Name __________________________________________
Summer Math Assignment
Entrance into Geometry/Algebra 2/ Foundations of College Mathematics
Directions: 1) Use a pencil
2) You are to show ALL your work neatly on a separate sheet of paper- DO NOT WRITE ON
THIS PACKET
3) Complete the following questions without using a calculator
4) We will be going over the answers in class during the 1st week of school
5) A test of similar questions will be given by the end of the 1st week of school. THE TEST
WILL BE YOUR 1st MATH GRADE OF THE NEW SCHOOL YEAR.
** It is your responsibility to research or seek help for any concepts/topics that have been forgotten.
You may contact Mr. Barth ([email protected]) or Mrs. Schildwachter
([email protected]) for assistance prior to August 15, 2015, if necessary.
An additional resource for help is http://www.khanacademy.org (this site has videos of hundreds of
math topics) or http://www.purplemath.com (a great algebra site).
Part A: Fraction Computation. All answers should be in lowest terms. Convert any improper fraction to
a mixed number.
1)
2
1
+
3 12
2)
4)
13 7
15 20
5)
7)
5
1 2
+ 6
2 3
8)
10) 3
1
6
�1
2
7
5 1
9 4
1
3)
4
7
+2
5
9
4
� - 20
5
11) 36 ÷
3
4
5
9
+
12 16
6) 3
1 2
9 3
9) -
12)
1
5
�10
6
2 5
÷
7 6
13)
8
5
÷
9
36
14) 1
2
5
÷ 2
5
7
15) 45
5
1
÷ 18
6
3
Part B: Use order of operations to simplify each expression. Leave answers in fraction form if it does not
simplify to a whole number.
16) 3 – 32 ÷ 2 ∙ 8
19)
5 + 7 �3
31 - 2 � 32
17) 2 ∙ 52 – (12 ∙ 6)
18) 30 - 42
20) ( 8 – 2)2 – 3(-4)(2)
21) 8 + 5 ∙ 43 – 10 – 3(8 – 6)
Part C: Solve the following linear equations. Leave your answers on fraction form if it does not simplify
to a whole number.
22) 2x + 1 = 7x – 3
23) 3 – 5n = 6 + 4n
25) 6(x + 4) + 12 = 5(x + 3) + 7
26)
28) -4x – 3(2 – 2x) = 7 + 2x
31) y = 9(7 – 2)2 – 12
24) 8(2 – 3y) = -56
27)
3a + 1 3
=
a
2
29) 5 + 3(x – 4) = 7x – (4x – 1)
30)
x
x
= -2
3
2
32) 162 + b2 = 202
33) 82 = 167 – 2n – 52
3
9
=
m+4
14
Part D: Solve the following inequalities and graph the solution on a number line. When you draw your
number lines, not every number needs to be included and the number line should be symmetric.
2
x<8
3
34) 13 – 4k < 27
35) 6 -
37) 90 > 5(2x + 6)
38) 6d + 3 > 5d – 2
39) 9z + 2 > 4z + 15
40) 2(g + 4) < 3g – 2(g – 5)
41) 9x + 12 < 23 + 10x
42) 4(2x + 3) – (6x + 9) < 2( x – 4)
36) 2(4x + 9) <18
Part E: Functions, Slopes and Linear Equations
43) Find the slope of a line that passes through the points (-3, -4) and (5, -1).
44) Find the slope of a line that passes through the points (3, -5) and (-7, -9).
#44 – #47 Find the domain and range of the following relations. THEN determine if the relations are
functions. If the relation is not a function, explain why not.
44) { (2, 3) , ( 3, -1), (2, 7), (1, 8)}
45) {(1, 3), (2, 3), (4, 3), (5, 3)}
46)
47)
Graph the following linear equations on a separate sheet of graph paper. Make a separate coordinate
grid for each equation. Use the method for graphing as directed for each equation. Label the graphs by
number.
48) y = 2x – 5
(slope and y-intercept)
49) x + 4y = 20
(x- and y-intercepts)
50) y = 4
51) x = -4
52) x – 3y = 6
(t-table)
53) 3x – 2y = -6
(x- and y-intercepts)
54) Write a linear equation in slope-intercept form that has a slope of
1
and passes through (5, -7).
3
55) Write a linear equation in slope-intercept form that is parallel to y = 4x - 6 and passes through the
point (-1, -2).
56) Write a linear equation in slope-intercept form that is perpendicular to 4x – 5y = 10 and passes
through the point (-2, -7).
Part F: Monomials and polynomials: Simplify the following. Read your signs carefully and remember all
answers should have positive exponents.
57) x4 ∙ x3
0
60) 3x
58) (a5)2
59) (3a4)3 (2a2)4
(2 x3 y 4 )3
61)
6 xy 3
5 6
z
24 x 6 y −−
62)
−−−
3
5 2
18 x y z
63) (-6x3 + 5x2 – 8x + 9) + (17x3 + 2x2 – 4x – 13)
64) (-4x3 – x2y + xy2 + 3y3) – (x3 +2x2y –y3)
65) 3x2y(4x2 + 5xy – 3y2)
66) (x – 5) ( x + 7)
67) (x + 4) (x – 4)
68) (x – 3) (x2 – 1)
69) (x – 2) (x2 +2x + 4)
70) (7x – 2y) (2x + 7y)