Answer Key
Precalculus Summer Math Packet
-
University:
Winston-Salem Forsyth County Schools -
Course:
AP Pre-Calculus Academic year:
2017
-
Views:
196
Pages:
29
Author:
neradnomjb4
PRECALCULUS Summer Math Packet
In preparation for Pre-Calculus, we have prepared a packet of concepts that students should know how to do.
These concepts have been taught in previous math classes. This packet does not require you to use a calculator;
in fact you should not use a calculator at all on any of these problems. Pre-Calculus builds on the concepts in
this packet. We start teaching Pre-Calculus concepts on the first day of school. We expect you to know the
concepts in the packet in order to help you be successful in Pre-Calculus.
If you are struggling with this packet, get help from a friend, parent, or tutor. If you can’t find someone to help
you, there are tutors available. A list of tutors can be found by calling Reagan High School. Keep in mind
these tutors may charge a fee.
You will have a graded assignment within the first two weeks of school. The graded assignment will cover all
the concepts in the packet, but will not be the exact same problems. The graded assignment will be without a
calculator.
You can go to youtube and type in the name of the concept and watch math
teachers explain the concepts FOR FREE. DO THIS IF YOU FORGET HOW TO
DO SOMETHING!!!!!!!!
TABLE OF CONTENTS
1) Multiplying Polynomials
2) Factoring
3) Adding & Subtracting Fractions
4) Multiplying & Dividing Fractions
5) Rationalize the Denominator
6) Solve Quadratic Equations
7) Parent Function Graphs & Finding Domain
8) Rational Equations
9) Logarithms
10) Radical Equations
11) Absolute Value Equations
12) ANSWER KEYS
page 1 (KEY p. 15)
page 2 (KEY p. 16)
page 3 (KEY p. 17)
page 4 (KEY p. 18)
page 6 (KEY p. 20)
page 7 (KEY p. 21)
page 8 (KEY p. 22)
page 9 (KEY p. 24)
page 10 (KEY p. 25)
page 12 (KEY p. 27)
page 13 (KEY p. 28)
page 14 1) Multiplying Polynomials
No Calculator!!!
1. x 7
2
2) x 11
2
3. x 4
3
4. x h
3
5. x 1x 2 3x 4
6. x h x 2 3xh 8
7. a b
2
1 2) Factoring
No Calculator!!
Factor each polynomial completely. If the polynomial cannot be factored write prime.
1)
2 x 2 128
2)
x 2 10 x 24
3)
a3 64b3
4)
5x 2 40 x 10
5)
2 x 2 11x 12
6)
x 3 16 x 2 64 x
7)
x 3 3x 2 4 x 12
8)
24 x 2 54
9)
6 x 3 18x 2
10)
5c 2 4cd d 2
11)
27 y 3 125
12)
20 x 2 4 x 72
13)
x 2 100
14)
4 x 4 64
15)
a 4 2a 2 1
16)
9 x3 12 x 2 45 x
17)
n 2 2n np 2 p
18)
24 x 2 4 x 60
2 3) Adding & Subtracting Fractions
No Calculator!!!
Simplify each expression.
1.
2 5
3 7
2.
1 5
6 18
3.
6
5
x
4.
3x
7
4y
5.
3 4
x2 x
6.
x
7x
2
x 5 x 25
7.
6
4
1
5 x 9 x 3x
8.
8
2
x 4x 4 x 2
9.
x
5
x 9 4 x 12
10.
5x
x5
x 5 x 2
2
11.
2
3
4
x 3 3x
3 4) Multiplying & Dividing Fractions
No Calculator!!!
Simplify each expression.
4 2
1.
5 3
1 3
2.
9 7
11
4. 7
7
18
7.
4 x
13 7
8
10. 3 x
5x
7
5.
8.
2
3. 7
4
9
x
6. 5
3
2
3
5
x2 7
5x 4 x
9.
11
9x
10
7x 2
5x 3
9x 4
6x 7
11.
4 12.
x
2
5
3
7
14.
1
4
7
y
13. z
7
Remember you cannot cancel at the beginning!!!
1
1
x
15.
1
1
x
2
x
4
3
16.
x
7
3
5 5) Rationalize the Denominator
No Calculator!!
1)
2)
3)
4)
5)
6)
7)
2
3 2
7
34
4 3
2 3
2 2
6 2
3i 2
5i 3
6i 2
6i 2
3 7i
7i
6 6) Solve Quadratic Equations
No Calculator!!
Find all real and imaginary solutions for all problems.
Solve the following by factoring.
1)
x 2 3x 4
4)
x x 5 36
2)
9 x 10 x 2
5)
x 6 x 8 24
Solve the following by using the square root property.
6)
7)
3x 2 2 0
x 52 12 0
9)
54 x 3 30
2
10)
y 42
2
3)
8x2 2 x 1
8)
2 x 52 11
13)
2 x 2 16 x 39 0
18
Solve the following by completing the square.
11)
x 2 10 8x
12)
x2 5x
41
0
4
Solve the following using the Quadratic Formula. You should have the Quadratic Formula memorized.
3x 2 2 9 x
5 x 2 2 x 4
12 x 2 x 6
14)
15)
16)
7 7) Parent Function Graphs & Finding Domain
No Calculator!!
PART 1: Be able to sketch the following 11 parent function graphs: [“c” implies any one constant number]
y c, y x, y x , y x 2 , y x3 , y x , y a x , y log x, y
1
, y sin x, y cos x
x
PART 2: State the domain of each function using interval notation. See answer key for further explanation if
needed.
x
1)
2)
3)
f x 4 x 5
f x 2 x 5
f x
5 x
4)
f x 3x 2 4 x 9
5)
7)
f x
1
8) f x x 2 10 x 24
1
3x 27
2
f x
x
x4
6)
f x 2 x 5
8 8) Rational Equations
No Calculator!!!
Solve each rational equation. Remember the quadratic formula!!!
1.
x
2
x 3 5
2. 4
3.
2 3x 1
4
x x3
4.
4x 3
x6
6
x2
x2
5.
2
6
3
2
x 5 x 25 x 5
6.
13x 20
4
6
x 13x 42 x 6 x 7
5 2
x 3
2
9 9) Logarithms
No Calculator!!!
Write each equation in logarithmic form.
2. 5 3
1. 4 2 16
1
125
Write each equation in exponential form.
3. log 3 81 4
4. log 49 7
1
2
Evaluate each expression.
5. log 100
6. log 2 32
8. log 64 4
9. log 5 58
7. log 3
1
81
Solve each equation.
10. log 7 x 3
11. log 8 5 x 11 2
12. log x 6
1
2
10 13. log 3
1
x
27
14. log 4 x 3 log 4 5 x 2
15. log 125 3 log x
16. 2 log 9 3 log 9 5 log 9 x
17. log 4 x log 4 2 3
18. log 3 x 1 log 3 x 1 4
11 10) Radical Equations
Solve each equation.
x7 8
1.
x 5
2.
3.
2 x 3 15
4. 5 x 7 15
5.
4x 1 2 x
6.
7.
3x 3x 8 2
x 2 1 x
12 11) Absolute Value Equations
Solve each of the following equations. Remember to set up 2 equations.
1. x 4 6
2. 2 x 3 51
3. 5 x 4 x
4. 6 x 7 x
5. 3 x 1 x 3
6. 4 x 5 5 x 4
13 ANSWER
KEYS
14 1) Multiplying Polynomials – ANSWERS
No Calculator!!!
1. x 7
2
x 2 14 x 49
2) x 11
2
x 2 22 x 121
3. x 4
3
x 3 12 x 2 48 x 64
4. x h
3
x 3 3x 2 h 3xh 2 h 3
5. x 1x 2 3x 4
x 3 2x 2 7 x 4
6. x h x 2 3xh 8
x 3 4 x 2 h 3xh 2 8 x 8h
7. a b
2
a 2 2ab b 2
15 2) Factoring – ANSWERS
No Calculator!!
Factor each polynomial completely. If the polynomial cannot be factored write prime.
1)
2 x 2 128
2)
5x 2 40 x 10
5)
5 x2 8x 2
7)
x 3 3x 2 4 x 12
5c 2 4cd d 2
8)
x 2 100
11)
9 x3 12 x 2 45 x
3x 3x 5 x 3
24 x 2 54
27 y 3 125
14)
4 x 4 64
9)
n 2 2n np 2 p
n 2 n p
6 x 3 18x 2
6 x 2 x 3
12)
20 x 2 4 x 72
4 5 x 9 x 2
15)
4 x 2 4 x 2 x 2
17)
x 3 16 x 2 64 x
x(x+8)(x+8)
3 y 5 9 y 2 15 y 25
10 x 10 x
16)
6)
6 2 x 3 2 x 3
5c d c d
13)
2 x 2 11x 12
a3 64b3
a 4b a 2 4ab 16b 2
2 x 3 x 4
x 3 x 2 x 2
10)
3)
x 4 x 6
2 x 8 x 8
4)
x 2 10 x 24
a 4 2a 2 1
a 1 a 1 a 1 a 1
18)
24 x 2 4 x 60
4 3 x 5 2 x 3
16 3) Adding & Subtracting Fractions – ANSWERS
No Calculator!!!
Simplify each expression.
1.
2 5
3 7
2.
29
21
4.
3x
7
4y
5.
6
4
1
5 x 9 x 3x
59
45 x
10.
5x
x5
x 5 x 2
6 x 2 10 x 25
x 2 3x 10
3.
8.
6
5
x
6 5x
x
1
9
3 4
x2 x
6.
x
7x
2
x 5 x 25
x 2 2x
x 2 25
3 4x
x2
3x 28 y
4y
7.
1 5
6 18
8
2
x 4x 4 x 2
2
9.
x
5
x 9 4 x 12
2
9 x 15
4 x 2 36
2
x2
11.
3
4
x 3 3x
5x 12
3x 2 9 x
17 4) Multiplying & Dividing Fractions – ANSWERS
No Calculator!!!
Simplify each expression.
4 2
1.
5 3
1 3
2.
9 7
8
15
11
4. 7
7
18
7.
4 x
13 7
4x
91
8
10. 3 x
5x
7
56
15 x 2
8.
9
14
1
21
x
6. 5
3
2
3
5
5.
198
49
2
3. 7
4
9
2
15
x
15
x2 7
5x 4 x
9.
7 x 14
20 x 2
11
9x
10
99x
10
7x 2
5x 3
9x 4
6x 7
11.
42 x 2 61x 14
45 x 2 7 x 12
18 12.
x
2
5
5x
2
2
y
7z
Remember you cannot cancel at the beginning!!!
1
1
x
15.
1
1
x
x 1
x 1
3
7
14.
1
4
7
y
13. z
7
17
27
x
4
16. 3
x
7
3
x 12
x 21
19 5) Rationalize the Denominator – ANSWERS
No Calculator!!
1)
2)
3)
4)
5)
6)
7)
2
3 2
7
34
4 3
2 3
2 2
62 2
7
21 4 7
13
11 6 3
6 2
5 2 2
17
3i 2
5i 3
21 i
34
6i 2
6i 2
17 6 2
i could write the answer all over 19 as one fraction
19 19
3 7i
7i
7 3i
7
20 6) Solve Quadratic Equations – ANSWERS
No Calculator!!
Find all real and imaginary solutions for all problems.
Solve the following by factoring.
1)
x 2 3x 4
2)
9 x 10 x 2
X 1,4
4)
x x 5 36
X 0,
5)
X 9,4
3)
x 6 x 8 24
x = 2, 12
9)
i 6
3
54 x 3 30
2
X
1 1
X ,
2 4
9
10
Solve the following by using the square root property.
6)
7)
3x 2 2 0
x 52 12 0
X
8x2 2 x 1
8)
X
X 5 2 3
10)
3 6
4
y 42
2
2 x 52 11
5 i 11
2
18
x = 10, -2
Solve the following by completing the square.
11)
x 2 10 8x
X 4 6
12)
x2 5x
X
41
0
4
5 4i
5
2i or
2
2
13)
X 4
2 x 2 16 x 39 0
i 14
8 i 14
or
2
2
Solve the following using the Quadratic Formula. You should have the Quadratic Formula memorized.
12 x 2 x 6
5 x 2 2 x 4
3x 2 2 9 x
14)
15)
16)
x
9 105
6
x
1 i 19
5
3 2
x ,
4 3
21 7) Parent Function Graphs & Finding Domain – ANSWERS
No Calculator!!
PART 1: Be able to sketch the following 11 parent function graphs: [“c” implies any one constant number]
22 PART 2: State the domain of each function using interval notation.
[Exclusions or restrictions of domain are results of “problems” in the equations when variables are
replaced with numbers in various circumstances. For instance, square rooting a negative cannot be
graphed on a real number plane because the answer is imaginary. Also, when a denominator equals 0,
the answer is undefined and cannot be graphed on a real number plane. These “problems” result in
numbers that must be excluded from the domain. If no “problems” exist, there are no restrictions or
exclusions and the domain is all real numbers written as (, ) .]
1)
f x 2 x 5
2)
5
2 ,
4)
f x 3x 2 4 x 9
f x
x
5 x
3)
,5 5,
5)
f x
x
x4
,4 4,
,
7)
f x
1
3x 27
2
,3 3,3 3,
f x 4 x 5
,
6)
f x 2 x 5
5
,
2
1
8) f x x 2 10 x 24
,4 4,6 6,
23 8) Rational Equations – ANSWERS
No Calculator!!!
Solve each rational equation. Remember the quadratic formula!!!
1.
x
2
x 3 5
2. 4
3
2
-2
3.
2 3x 1
4
x x3
4.
2
6
3
2
x 5 x 25 x 5
-19
4x 3
x6
6
x2
x2
9 105
2
11 145
2
5.
5 2
x 3
6.
13x 20
4
6
x 13x 42 x 6 x 7
2
44
3
24 9) Logarithms – ANSWERS
No Calculator!!!
Write each equation in logarithmic form.
2. 5 3
1. 4 2 16
log 4 16 2
log 5
1
125
1
3
125
Write each equation in exponential form.
3. log 3 81 4
4. log 49 7
1
2
1
49 2 7
34 81
Evaluate each expression.
5. log 100
2
6. log 2 32
5
8. log 64 4
1
3
7. log 3
1
81
-4
9. log 5 58
8
Solve each equation.
10. log 7 x 3
343
11. log 8 5 x 11 2
15
12. log x 6
1
2
36
25 13. log 3
1
x
27
-3
15. log 125 3 log x
5
17. log 4 x log 4 2 3
32
14. log 4 x 3 log 4 5 x 2
64
5
16. 2 log 9 3 log 9 5 log 9 x
9
5
18. log 3 x 1 log 3 x 1 4
41
40
26 10) Radical Equations – ANSWERS
Solve each equation.
1.
x 5
2.
25
3.
2 x 3 15
71
4. 5 x 7 15
111
5.
4x 1 2 x
No solution
7.
x7 8
2
6.
x 2 1 x
1/4
3x 3x 8 2
No solution
27 11) Absolute Value Equations – ANSWERS
Solve each of the following equations.
1. x 4 6
2. 2 x 3 51
2, -10
27, -24
3. 5 x 4 x
2/3, 1
5. 3 x 1 x 3
No solution
4. 6 x 7 x
no solution
6. 4 x 5 5 x 4
1
28
Precalculus Summer Math Packet
of 29
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