Math for College Readiness Summer Math Packet
Name ___________________________________________
This work is important to prepare you for Math For College Readiness. You must print and complete all work on paper. DO NOT
USE A CALCULATOR. This work will be collected for a grade on the first day of school. The first major assessment of the
quarter will rely heavily on this summer content. Have a great summer!! =)
Find the GCF for the list.
1) 56, 10, 35 1)
2) 64a9b4, 40a5b9 2)
Write the fraction in lowest terms.
3) 33
44
3)
Write the fraction as an equivalent fraction with the given denominator.
4) 2
3
with a denominator of 21 4)
Add or subtract as indicated. Write the answer in lowest terms.
5) 1
3
+
5
7
5)
Evaluate.
XXXXXXXXXX)
1
XXXXXXXXXX)
8) 1
6
3
8)
Simplify the expression.
9) 8[ XXXXXXXXXX)] 9)
XXXXXXXXXX)[ XXXXXXXXXX)] 10)
XXXXXXXXXX
13 - 1
11)
Evaluate the expression for the given replacement values.
12) x
2 + z
y2 - -3z
x = 2, y = 3, z = 11 12)
Find the square root. Assume that all variables represent positive real numbers.
13) 4
9
13)
2
XXXXXXXXXX)
Find the cube root.
15)
3
-64 15)
Write the sentence as an equation or inequality. Use x to represent any unknown number.
16) Two subtracted from eleven is equal to three squared. 16)
Name the property illustrated by the statement.
XXXXXXXXXX = XXXXXXXXXX)
18) (5 ·6) ·1 = 5 · (6 · 1) 18)
Simplify the expression.
XXXXXXXXXX
32 - 4
19)
3
Add.
20) 4
5
+ -
3
5
20)
XXXXXXXXXX)
22) [6 + (-1)] + [ XXXXXXXXXX)] 22)
Subtract.
23) 6
9
-
3
8
23)
Multiply.
24) - 3
4
-
6
23
24)
XXXXXXXXXX
15
3
8
25)
4
26) 0 · -12 26)
XXXXXXXXXX)
Divide.
28) - 7
10
÷ -
3
4
28)
Evaluate.
XXXXXXXXXX)
Decide whether the given number is a solution of the given equation.
30) Is 3 a solution of -8x + 2 = -22? 30)
31) Is 3 a solution of -5x - 4 = x + 5? 31)
Simplify the expression. First use the distributive property to remove any parentheses.
32) - 2
7
(z XXXXXXXXXX
14
z 32)
5
Simplify the expression by combining any like terms.
33) 9x2 + 5x + 2 + 3x + 8 + 5x2 33)
34) 5.5w XXXXXXXXXX1w XXXXXXXXXX8w 34)
Simplify the expression. First use the distributive property to remove any parentheses.
35) -3(10r XXXXXXXXXX2r XXXXXXXXXX)
36) -(5y - 2z XXXXXXXXXX)
37) -3(10r XXXXXXXXXX2r XXXXXXXXXX)
Solve the equation. Use mental math.
38) 18 = r + 3 38)
39) 1
7
y = -6 39)
6
Solve the equation.
40) 4n - 9 = 11 40)
41) x
8
+ 6 = 14 41)
42) 6z XXXXXXXXXXz + 1) = -(3z XXXXXXXXXX)
43) 8(3x + 7) = 25x 43)
44) 3n - 2n - 2 = -2 44)
45) 6y = 7(5y XXXXXXXXXX)
46) 2(y + 6) = 3(y XXXXXXXXXX)
7
Solve the equation.
47) x
6
- 8 = x
6
47)
48) 3(2z - 4) = 5(z XXXXXXXXXX)
49) 1.3x + 4.4 = 0.7x XXXXXXXXXX)
50) x
7
- 9 = -5 50)
51) -6x + 7(-2x - 2) = -29 - 5x 51)
52) 4(x + 6) = (4x XXXXXXXXXX)
53) 7x - 5 - 7x + 1 = 6x - 6x - 7 53)
8
Write the phrase as a variable expression. Use x for the unknown number.
54) The sum of -18 and twice a number 54)
55) Three times a number 55)
56) A number subtracted from -2 56)
Substitute the given values into the formula and solve for the unknown variable.
57) d = rt; t = 2, d = 8 57)
58) I = prt; I = 157.5, p = 250, r = XXXXXXXXXX)
Solve the formula for the specified variable.
59) d = rt for r 59)
60) I = Prt for P 60)
9
Solve. Round all amounts to one decimal place.
61) What number is 80% of 100? 61)
62) 3 is what percent of 12? 62)
The circle graph below shows the number of pizzas consumed by college students in a typical month. Use the graph to
answer the question.
63) What percent of college students consume more than 7 pizzas in a typical month? 63)
Find the slope of the line that passes through the given points.
64) (7, 2) and (3, 8) 64)
10
65) (-6, -3) and (9, 4) 65)
66) (-2, 9) and (-10, 19) 66)
Find the slope of the line.
67) 67)
68) 68)
11
Find the slope of the line if it exists.
69) 69)
70) 70)
Find the slope of the line.
71) y = -5x - 4 71)
Evaluate the function.
72) Find f(0) when f(x) = x2 + 5x XXXXXXXXXX)
73) Find f(-4) when f(x) = x2 - 2x XXXXXXXXXX)
12
Evaluate the expression.
74) 1
6
2
74)
Evaluate the expression with the given replacement values.
75) 7x2; x = 5 75)
76) 5
9x2
; x = -4 76)
Use the product rule to simplify the expression. Write the result using exponents.
77) x2 ·x7 77)
Use the power rule to simplify the expression.
78) (x9)3 78)
Use the quotient rule to simplify the expression.
79) s
10t4
s2t
79)
13
Use the power rule and the power of a product or quotient rule to simplify the expression.
80) (-8x3)2 80)
Simplify the following by combining like terms.
81) -3r - 14r4 - 15r4 - 9r 81)
Perform the indicated operation.
82) (8x XXXXXXXXXX10x XXXXXXXXXX)
83) (-19x XXXXXXXXXX6x XXXXXXXXXX)
Multiply.
84) -7x(9x XXXXXXXXXX)
85) 6z2(6z2 + 5z XXXXXXXXXX)
14