Download Honors Geometry Summer Math Packet Summer 2013

Honors Geometry
Summer Math Packet
Student Name: ____________________________________
Summer 2013
This packet has been designed to help you review various
mathematical topics that will be necessary for your success
in Honors Geometry. You may use your notes from
previous mathematics courses to help you. You must do all
work without any help from another person.
Instructions:
DO ALL PROBLEMS WITHOUT A CALCULATOR.
Show all work that leads you to each solution in the space
provided. Please write neatly and an appropriate size to fit
in all your work.
ENJOY YOUR SUMMER!! WE ARE LOOKING
FORWARD TO SEEING YOU IN THE FALL.
Fractions
Write the following mixed numbers as improper fractions:
1
7
1. 2 =
2..  5 =
7
8
3. 6
3
=
7
Perform the indicated operation, and simplify if necessary:
4.
6 3
 =
7 2
7. 6 
4
=
5
3 2
5.   =
5 7
8. 15 
6. 
3
=
8
9.
Order of Operations
Evaluate each expression:
1.
4 [ 5( 9 + 3 ) – 3( 4 – 2 )]
2.
49 – ( 5 + 2 )2 + 14
3.
1
( 2 + 4)2
3
4.
14 – ( 43 ÷ 16 ) * 5
4 1
 =
5 6
2
 14 =
7
Proportions
Solve each proportion for the missing value:
x2 4
1.

2
3
2.
2 15

0.4 t
Exponents
Simplify the following expressions:
x3 y5
1. 4 2
2. a-5 · b2
x y
15a 4 b 2 c 3
4.
5ac 5
 2h 3 

5. 
 3 
3. (2x3)2
2
6. t4 · t2 ÷ t7
Solving Equations
Solve the following equations.
r 8
1.
 2
3
3. 2(a – 3) + 5 = 3(a – 1)
2. 3(x+2) = 18
4. 3 
2
2
y  11  y
5
5
Solving Equations II
Solve the following equations.
m
64
1.
5
3. 4c + 5c – 10c + 27 = 13 + 6
2. 9 - 5(4-3) = -16 +
x
3
4. 3(7 + x ) = 5(7 – (-4))
Systems of Equations
Find the value of x, and y that satisfy each system of equations below.
 y  4x
1. 
3x  2 y  44
3x  2 y  12
2. 
 x  2y  6
 2x  y  3
3. 
4 x  2 y  12
 y  3x  8
4. 
 y  4 x
Factoring Quadratic Equations
Factor the following expressions.
1. x2 - 12x + 20
2. x2 +4x – 32
3. 4x2 – 25
4. 2x2 +5x + 3
5. 3x2 -3x – 6
6. 8x2 – 2x -10
Solving Quadratic Equations
Solve the following quadratic equations by factoring.
1. x2 + 7x + 12 = 0
2. x2 - 9x -36 = 0
3. 5x2 = 5x + 60
4. x2 – 81 = 0
5. 7x2 + 42x = 0
6. 3x2 -3x = 3(x +15)
Solve the following equations by using the quadratic equation.
7. 2x2 + 6x = 5
8. 8x + 4 = 2x2