Pre-AP Algebra II Summer Packet 2014
Name: __________________________________ Period: ________
PLEASE READ THE FOLLOWING!!!!!!!
Wait until a few weeks before school starts to work through this packet so that the material will be fresh when you
begin Pre-AP Algebra II. The problems should be done without a calculator. All Work/Steps must be shown in an
orderly manner and the work must be neat to receive credit. Box all answers. Place answers on the given answer
sheets (attached at the end of packet). The packet will be due the second day of class, with a test the following
week. You may need to look on the internet for examples to help if you are having difficulty. Please do the work
yourself since you will be tested on your own.
******You will have access to a graphing calculator in class next year but it is important that you have access to one for
use at home if at all possible. The best time to buy one is before school starts when stores are having back to school
sales because that is when you will find the best price. TI-83 Plus graphing calculator or better (TI-84 Plus is faster)
I look forward to seeing you when school starts.
If you have questions e-mail Nancy McWhorter at [email protected]
Order of Operations – Simplify each expression showing all work.
1) 7  2  20  3  9  39  3
3)
4  3(6  2) 2  2  3
2)
32  7  2  3  2
4)
2[2(3  2  3) 2  (3  6)]  3
Fractions – Simplify each expression and write in reduced fraction form, leaving improper fractions where applicable.
No decimal answers. Show all work.
5)
7)
5

 5
 4   3 2 
6

 6
4 3 5
   3
9 2 6
6)
8)
1 5 3 2
   
3 6 4 3 
3 3 3
 
2 4 8
21
Simplifying Expressions – Simplify each expression. Show all work.
9) –6b(8b – 2) – 3b(4 + 4b)
10) 4(p + 8) – (p – 5)
11)
–3(6r + 8) – 7r(–2 – 8r)
12) 5x(x2 + 4) + 3(2x2 – x3)
Solving Linear Equations –Solve each equation. No decimal answers. If solution is a fraction, leave as improper
fraction where applicable and remember to reduce. (check your solutions) Show all steps. Box answers.
13)
–4 = –4(1+8n)
14)
7
p  4  10
3
15) 75 – 9g = 5 (–4 + 2g)
16)
x  6 3x

6
8
17) 3(a + 1) – 5 = 3a – 2
18) 6 – 3(x + 5) = 3(x – 1)
19) 4 – 2(3x + 4) +2x = –2 + 6(x + 2)
Solving Inequalities & Compound Inequalities – Solve each of the inequalities and graph your solutions
on a number line. (check your solutions)
20) 15 – 3x > 6
21) 2 + 3(n + 5) > 4(n + 3)
22) –6 < 2x + 4 < 10
Multiplying Polynomial Expressions - Find each product. Remember to combine like terms. Box answers.
23)
–3x (4x – 6)
24)
(x + 11) (x – 11)
25)
(5t – 4)(2t – 6)
Multiplying Polynomial Expressions - Find each product & combine like terms. Show all work. Box answers.
26)
(3x + 7)(4x – 6)
27)
(2x – 3)2
28) (5x – 3y)(5x + 3y)
29) (x – 2)(x +2)(x + 4)
Factoring - Factor each expression completely.
Remember: factor out GCF first.
30)
9n2 – 12n
31) x2 – 25
32)
x2 + 7x + 12
33)
x2 – x – 6
34)
2x2 + 6x – 8
35)
2x2 – 8
36)
2r2 +5r + 3
37)
p2 – 8p + 16
38)
2x2 – 10x – 12
41)
–2x2 – 8x + 24
39) 2x2 – 5x – 7
40) 6x5y2 – 9xy3
Solve each equation by factoring and using the Zero Product Property. (remember to the set the equation = to 0)
Factor and set the factors = to 0 to solve.
42) 2x2 – 12x = 0
43) n2 – 16 = 0
44) x2 – 4x = 32
45) 2x2 + 9x + 10 = 0
46) x2 = 9x – 8
47) 2n3 – 26n2 + 72n = 0
Exponents – Simplify each expression. The simplified expression should have NO negative exponents.
48) 3(2 xy ) 0 (2 x 4 y 5 ) 3
51)
49)
3x 4 y 7 z 3 (2 xy 0 z 5 )
4x3 y 7 z
20 x 5 y 10 z 3
52)
50)
2 y(4 x 3 y 4 ) 2
2 x 3 y 2
16 x 3 y 8
Radicals – simplify each expression. Write your answer in simplified radical form. No decimals.
53)
18
54)
12  3
55) 3 72
56)
12  8
57)
9x12
58)
4a 8 c 5
Radical Equations - Solve each equation by taking square roots. No decimals.
59)
60) 25x2 – 8 = 28
4x2 + 2 = 102
Solve each equation using the quadratic formula.
Standard form: ax2 + bx + c = 0
Simplify and reduce final answer (no decimals)
61)
4x2 – 5x + 1 = 0
62)
6x2 – 2x – 1 = 0
Quadratic Formula:
x
 b  b 2  4ac
2a
63)
4x2 = 12x – 9
Graph each linear equation using x- and y-intercepts. (Show how you get the intercepts) There are graphs provided
on answer sheets.
64)
2x + 3y = 6
65)
6x – 3y = 12
66)
y + 2 = –2(x + 3)
67)
3x = 22 – 4y
Slope - Find the value of x or y so that the line through the points has the given slope OR find the slope through the given
points.
m
y2  y1
x2  x1
68) (19, 7) and (20, y); slope(m): 6
69) ( 7, –12) and (x, 9); slope(m):
7
3
70) (8, - 6) and ( -4, 3) slope (m) =
Graph each linear equation using slope & y-intercept: y = mx + b. There are graphs provided on answer sheets.
71)
4x – 5y = 10
72)
x + 4y = 12
Linear Equations – Write the point-slope and slope-intercept form of the equation of the line given the following
information. Show all work. No decimals. All fractions reduced. On answer sheet, write point-slope form first and then
write slope-intercept form.
73) through the point (1, –2), slope (m) = –5
74) through the points (-2, 5) and (6, 1)
Linear Equations – Write the slope-intercept form of the equation of the line of the equation of the line given the
following information. Show all work. No decimals. All fractions reduced.
75) through the point (1, –4), slope (m) = undefined
76) through the point (3, 5), slope(m) = 0
77) through (0, -1) and parallel to a line with a slope of
3
4
78) through (3, 5) and perpendicular to a line with a slope of 3
System of Equations - Solve the following systems by graphing (the point of intersection is the solution) Graphs are
provided on the answer sheets. Solution is shown as an ordered pair.
79)
y = 3 x 1
80)
3x + y = –2
81) 2x + 3y = 12
4
x+y=6
y = –3x + 5
2x – y = 4
Solve the following systems using the substitution method. Solution is shown as an ordered pair.
82)
x = 8y – 11
6x – 6y = –24
83)
y = 3x + 4
y = 6x – 8
Solve the following system using the elimination method. Solution is shown as an ordered pair.
84)
x – 3y = –12
2x + 11y = –7
Name: _____________________________________________________________
Period: ___________
Pre-AP Algebra 2 – Summer Packet 2014 – Answer Sheet
1.
26.
51.
2.
27.
52.
3.
28.
53.
4.
29.
54.
5.
30.
55.
6.
31.
56.
7.
32.
57.
8.
33.
58.
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34.
59.
10.
35.
60.
11.
36.
61.
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37.
62.
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38.
63.
14.
39.
64 – 67. (attached graphs)
15.
40..
68.
16.
41.
69.
17.
42.
70.
18.
43.
71 – 72. (attached graphs)
19.
44.
73.
20.
45.
74.
21.
46.
75.
22.
47.
76.
23.
48.
77.
24.
49.
78.
25.
50.
79 – 81. (attached graphs)
82.
83.
64.
84.
65.
66.
x – intercept (
,
)
x – intercept (
,
)
x – intercept (
,
)
y–intercept (
,
)
y–intercept (
,
)
y–intercept (
,
)
Slope ________
Slope ________
67.
71.
x – intercept (
y –intercept (
Slope ________
,
,
)
)
Slope-intercept form: _________________________
72.
79.
Slope-intercept form: _________________________
80.
Solution
____________________
81.
Solution
____________________
Solution
____________________