8th Grade Math Honors Summer Packet
Name:
Section I: Simplifying Expressions
1. Simplify the following expressions
a) 12 (y – 4) + 6
b) 2 – 3(9 – x)
d)
1
4 (4x − 16) e)
1
2x
Date:
c) 12 – 6z – 3 + z
− 35 x
2. Evaluate the following expressions when x = -2, y = -5, and z = 3
a) ​
-2(x – y)
b) ​
x -y - z
c)
​
xz
xy 3. Write an algebraic expression to ​
represent ​
each of the following situations.
a) Mary is 2 years younger than triple her sister‛s age. What is the sum of their
ages?
b) James is 3 years younger than Jeff. Sarah is twice as old as James. What is
the sum of their ages?
c) The length of a rectangle is double the width.
a) What is the perimeter of this rectangle?
b) What is the area of this rectangle?
Section 2. Properties
4. Determine if the following statements are always, sometimes, or never true.
Explain your reasoning.
a) x + y ∙ z = z ∙ y + x
b) 6c + a = 6c
c) -12 + 4x = -4(3 – x)
5. Use one of the properties (commutative, associative, distributive, identity) to
rewrite the following expressions. Describe how you used the property to rewrite
the expressions.
a) 2(x - 3)
b) ax + by + c
c) Choose all of the following that are equivalent to
4x + 2y
a)
b)
c)
d)
e)
2x + 4y
2(2x + y)
4(x + y)
2y + 4x
6xy
6. The area of the largest rectangle below is 192 square feet. Find x. Show all
steps and all work.
Section 3: Equations
7. Solve the following equations. Show all your work and every step!
​
a) 3x​
– x = 50
c)
e)
x − 4
3
=− 8 - 2(n + 3) = 16 – 3n
b)
2
3 x + 3 d)
√x = 4
= 13 x − 8
f) 12 (x + 1) = 2x
g) 3(x - 2) + x = 2x - 2 + 2x
8. To be a member of World Fitness Gym, it costs a $60 flat fee and $30 per
month. Maria has paid a total of $210 for her gym membership so far. How long
has Maria been a member of the gym? Write an equation to represent this
situation. Then solve the equation.
9. Two angles are supplementary. ∠1 ≅2x - 5 and ∠2 ≅4x + 5. Find the value
of x. Then find the measure of each angle.
10. Two angles are congruent and complementary. Write an equation to represent
this and find the measure of each angle.
11. The perimeter of a rectangle is 80 inches. The length of the rectangle is 4x 2 and the width is 3x. Find the dimensions of the rectangle.
Section 4 Graphing
14. Determine the equation of each of the following graphs.
a)
b)
15. Graph the following equations on the coordinate planes below.
a) y = 3 - ½x
x
b)
y = -3 + 2x
x
y
y
16. The following graph represents the distance a car travels over time.
a) How fast is the car traveling per mile?
Explain how you know
b) How far will the car travel after 12
hours?