Welcome to Geometry
Here is your summer 2013 practice. It is due the first week of the 2013-2014 school year.
The following is a list of topics with practice exercises you should do over the summer in order to have
smooth transition into Geometry. This assignment will be due the first week of school, and will be the
first grade recorded. Practice throughout the summer is the best approach. If you wait until the end of
the summer you will be overwhelmed. Do your work in a neat and organized fashion. They will be
posted in the hallways at the start of the year. There are problems to work, equations to find and learn,
and there is also a project and a story to write. I Go for it – impress your teacher from the beginning of
the year.
Topics: The may not all be covered every week
Perfect Squares
Prime Factorization
Area Equations
Volume Equations
Order of Operations – complete attached
Balancing Equations– complete attached
Equations of a Line
Week 1
Definitions:
Square a number
Prime number
Composite number
Balance Equations
Area
Volume
Radius
Diameter
Practice:
Perfect Squares – You need to practice and learn the perfect squares from 1 to 14 this week:
Base
1
2
3
4
5
6
7
Perfect Square
Base
8
9
10
11
12
13
14
Perfect Square
Prime FactorizationList the first seven prime factors
_______ _______ _______ _______ _______ _______ _______
Geometric EquationsList the area or volume equations
Shape
Circle
Square
Triangle
Rectangle
Area
Volume
Equations of a Line - None
Week 2
Definitions:
Horizontal
Vertical
Diagonal
y-intercept
Practice:
Perfect Squares – Practice the perfect squares from 15 – 20
Base
Perfect Square
15
16
17
18
18
20
Prime FactorizationDo the prime factorization of the following numbers:
20, 27, 30, 265, 16, 1296
Geometric EquationsList the area and/or volume equations
Shape
Cylinder
Rectangular Prism
Square Prism
Square Pyramid
Area
Volume
Equations of a Line What form is this equation in? y = 4.5x + 5 ________________
What form is this equation in? (y + 4) = 1/2 (x -3) _________________
Week 3
Definitions:
Reciprocal
x-intercept
Inverse operation
Practice:
Perfect Squares – You need to practice and learn the perfect squares from 1 to 14 this week:
Base
1
2
3
4
5
6
7
Perfect Square
Base
8
9
10
11
12
13
14
Perfect Square
Prime FactorizationList the factors of 12, 25, 32, 47, 73, 85
Geometric EquationsList the area and volume equations
Shape
Circle
Square
Triangle
Rectangle
Area
Volume
Equations of a Line –
Write an equation of a line in standard form
Write an equation of a line in point-slope form
Write and equation of a line slope-intercept form
Week 4
Define:
Rotation
Reflection
Translation
Practice:
Perfect Squares – Practice the perfect squares from 15 – 20
Base
Perfect Square
15
16
17
18
18
20
Prime FactorizationPrime Factor the following
54
1080
84
151
Geometric Equations- Practice the equations for area and volume
Equations of a Line –
Given a point (7 , -4) and a slope of 3, write the equation of the line in point-slope
form._____________________________
Given the points ( 9, 3) and (5, -2) find the slope of the line and write it in slope-intercept form.
Week 5:
Practice:
Perfect Squares – You need to practice and learn the perfect squares from 1 to 14 this week:
Base
1
2
3
4
5
Perfect Square
Base
8
9
10
11
12
Perfect Square
6
7
Prime FactorizationFind the greatest common factor
75 and 700
34x2 and 42x3
13
14
Geometric Equations- Make a fold able (like a menu) or poster of the general formulas for area and
volume. Also work out examples for each one.
Equations of a Line Find the equation of the vertical line passing through point ( -4, 5) ______________________
Find the slope of the line passing points ( 8, -3) and ( -5, 23) ____________________________
Week 6
Practice:
Perfect Squares – Practice the perfect squares from 15 – 20
Base
Perfect Square
15
16
17
18
18
20
Prime FactorizationWhat are the first seven prime numbers?
Geometric Equations- Work on the visual representation
Equations of a Line - None
Week 7
Practice:
Perfect Squares – You need to continue practicing the perfect squares from 1 to 20 this week:
Base
Perfect Square
1
2
3
4
5
6
7
8
9
10
Prime Factorization- None
Base
11
12
13
14
15
16
17
18
19
20
Geometric Equations- Work on the visual representation
Equations of a Line –
Change the form of the line (y + 3) = -4/5(x – 12) into:
Perfect Square
Point-slope form _______________________________
Slope-intercept form ____________________________
Week 8
Practice:
Perfect Squares – You need to continue practicing the perfect squares from 1 to 20 this week:
Base
1
2
3
4
5
6
7
8
9
10
Prime FactorizationList the factors of
169
250
Perfect Square
Base
11
12
13
14
15
16
17
18
19
20
Perfect Square
34
Geometric Equations- Complete the visual representation
Equations of a Line –
Parallel lines have __________________ slopes.
Perpendicular lines have ____________________ slopes.
Practice:
Perfect Squares – You need to continue practicing the perfect squares from 1 to 20 this week:
Base
Perfect Square
1
2
3
4
5
6
7
8
9
10
Prime Factorization- None
Base
11
12
13
14
15
16
17
18
19
20
Perfect Square
Geometric EquationsMake a drawing that includes a circle(s) with 1” radius, rectangle(s) with a 2” base and 3” height , and
triangle(s) 2” tall with a base of 1”.
Create a story to go with your picture.
Equations of a Line List the three equations of a line and give examples of each.
Week 10
Practice:
Perfect Squares – You need to continue practicing the perfect squares from 1 to 20 this week:
Base
1
2
3
4
5
6
7
8
9
10
Prime Factorization-
Perfect Square
Base
11
12
13
14
15
16
17
18
19
20
Perfect Square
Geometric Equations- Complete your story and picture.
Make sure that you know and can use the basic shape equations for area and volume.
Equations of a Line 1. Write the equation of a line passing point (4, 3) with a slope of -3/4
2. Write the equation of the horizontal line passing point (9, -1)
3. Change the line to slope-intercept form (y – 3) = 2 (x+ 5)
Order of operations
Complete at two to three problems per day. Have all of the problems done by the start of the school
year.


2.
4  5  9
4.
9
1  2  8  7
6.
8  3 1
7.
6
2
 1 1
8.
4
9.
3
2
 4 1

10.
4  6  9  3  2
11.
3
2
9 6

12.
9  4
13.
4 2  6  6  8
14.
4
15.
7

16.
6  3  2
17.
4  8  5  2  4
18.
9  8  6 2  8
19.
1  6
20.
1  3 1
21.
2
22.
7  5  72  72  8
1.
7 2  9  22  1  5
3.
2  2  22  4
5.

2
2


 32  8  3
2

1

 5 2  12  9  4
2
2
2

 4 1

1  8  5
2

8

 12  3


Solving Linear Equations
Complete at two to three problems per day. Have all of the problems done by the start of the school
year.
SOLVING LINEAR EQUATIONS Worksheet Answers
1.
2.
3.
4.
5.
x  7  13
14.
 5  2x  17
15.
9
x  17  19
10
16.
7
t  8  34
8
17.
5t  12  3t  6
18.
4x  6  x  9
19.
 3a  8  5a  12
20.
2b  5  8b  1
21.
1  9m  6m  14
3x  24
1
x  10
2
11.
5  3a  32
 x   3  5
7.
10.
13.
 8  a  12
 8x  48
9.
8a  7  41
y  6  14
6.
8.
12.
2
a  12
3
5n  3  33
3t  17  5
3n  4  17
ORDER of OPERATIONS Worksheet Answers
1.


7 2  9  22  1  5
2.
 7 2  9  4   1  5
4  5  9
 99
 7 2  13  1  5
 49  13  1  5
0
 32
3.

2  2  22  4

4.
1  2  8  7
6
2
6.

 1 1
8.
2

 4 1
2

9 6

1  8  5
 25
 10
10.
4  6  9  3  2
 4  54  3  2
 4  162  2
 13  1
 13
3
2
 16  8  5
 9  4   1
11.
4
 16  1  8  5
 36  1
 37
3
8  3 1
 24  1
 24
 36  1  1
9.

 4 1
 324  1
 325
 1  17 
 18
7.
2
 81  4  1
 2  2  4  4
 2  10
 12
5.
9
 166  2
 81
12.
9  4
2

8
 9  9  6
 9  16  8
  7  8
 81  6
 486
13.
1
4 2  6  6  8
14.
 4 2  36  8
7
2

 32  8  3
16.
 49  9   8  3
4  8  5  2  4
18.
 4  80  4
 80
1  6
2

1
20.
 1  36  1
2
2
9  8  6 2  8
1  3 1
 4  1
4
 1  36 
 37
21.
6  3  2
 17  6 2  8
 17  36  8
 612  8
 604
 4  8  10  4
19.

 12  3
 18  2
 20
 40  8  3
 45
17.
2
 16  1  3
 12
 16  36  8
 12
15.
4

 5 2  12  9  4
22.


7  5  72  72  8
 7  5  49   7 2  8
 4  25  1  9  4
 21  4
 84
 7  54  7 2  8
 7  54  49  8
 7  21168
 21175
23.
2  8 1  6
9  9
2
5  2
2
4

 5  4  4
5
 286
4
25.
24.

1
 9  81  1
 71
SOLVING LINEAR EQUATIONS Worksheet Answers
1.
 7  7
x6
2.
3 2
3
 a  12 
2 3
2
a  18
x  7  13
9.
5n  3  33
y  6  14
 3  3
 6  6
y  20
3.
5n 30

5
5
n6
 8  a  12
8
4.
5n  30
 8
a  4
10.
3t  17  5
 17  17
 x   3  5
3t  12
3t  12

3
3
t  4
 x35
 3  3
x2
x
2

1 1
x  2
5.
3n  4  17
 4  4
3n  21
3x  24
3 x 24

3
3
x8
6.
11.
3n 21

3
3
n7
12.
8a  7  41
 8x  48
 7  7
8a  48
 8 x  48

8
8
x6
7.
1
x  10
2
8a 48

8
8
a6
13.
5
2 1
2
 x  10 
1 2
1
x  20
8.
5  3a  32
5
 3a  27
 3a 27

3 3
a  9
2
a  12
3
14.
 5  2x  17
5
 5
 2 x  22
19.
 5a
 2 x 22

2 2
x  11
15.
 8  8
2a  20
2a 20

2
2
a  10
20.
 8b
 6b  5  1
 5  5
7
t  42
8
8 7
8
 t  42 
7 8
7
t  48
 6b
6

6
6
5t  12  3t  6
b  1
- 3t
 3t
2t  12  6
 12  12
2t  18
2t  18

2
2
t  9
18.
2b  5  8b  1
 8b
7
t  8  34
8
 8  8
17.
 5a
2a  8  12
9
x  17  19
10
 17  17
9
x  36
10
10 9
10
 x  36 
9 10
9
x  40
16.
 3a  8  5a  12
4x  6  x  9
 x  x
3x  6  9
 6  6
3 x  15
3 x 15

3
3
x5
 6b  6
21.
1  9m  6m  14
 9m  9m
1  15m  14
 14 
15  15m
1 m
 14
Next Year I would change the Order of Operations worksheet to This more challenging (it has
Fractions!!!) one.
Evaluate each expression showing each step.
1. (16 - 4) • 2
2. 16 – (4 • 2)
3. 3 • (5 + 7)
4. (16 - 4) ÷ (3 + 1)
5. (8 + 4) ÷ (4 + 2)
6. 9 ÷ 1 + 3
22
3 • 4 + 52
8. 6 + 8 • 4
7-2
7.
9. (8 + 6) ÷ (7 - 5)
10.
22   1
3•4-5
11. 3 + 7 • (-2)2
13. 8 + (2 • 3)
5-3
12. 23 • 2 + 5 • 4
14. (2 + 3) • (4 + 1)
15. 42 • 4 + 4 ÷ 2
16. 4  8  2
17. 6 + 2 ÷ 2 + 2
32
18. (3 -2) • (9 - 3)
19. 72 + 4 • 3
20. 5 + 42
22 - 1
21. (5 + 4 - 2)2
22. 5 • 3 + (-2)3
23. (16 ÷ 4)3 – 6
24. 6 ÷ 3 • 23
2
25. 12  7  3
2
26. 4  1   3  3  8