Geometry Summer Practice 2024
Purpose:
This summer practice assignment was created to
• communicate to each student what she is expected to know prior to entering Geometry.
o The topics in this assignment were taught in previous math courses.
• provide an opportunity for students to practice those skills and concepts necessary for success in Geometry.
• provide your Geometry teacher with information about the skills in which you may need more practice.
Expectations:
• Students are expected to complete this assignment independently.
• For each question in this assignment, show all of your work on loose leaf paper. Please use both sides of the paper.
o Your work must be clearly labeled and easy to follow.
• Box your final answers.
• Check your final answers with the key.
• This assignment will be graded for completion and entered as a quiz grade.
o You are expected to
▪ complete every problem.
▪ check your answers with the key.
▪ mark the questions you answered incorrectly.
• This assignment is DUE on the first day of your Geometry class.
o They will be collected at the beginning of class.
o If you turn in this assignment after the first day of class, 10 percentage points will be deducted for each
day it is late.
Students entering Geometry are expected to know how to:
• Solve multi-step linear equations
• Solve and graph multi-step linear inequalities
• Recognize positive, negative, zero and undefined slope
• Write equations of lines in slope-intercept or standard
form given
o two points
o the x and y intercepts
o slope and one point
o a point and the equation of a line parallel
o a point and the equation of a line
perpendicular
o a graph
• Write equations of vertical and horizontal lines
• Set up and solve proportions
o apply proportions to similar figures
• Solve systems of linear equations in two variables
using any algebraic method (elimination and
substitution)
• Simplify polynomial expressions (add, subtract and
multiply)
• Factor polynomial expressions
• Solve quadratic equations
o using square roots
o by factoring
• Simplify radicals (Ex.
8 2 2=
)
o Add, subtract, multiply and divide radicals
o Rationalize the denominator
▪ (Ex.
13
3
3
=
)
These skills will be incorporated into the Geometry course throughout the school year.
As a member of the Sacred Heart Community,
I pledge to act in a moral, ethical, honest, and honorable way in all that I do.
_________________________________________________________
Student Signature
For each question in this assignment, show all of your work on loose leaf paper. Use both sides of the paper.
Remember to check your final answers with the key and mark the questions you answered incorrectly. Your work
must be clearly labeled and easy to follow.
Topic 1: Solving multi-step linear equations
Solve each equation. Write your final answers as improper fractions if necessary.
1.
53
11
2
x−
=
−
2.
1
89
2
x +=
3.
( )
10 4 5 3 7 6x x x+ − + = − −
4.
5.
( ) ( ) ( )
2 9 3 4 5 2 3x x x+ − − = − −
6.
( )
3 11 12 3yy+ = +
7.
( )
1
4 3 9 12
3
yy+ = +
Topic 2: Solving and graph multi-step linear inequalities
Solve each inequality and graph the solution(s) on a number line. Write your final answers as improper fractions if
necessary.
8.
4 7 1x −
9.
8 2 26n−
10.
7 11 3 3 4p p p− + −
11.
( )
2 3 1 2 5nn− − − +
12.
9 3 12 33x +
13.
14 5 or 6 42xx+ − −
14. Write an inequality or compound inequality to represent
8, 7, and 4x x x −
.
15. Write an inequality or compound inequality to represent
2, and 6xx
.
Topic 3: Recognize positive, negative, undefined and zero slope
Find the slope of the line that passes through the given points. Write your final answers as improper fractions if necessary.
16.
( ) ( )
1,4 & 7, 2− − −
17.
( ) ( )
11, 14 & 11, 21−−
18.
( ) ( )
5, 14 & 1, 14− − −
19.
( ) ( )
4, 5 & 11, 8− − −
20. Find the slope of each line.
a) b) c)
Topic 4: Write equations of lines in slope-intercept and standard form
Use the given information to write the equation of the line in slope-intercept form. If it is not possible to write the equation in
slope-intercept form, write the equation in standard form. Use improper fractions in your final answers if necessary.
21.
( ) ( )
10,7 & 5, 3−−
22.
( ) ( )
5,12 & 5, 4− − −
23.
( ) ( )
11, 3 & 6, 3− − −
24. passes through the point
( )
3,5
and has a slope of
2
25. x-intercept is
4
and y-intercept is
2−
26. passes through the point
( )
2,3−
and is parallel to the line
2 4 10xy−=
27. passes through the point
( )
3,2−
and is perpendicular to the line
2 4 10xy−=
28.
29. passes through the point
( )
7, 5−−
and is perpendicular to the line
4y =−
30. passes through the point
( )
3, 11−
and is parallel to the line
8y =
Topic 5: Write equations of vertical and horizontal lines
31. Write the equation of the horizontal line that passes through the point
( )
9, 6 .−
32. Write the equation of the vertical line that passes through the point
( )
9, 6 .−
Topic 6: Set up and solve proportions
Solve each proportion. Write your final answers as improper fractions if necessary.
33.
7
53
x
=
34.
78
10c
=
35.
69
17m
=
−
36.
39
10
x
x
−
=
37.
58
95rr
=
−+
38. Mary reduced the size of a painting to a width of
3.3 inches
. What is the new height if it was originally
32.5 inches
tall and
42.9 inches
wide? Round your answer to the nearest tenth.
Each pair of figures is similar. Find the value of
.x
Write your final answers as improper fractions if necessary.
39. 40.
41.
Topic 7: Solve systems of linear equations in two variables using any algebraic method (elimination and substitution)
Solve the linear system by using substitution or elimination. Write your final answers as improper fractions if necessary.
42.
3 2 24
28
xy
yx
−=
= − +
43.
3 2 4
6 8 4
xy
xy
= − +
− + =
44.
43
3 2 1
yx
xy
=−
− = − +
45.
26
6 3 21
yx
xy
= − +
+ = −
Topic 8: Simplify polynomial expressions (add, subtract, and multiply)
Simplify each expression.
46.
( ) ( )
22
4 2 5 2xx+ + +
47.
( ) ( )
22
12 2 18 14 3 9x x x x− + − − +
48.
( )( )
2 8 3 9xx+−
49.
( )
2
4x+
50.
( )
2
31x−
51.
( )( )
5 2 5 2xx+−
52.
( )
5 4 8xx++
53.
( )( )
4 1 4 1xx−+
54.
( ) ( )
2 2 2
3 7 11 2 5 12x x x x x x− + − − −
Topic 9: Factor polynomial expressions
Factor each expression completely.
55.
2
87xx++
56.
2
13 40yy− + −
57.
2
2 4 48nn+−
58.
2
4 4 8mm− + +
59.
2
3 8 4zz−+
60.
2
4 17 4dd−+
61.
2
15 27 6pp−−
62.
2
5 20xx−
63.
3
7 28xx−+
Topic 10: Solve quadratic equations
Solve each equation. Write your final answers as improper fractions or simplified radicals if necessary.
64.
2
8 80x +=
65.
2
2 2 144y −=
66.
2
6 18xx=−
67.
2
8 11 5x x x−=
68.
2
2 9 4yy− − =
69.
2
12 2 11vv+=
70.
2
10 16zz− − =
71.
2
8 6 5mm−=
72.
2
10 2nn− = −
73.
2
3 10xx− − = −
OPTIONAL SECTION:
If you do not know how to complete the questions below without help, please leave them blank.
Topic 11: Radicals – simplify (add, subtract, multiply and rationalize the denominator)
Simplify each expression.
74.
45
75.
3 48
76.
200
77.
7 5 5 5+
78.
3 8 2 8+
79.
6 6 9 6−
80.
3 10•
81.
3 5 2 12•−
82.
3 3 3•
83.
( )
2
19
84.
2
5
85.
6
2
86.
12
3
87.
10
10
88.
1
5
Answers:
1.
9x =
2.
17
16
x =
3.
1x =
4.
13
9
y =
5.
7
9
x =−
6. No solution
7. All real numbers 8. 9.
10. No Solution; 11. All real numbers; 12.
13. 14.
4 8;x
15.
6;x
16.
1m =
17.
undefined
18.
0m =
19.
1
5
m =−
20. a)
3
2
m =
b)
2m =−
c)
undefined
21.
21
33
yx= − +
22.
5x =−
23.
3y =−
24.
21yx=−
25.
1
2
2
yx=−
26.
1
4
2
yx=+
27.
24yx= − −
28.
38yx=+
29.
7x =−
30.
11y =
31.
6y =−
32.
9x =
33.
21
5
x =
34.
35
4
c =
35.
17
3
m =
36.
30x =
37.
97
3
r =
38.
2.5 inches
39.
36x =
40.
7x =
41.
10x =
42.
( )
8,0
43. Infinitely many solutions 44.
( )
1, 1−−
45. No solution
46.
2
76x +
47.
2
29xx− + +
48.
2
6 6 72xx+−
49.
2
8 16xx++
50.
2
9 6 1xx−+
51.
2
25 4x −
52.
2
5 4 8xx++
53.
2
16 1x −
54.
4 3 2
3 9 16 12x x x x− + +
55.
( )( )
17xx++
56.
( )( )
58yy− − −
57.
( )( )
2 6 4nn+−
58.
( )( )
4 1 2mm− + −
59.
( )( )
3 2 2zz−−
60.
( )( )
4 4 1dd−−
61.
( )( )
3 5 1 2pp+−
62.
( )
54xx−
63.
( )( )
7 2 2x x x− + −
64.
62x =
65.
73y =
66.
0 or 3xx= = −
67.
0 or 2xx==
68.
1
4 or
2
yy= − = −
69.
21
or
34
vv==
70.
8 or 2zz= − = −
71.
15
or
24
mm= − =
72.
5
2 or
2
nn= = −
73.
5
2 or
3
xx= − =
74.
35
75.
12 3
76.
10 2
77.
12 5
78.
10 2
79.
36−
80.
30
81.
12 15−
82.
9
83.
19
84.
5
85.
32
86.
43
87.
10
88.
5
5