how you know.
15
Write an equation of a line with slope -2 whose graph will cross the y-axis at the point (2, 5) algebraically, not graphing.
16
Find the equation of each graph shown:
a
a. slope = _____ y-int = ( 0, _____ )
Equation: __________________
b. slope = _____ y-int = ( 0, _____ )
Equation: __________________
b
17
Solve for y and graph the line on the grid
provided. State the slope and intercepts.
2x + 4y = 8
18
Examine the rectangle at right. If the perimeter of this shape is 88 cm, which equation below
represents this fact? Once you have selected the appropriate equation, solve for x.
a. 2x  5  6x  1  88
b. 4(6 x  1)  88
c.
2(6 x  1)  2(2 x  5)  88
d. (2 x  5)( 6 x  1)  88
2x  5
6x  1
(Don’t forget to solve here)
x = ____________
19
For each figure, draw the transformation described and label with primes (‘).
(a) Rotate ABC 90 clockwise ()
(b) Reflect PQR across line l. (c) Translate ABC into the fourth quadrant
about the origin
so A’ has the coordinates (2,-1)
Q
A
A
P
B
R
C
C
B
l
20
There are 26 letters in the alphabet. What is the probability that a letter chosen at random is in the word Geometry?
21
For a standard deck of cards, what is the probability of drawing a card smaller than a 10? (Aces are high.)
22
Tiffani has the following shapes: Rhombus, Rectangle, Square, Kite, Isosceles Triangle and a Trapezoid.
a.
Using the Venn Diagram below, write the names of the shapes in the correct position.
Has at least one
pair of equal
sides.
Has at least one
pair of parallel
sides.
b.
If Tiffani randomly selected one of the figures, what is the probability that it will be
in both circles?
23
Find the measure of each angle in the diagram below. Name any relationship you use to help you find each measure.
a = _______reason______________
c
b e
140°
b = _______reason______________
c = _______reason______________
150° a
h
110° i
d = _______reason______________
d
j f
e = _______reason______________
f = _______reason______________
g = _______reason______________
g
h = _______reason______________
i = _______reason______________
j = _______reason______________
Solve for x in each equation below, show all steps leading to your solution, and check your answer.
2x  (5  x)  3x  2(x  7)
a. 3(x  7)  2  2x  1
b.
24
25
Identify the kinds of angles in each diagram and state whether the angles are equal or supplementary.
a.
b.
c.
d.
26
For each diagram find the value of x. Show your work and include an explanation of what you used - definitions and
conjectures - to solve the problem. Justify your work.
a
3x
x + 20
b
c
3x – 10
2x + 30
x - 15
2x
27
a
Use the diagram to the right for the next three questions
1 and 7
(A)
(D)
b
2 and 3
(A)
(D)
c
29
30
31
(C) Alternate Interior
5 6
8 7
1
2
are ____________ angles.
Corresponding
Supplementary
(B)
(E)
m
Vertical
None of these
(C) Right
Corresponding
Supplementary
(B)
(E)
Vertical
None of these
(C) Perpendicular
n
C
The measure of A = ?
(A) 40°
(B) 60°
(C) 65°
(D) 75°
(E) none of these
(2x – 5)
A
x
(x + 25)
The my is :
(A) 19
(B) 20
(C) 85
(D) 95
(E) none of these
The value of x is
(A) 65
(C) 13
(E) None of These
B
6x – 25
(B) 48
(D) 142
4x + 15
y
2x + 12
38
22’
Find the area and perimeter of the shape below. Use the correct units (hint: ‘ means feet)
10’
14’
10’
32
o
3 4
6 and 1 are ____________ angles.
(A)
(D)
28
are ____________ angles.
Supplementary
(B)
Parallel
Corresponding
(E)
None of these
For each diagram,
 Draw a height to the labeled base and label it
 Find the area of the figure.
a.
b.
base
12"
base
8"
6" long.
c.
6’
9"
base
11"
33
Sherlock forgot the formula for finding the area of this triangle. However, he does
know how to find the area of a rectangle. Explain to him a way to find the formula.
h
b
34
Find the area of each figure.
a.
b.
c.
25
12
10
4
8
9
10
3
35.
12
Complete each conditional statement
a. If I have a 90% in this class, ___________________________________
b. _________________, then the Farmers will be State Champs.
36. Match the Term with the correct definition. Remember, a word can be used more than once!
1.
Transformation that “turns” around a point
A
Complementary Angles
2.
Angles at the same position at different intersections of a transversal.
B
Vertical Angles
3.
Two angles that add to 180 degrees.
C
Corresponding Angles
4.
Two angles that add to 90 degrees.
D
Supplementary Angles
5.
Property that means same size and shape
E
Alternate Interior Angles
6.
Angles inside two parallel lines on the same side of the transversal
F
Congruent Angles
7.
Line that crosses two or more other lines
G
Translation
8.
Angles inside two parallel lines on opposite sides of the transversal
H
Transversal
9.
Transformation that “slides” without changing direction
I
Rotation
J
Same-Side Interior Angles
10. Two angles that are opposite each other when 2 lines cross.
37
Solve for x in each of these figures.
a.
b.
17
A square with area 5280 sq.
ft.
32
A = 5280
x
x
14
38. Find the area and perimeter of this figure
10
5
6
39
a)
Graph each equation by the method of
your choice:
y  2x  6
y  3 x  6
b)
40
Find the area of the triangle formed by the
two lines and the x-axis.
Will the lengths 4, 9, and 6 form a triangle? Explain why or why not.
c.
A rectangle with
perimeter 132 inches.
3x +1
x–7
41
Find the maximum and minimum values for x.
42
Find the exact value of x in each of the following..
a.
x
11
23
b.
2x
15
in
10
15
3x
43
x
Find x, JUSTIFY!
44
The point A(-4, 1) is rotated 90 clockwise about the origin. The coordinate of A is
45
An equation of a line perpendicular to y  2 x  5 is
(A) y  2 x  5
46
47
48
2x + 10
(B)
50
y  12 x  5
y  2x  2
(C)
3
61
(A)
(B)
(C)
11
An equation of a line that is parallel to y = -3x -5 is
(A) y = -3x - 2
(B) y = 3x - 1
(C) y = 1/3x + 5
13
Find the area of the trapezoid shown to the right:
in
49
If the perimeter of ABC is 56 cm, the length of AB is
50
Use the diagram to the right for the next
three questions
(A)
(D)
51
y = -1/3x - 5
(E)
None of these
(E)
None of These
7
4x – 4
2
3
4
are ____________ angles.
SS Interior
Corresponding
2 and 6
(B)
(E)
Parallel
None of these
(E) None of These
C
12
in
(C) Alternate
m Interior
are ____________ angles
(A)
(D)
c
(D)
41
15
in
1
6
8
1 and 6
(D)
B
5
b
y   12 x  6
The length of the line segment joining the points (5, -1) and (1, -4) is
10
in
a
(D)
Corresponding
(B)
Vertical
Supplementary
(E)
None of these
6 and 8 are ____________ angles.
(A)
Corresponding
(B)
Vertical
(D)
Supplementary
(E)
None of these
Dilate the shape below using a zoom factor of 2 from origin.
(C) Right
(C) Perpendicular
55
2x + 6
70
A