Rising Geometry
Students
Summer Skills
Workbook
June 2014
Name____________
This booklet is a review of the main Algebra
I concepts. You should complete each page.
Pages 1 through 17 have the answers at the
bottom. Please place the number of each
problem in the space that matches the
answer. For page 18, please complete the
questions in the spaces provided.
Turn this booklet in the first Day back to
school.
Please be sure to not
use the calculator
when you see this symbol.
For questions or comments, please email Chariya Fisher at
[email protected]
Rising Geometry Students Summer Skills Work
Page 1
Evaluate the following when x = 4, y = -2, and z = 5. Show all work.
Evaluate means to substitute the value in for each variable and simplify the expression.
1) 3x – y
2) xy + z
3) 4x – 3z
4) xyz
5) x – 2y + 3z
6) x (y – 2z)
7) x 2  y 2
8)
10) xy
11) z  x
1
x  y2
2
9)
x y
3
12) 2 z  3 y
Place the number to the correct answer for questions 1 through 12 in the box below.
14
12
-3
6
1
-2
-40
8
23
9
-48
16
Rising Geometry Students Summer Skills Work
Page 2
Simplify the following by combining like terms. Like terms have the same variable and
exponent. These terms can be combined with addition and subtraction without changing the
exponent of each term.
1) 5x – 3x
2) 4y – 7y
3) y  6 y 2  y 2  3 y
4) 5x – 3y – x + 7
5) 7y – 12 – 3y
6) 2x – 4 + 3x + 8
7) 5y + 3x – 2z – 3y + 6x + 8
8) 4(x – 2) – 3(x + 7)
9) 4 – 3(x – 5) + 2x
10) x  3x  2 x  8  4 x
11)
2
7 x2 y  3xy  2 x 2 y  8xy 2  4 xy
2
12) x y  3 y  5 x y  4 x y  4 y
2
13) 5(x – 2y + 3) – 2(2y + 3x + 7)
14)
2
2
2
2
2 y2  3y  9 y  7 y2  4 y
Place the number to the correct answer for questions 1 through 14 in the box below.
9x + 2y - 2z + 8
5x + 4 -x + 19
2x
x - 29
3x 2  7 x  8
 5 y2  2 y
9 x 2 y  8xy 2  7 xy -3y
4y -12
5 y 2  2 y
3x 2 y 2  5 x 2 y  7 y
-x – 14y + 1
4x - 3y + 7
Rising Geometry Students Summer Skills Work
Page 3
Use order of operations (PEMDAS) to simplify the following.
1) 8 + 6 – 3
2) 15 – (7 – 2) – 3
3) 5(4) – 10
4) 24 – 21 ÷ 3
5) 18 – 12 ÷ 4
6) 12 – (4 + 7)
7) 7(3 + 4)
8) 12 ÷ 3 · 4
9) (11 + 4) ÷ 5
10) (12 · 4) ÷ (2 · 2)
11) 30 ÷ 6 – 1
12) 42 ÷ (5 + 2) · 3
13) 4 + 3(7 – 2)
14) 5(6 – 8)
15) 15 – 2(8 + 3)
16) 2 – 8 ÷ 4
17) 4 – 8 + 6
18) 10 - 3(4)
Place the number to the correct answer for questions 1 through 18 in the box below.
11 16 -10 7
3
-7
10 12 17 -2
15 1
18 2
4
0
49
19
Rising Geometry Students Summer Skills Work
Page 4
Simplify the following:
1)
1
3

2
5
2)
4)
2
4

7
9
5) 2
7)
3
2

5
9
8) 1 
10)
3
3

4
5
11)
4
3
1
5
5
3) 2
2
 5.256
5
6)
1
5
9) 2
5
6
1
3

4
4
1
2
1
3
5
3

5
2
3

3
10
3
3
1
4
5
12) 3
1
1
 1
7
4
Place the number to the correct answer for questions 1 through 12 in the box below.
46
63
14
15
4
5
11
10
2
15
1
957
125
88
35
5
4
29
30
1
3
22
5
Rising Geometry Students Summer Skills Work
Page 5
A number is expressed in scientific notation if it is written as a number between 1
and 10 multiplied by a power of 10. For example, 3.2 x 10 is the number 32
written in scientific notation.
Write each number in scientific notation:
1) 6,780,000
2) .0678
3) 678
4) 67,800
5) .678
6) .000678
7) 678,000
8) 678,000,000
9) .00678
10) .00000678
11) 678 x 1014
12) 67.8 x 108
13) .678 x 10-10
14) .0678 x 109
15) 678 x 10-12
16) 6,780
Place the number to the correct answer for questions 1 through 16 in the box below.
6.78x1016 6.78x102 6.78x10-1
6.78x10-4
6.78x105 6.78x106
6.78x107
6.78x108
6.78x109
6.78x10-3
6.78x104 6.78x10-6
6.78x10-10
6.78x10-11
6.78x103 6.78x10-2
Rising Geometry Students Summer Skills Work
4 x
Ex: 
5 15
Page 6
Cross Multiply
5●x = 4●15
Then solve
x = 12
Solve the following proportions:
1)
3
n

4 16
2)
2
24

3
n
3)
n
56

2 112
4)
14
28

n
4
5)
5
n

6 18
6)
2 14

n
35
7)
n
9

4
n
8)
n 2
6

4
5
9)
n 2
2

3
4
12)
4
n

n
25
10)
4
5

n3
n 1
11)
4
n 1

n
3
Place the number to the correct answer for questions 1 through 12 in the box below.
10
36
12
6
5
2.8
15
-0.5
2
-19
1
4, -3
Rising Geometry Students Summer Skills Work
Page 7
Solve for x. Show all work.
1) .5x = 3.5
2)
x 7

2 4
3)
2
x  309  711
3
4) 3x – 4 = -22
5) 5 – x = 12
6)
x
5 7
3
7) 5(x – 3) = -20
8) -3(4 – x ) = 12
9)
2
 x  9  14
3
10) 4(x – 3) = 3(x + 7)
11) 5(2x + 3) = 7(x – 3)
12) 2(x – 3) – 4 = 10
13) 5(x – 2) – 3(x + 4) = -20
14) 5x – 13 = 2x + 14
15) 12 – 7x = -3x – 8
Place the number to the correct answer for questions 1 through 15 in the box below.
30
10
-1
8
-3.5 603
33
5
-7
9
6
1
7
-6
-12
Rising Geometry Students Summer Skills Work
Page 8
Solve the following multi-step equations:
1) 2x + 4 = 8x - 26
2) 3x – 9 = 2x + 8
3) x - 12 = 5x
4) 7x – 9 = 4x
5) 3x – 8 = x + 12
6) 4x + 8 = 2x + 7
7) 4(x – 3) = -12
8) 5(2x + 7) = -15
9) 4(x + 6) = 2(x – 4)
10) 3(2x – 7) = 6 + 2(x – 3)
11)
2x  1
5
3
12)
3x  4
 5
2
Place the number to the correct answer for questions 1 through 12 in the box below.
-0.5
10
3
0
-5
-16
5
17
-3
2
8
5.25
Rising Geometry Students Summer Skills Work
Page 9
Solve the following:
1) x + 4 < -8
2) x – 12 > 7
3) 4x > -12
4) 5 + x < 12
5) 6 – x > 7
6) 15 < -3x
7)
x
 3
5
8)
x
 2
5
9) 
x
2
7
10) 8 > x – 4
11) 7 < 4 + x
12) -5x > -20
13) 2x – 4 > 12
14) -3x + 5 < -7
15)
x
 42
7
Place the number to the correct answer for questions 1 through 15 in the box below.
x<42
x>4
x>8
x<4
x>3
x<12
x<-14
x<10
x<-12
x<-5
x<-1
x<7
x>-3
x>19
x<-15
Rising Geometry Students Summer Skills Work
Page10
The slope m of a line describes how steep it is. The slope is calculated
by finding the quotient of the vertical change (change in y) and the
horizontal change (change in x). Formula: m 
y2  y1
x2  x1
Find the slope of the line that contains each pair of points.
1) (2, 4), (4, 6)
2) (3, 2), (-2, -8)
3) (-1, 3), (-2, 5)
4) (8, -3), (10, 0)
5) (0, 0), (6, -3)
6) (3, 4), (-1, 4)
7) (-4, 7), (-7, 15)
8) (2, -2), (6, 5)
9) (4, 3), (4, -5)
10) (2, 8), (7, -7)
Place the number to the correct answer for questions 1 through 10 in the box below.
No
2
-3
1
0
3
1
7
8
slope
2
4
3
2
-2
Rising Geometry Students Summer Skills Work
Page 11
The number 18 is not a perfect square, but it does have a perfect square factor.
18  9  2 should be further simplified to 3 2 . Simplify the following radicals.
Think of the largest perfect square that can be simplified.
2) - 18
3)  8
4)  75
5)
6)
500
7)  242
8)  50
9)
700
10)
11)
20
12)
14)
12
15)  48
1)
28
98
13)  24
63
45
Place the number to the correct answer for questions 1 through 15 in the box below.
4 3 2 3 5 3 2 7 10 7 3 2 11 2 2 2 5 2 7 2 2 6 2 5 3 5 10 5 3 7
Rising Geometry Students Summer Skills Work
Page 12
Multiply the following either using Distributive Property or FOIL:
1)  x  4 ( x  8)
2)  x  4 ( x  7)
3)  x  5 ( x  8)
4)  x  9 ( x  8)
5)  x  3 ( x  6)
6)  x  7  ( x  8)
7)  x  10 ( x  8)
8)  x  11 ( x  2)
9)  x  12 ( x  4)
10)  x  15 ( x  3)
11)  2x  1 ( x  3)
12)  2x  3 ( x  5)
13)  2x  5 (3x  4)
14)  3x  5 (2 x  4)
Place the number to the correct answer for questions 1 through 14 in the box below.
x  3 x  28
6 x  7 x  20
x  3 x  18
x
2
2
2
2
 12 x
 45
x  12 x  32
2x
x  9 x  22
2x
2
2
2
2

7 x  15
x  13 x  40
x

7x  3
x  x  56
6x
2
2
2
 18 x
2
 80
 22 x  20
x  x  72
2
x  8 x  48
2
Rising Geometry Students Summer Skills Work
Page 13
Factor the following trinomials.
1) x 2  5 x  6
2) x2  9 x  8
3) x2  12 x  32
4) x 2  15x  26
5) x 2  7 x  12
6) x 2  7 x  6
7) x 2  7 x  10
8) x 2  9 x  20
9) x2  9 x  18
10) x2  9 x  14
11) x 2  9 x  8
12) x 2  10 x  24
13) x 2  10 x  11
14) x2  10 x  39
15) x 2  8 x  20
16) x2  5x  14
17) x 2  4 x  21
18) x2  4 x  12
19) x 2  8x  20
20) x2  11x  60
21) x2  9 x  10
Place the number to the correct answer for questions 1 through 21 in the box below.
 x 1 x  11
 x  2 x  5
 x  2 x  13
 x  4 x  5
 x  1 x  8
 x  2 x  6
 x  2 x  7
 x  3 x  13
 x  4 x  6
 x  2 x  10
 x  3 x  6
 x  2 x  3
 x  2 x 10
 x  4 x  8
 x  3 x  4
 x  1 x  6
 x  2 x  7
 x 1 x  8
 x  3 x  7
 x  4 x 15
 x  1 x  10
Rising Geometry Students Summer Skills Work
Page 14
Simplify the following using the rules for exponents:
1) x2  x3
2) x5  x  x4
3) 2 x5  3x4
4) 4 x3  3x
5) 3x3 y(2 x4 )( xy 4 )
6) x3 y  x 4 yz  xy 4 z 3
x 
2 4
7)
1 
10)  x 4 
2 
13)
8)
 x y
3
11)
3
5
9)
x  x 
4 3
 2 x   3x 4    x3  5 x 2 
 2x y 
4
3 3
12)  2 xy   3x 2 y 2 
2 5
3
14)  3x   4 y    2 y   7 x 
2
15) 7 x 2 y  3x  2 xy  5 y 2 
3
3
2
2
16) x 2 y 2  y 3  y  2 
Place the number to the correct answer for questions 1 through 16 in the box below.
x2 y5  x2 y3  2 x2 y 2
8x12 y9
x15 y 5
6x8 y 5
x5
21x3 y 14 x3 y 2  35x 2 y 3
184x 2 y 3
x8 y 6 z 4
12x 4
6x9
72x 7 y 7
.125x
12
x10
x8
x 22
11x5
Rising Geometry Students Summer Skills Work
Page 15
Identify the following formulas for the circle:
Circumference (C) = __________________ or _________________
Area = __________________
If π is used in the original information, leave your answer in terms of π, otherwise
use π ≈ 3.14. Given the missing part of the following:
1) C = 24 π cm
diameter = _______
radius = _______
Area = ___ π cm2
2) C = 10 π cm
diameter = _______
radius = _______
Area = ___ π cm2
3) C = 7 π cm
diameter = _______
radius = _______
Area = ___ π cm2
4) C ≈ 37.68 cm diameter = _______
radius = _______
Area = _____ cm2
5) C ≈ 15.7 cm
diameter = _______
radius = _______
Area = _____ cm2
6) C ≈ 87.92 cm diameter = _______
radius = _______
Area = _____ cm2
7) A = 49πcm2
diameter = _______
radius = _______
C = _____ π cm
8) A = 100πcm2 diameter = _______
radius = _______
C = _____ π cm
9) A ≈ 28.26 cm2 diameter = _______
radius = _______
C = _______cm
10) A ≈ 50.24 cm2 diameter = _______
radius = _______
C = _______cm
Place the number to the correct answer for questions 1 through 10 in the box below.
8 cm, 4 cm, 25.12 cm
14 cm, 7 cm, 14 π cm
24 cm, 12 cm, 144 π cm2
12 cm, 6 cm, 113.04 cm2
20 cm, 10 cm, 20 π cm
6 cm, 3 cm, 18.84 cm
7 cm, 3.5 cm, 12.25 π cm2
10 cm, 5 cm, 25 π cm2
28 cm, 14 cm, 615.44 cm2
5 cm, 2.5 cm, 19.625 cm2
Rising Geometry Students Summer Skills Work
Page 16
Leaving your answers in terms of π, find the Circumference and the Area of the
following:
1)
4)
12 cm
C = ________ A = ________
2)
4 cm
C = ________ A = ________
5)
10 cm
C = ________ A = ________
3)
3 cm
C = ________ A = ________
6)
9 cm
C = ________ A = ________
7 cm
C = ________ A = ________
Place the number to the correct answer for questions 1 through 6 in the box below.
9 π cm, 20.25 π cm2
12 π cm, 36 π cm2
6 π cm, 9 π cm2
10 π cm, 25 π cm2
8 π cm, 16 π cm2
14 π cm, 49 π cm2
Rising Geometry Students Summer Skills Work
Page 17
The Pythagorean Theorem is a 2  b2  c 2 where a and b are the legs of a right
triangle and c is the length of the hypotenuse.
1) Find the length of the hypotenuse of a right triangle whose legs are 5 cm and
12 cm.
2) Find the length of the hypotenuse of a right triangle whose legs are 7 cm and
24 cm.
3) Find the length of the hypotenuse of a right triangle whose legs are 15 cm
and 8 cm.
4) If the hypotenuse of a right triangle is 20 cm and the length of one leg is 12
cm, what is the length of the other leg?
5) If the hypotenuse of a right triangle is 10 cm and the length of one leg is 8
cm, what is the length of the other leg?
6) If the hypotenuse of a right triangle is 5 cm and the length of one leg is 3 cm,
what is the length of the other leg?
7) If the hypotenuse of a right triangle is 65 cm and the length of one leg is 16
cm, what is the length of the other leg?
Place the number to the correct answer for questions 1 through 7 in the box below.
4 cm
16 cm
25 cm
63 cm
6 cm
13 cm
17 cm
Rising Geometry Students Summer Skills Work
Page 18
A geometry student should be adept at remembering and incorporating formulas
into the Geometry curriculum.
Complete the following Formulas using the variables indicated
Perimeter
Rectangle
L
W
Square
S
S
Parallelogram
A
H
B
Trapezoid
A
B
H
C
D
Triangle
A
H
C
B
Area