Summer Mathematics Prep
Chesterfield County Public Schools
Department of Mathematics
Entering Algebra 2
Summer Mathematics Prep documents provide self-directed student review, practice, and preparation for high
school mathematics courses. Students are encouraged to first attempt these review problems on their own.
Checking accuracy against the solution document can help students identify their own strengths and areas of
challenge. Students can utilize instructional online resources to address areas of challenge. All of these
resources can be found at http://mychesterfieldschools.com/about/instruction/other-academicprograms/summer-programs/.
Basic Properties of Real Numbers
Identify the property of real numbers illustrated for each of the following:
1) 4 x 2  14 x  2 x2 x  7 
3) If x  1 
5)
2) 12  x   x  12  0
4
4
then  x  1
3
3
4) If 3  c and c  d , then 3  d .
2  x  9  2  x  9
Simplifying and Evaluating Expressions
Simplify each of the following expressions:
6)
10  4 2
7) 36  4  12  6
8)
( - 5)2
9) (36  4)  (12  6)
10)
6  208
8
Evaluate each expression using the given values:
9r  qr
2(b  2a )
; a = 3, b = 4
12)
; q = -2, r = 4
2b  a
q
Basic Laws of Exponents
Simplify each of the following using the properties of exponents:
3
4x3
5
2
x

x
14)
15)
16) 2x 5
8
10 x
11)
 
18) x 2 
9
19) 3x 0
13) y 2 
y  5  6x
; x = 10, y = 3
x y
17)
   
4 x5  6 x5
20) (4 x)0
Simplifying Radicals
Simplify each of the following radicals:
21)
128
Chesterfield County Public Schools
Department of Mathematics
22)
32x 20 y 25
23) 4 3 27
24)
3
216a6
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May 2012
Slope
Calculate the slope of the line passing through the given points:
25) (2, 3) and (7, 5)
26) (2, 7) and (6, 7)
27) State the slope of the line: 4 y  3 x  8 .
28) State the slope of the line x  3 .
Writing Equations of Lines
slope intercept form  y  mx  b 
standard form (ax  by  c)
29)
State the equation of the line pictured.
30)
Write the equation of the line that has a slope of 2 and passes through the point (8, 6).
31)
Write the equation of a line in standard form that passes through (5, 3) and (0, 2).
32)
Write the equation of a line that passes through (4, 3) and (4, 7).
33)
Write the equation of a line that passes through the point (1, 1) and is parallel to the line y  5 x  3 .
(Reminder – parallel lines have equal slopes)
Graphing Functions
Graph each function on the graph provided.
34) Graph y  9
Chesterfield County Public Schools
Department of Mathematics
35) Graph y  3x  2
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36) Graph 2 x  4 y  8
37) Graph y  x 2  5x  6
Operations with Polynomials
Simplify each of the following polynomial expressions.
38) (3x 2  4 x  5)  (6 x 2  5 x  8)
39) (4 x 3  5 x  19)  (3x 3  6 x  12)
40) ( x  1)( 4 x  1)
41) (4x - 3) 2
42) (5x - 3)(5x + 3)
43) 5x(3x2 - x + 3)
Solving Linear Equations
Solve each equation for the variable.
44) 2 y  16  3y  6
46)
2x
 4  8
3
48)
7a 4 13
 
2 3 6
45) 7  4 z  2(2 z  3)
47) 3.2(3 y  4)  4.6( y  3)
Solving Systems of Linear Equations
Solve each system using an appropriate method. Show all work.
x  2 y  1
2 x  4 y  6
49) 
50) 
3x  2 y  1
3x  2 y  5
Chesterfield County Public Schools
Department of Mathematics
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May 2012
Factoring
Factor completely each of the following expressions.
51) 2 x5  16x 3
52) x 2  64
53) x 2  3x  18
54) 3x 2  7 x  6
Solve by Factoring
55) x 2  12 x  35 = 0
56) x 2  13x  36 = 0
Statistics
x 

x  element ofthe data set
z-score ( z ) 
  mean of the data set
  standard deviation of the data set
57) A set of Mathematics exam scores has a mean of 70 and a standard deviation of 8. What is the z-score of
a student receiving a 78?
58) A set of English exam scores has a mean of 74 and a standard deviation of 16. What is the z-score of a
student receiving a 78?
59) For which exam (Math or English) does the score of 78 have a higher standing?
60) What would be the exam score of an English student with a z-score of 0.94?
Chesterfield County Public Schools
Department of Mathematics
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May 2012
Chesterfield County Public Schools
Department of Mathematics
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