Download - GUIDELINES FOR COMPLETING THE ASSIGNMENT
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Supplies needed for your first day of class
and every day after:
3 Ring Binder or Notebook
Filler Paper
Pencils/Erasers
Scientific Calculator (such as a TI-34)
We STRONGLY recommend you have a
Graphing Calculator (TI 84).
Contact a teacher:
John Marks
Email: [email protected]
Renee Canagon
Email: [email protected]
Summer 2015
Due date: September 8th
This packet was created
to help you succeed in
your upcoming
Precalculus class. Many
of the concepts were
taught to you in
previous classes. In your
upcoming math class we
will be building on these
concepts covered in this
packet.
You may find that you
have forgotten some of
these concepts. There
are many resources
available to you on the
internet to refresh your
memory. If you are
confused, be sure to
take the time to ask for
the help needed to
complete them.
This packet will count towards your first marking period grade. The packet will be graded for completeness and accuracy. Your teacher will be looking for supporting work to see that you understand each concept. We have given you our email addresses so you can contact one of us if you have questions. Please do not wait until the first day of school to ask for help! On Tuesday, September 8th, you will be given an assessment on the topics included in this packet to check for understanding. Have a great summer!
GUIDELINES FOR COMPLETING
THE ASSIGNMENT
RAHWAY HIGH SCHOOL
MATHEMATICS DEPARTMENT
Honors PRECALCULUS
Summer Assignment
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1
Order of Operations.
1. Perform operations in Parentheses.
2. Evaluate numbers with Exponents.
3. Multiply or Divide from left to right.
4. Add or Subtract from left to right
Evaluate the expression.
1. 8 + 2 · 5 2. 40 ÷ 8 – 7 3. 5 · 42 ÷ 8
4. 1 – 7 + 52 5.
6. (12 – 8)2 ÷ 25
7. 4 · 32 8. 10 ÷ 5 · 2 9. 32 ÷ 8 + 2 · 82
10. 4(3 + 8) – 82 ÷ 32 11. 10(3 – 6)3 + 41 12. (2-5)2 – (4·5)2
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2
Factor the following polynomials completely:
Formulas: Difference of 2 squares: a2 – b2 = (a + b) (a – b)
Sum of 2 cubes: a3 + b3 = (a + b) (a2 – ab + b2)
Difference of 2 cubes: a3 - b3 = (a - b) (a2 + ab + b2)
1) b 2 + 8b + 7 2) n 2 − 11n + 10 3) m 2 + m – 90 4) n 2 + 4n – 12
5.) n 2 − 10n + 9 6) b 2 + 16b + 64 7.) 2n2 + 6n − 108 8.) 5n 2 + 10n + 20
9.) 2n2 + 3n – 9 10.) 5n2 + 19n + 12 11.) 4n 2 − 15n − 25
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12) 4x2 − 35x + 49 13) −6a2 − 25a – 25 14) 16b2 + 60b – 100
15) 36k2 − 1 16) p2 – 49 17.) 3n2 − 75 18.) 25 – m2
19.) 9x 2 − 16y2 20.) 4x 2 − 4x + 1 21.) 3 + 6b + 3b2
22) 2x4 + 22x3 + 56x2 23.) x3 – 64 24.) 27 + 8x3
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Properties of Rational Exponents
Let a and b be real numbers and let m and n be rational numbers , such that the quantities in
each property are real numbers.
Property Name: Definition:
1. Product of Powers 1. am · an = am + n
2. Power of a Power 2. (am)n = amn
3. Power of a Product 3. (ab)m = ambm
4. Negative Exponent 4. a-m =
, a ≠ 0
5. Zero Exponent 5. a0 = 1, a ≠ 0
6. Quotient of Powers 6. am/ an = am-n, a≠ 0
7. Power of a Quotient 7. (
) m = am / bm , b≠ 0
Simplify completely. Use only positive exponents.
1) 2m2 ⋅ 2m3 2) m4 ⋅ 2m-3 3) 4r-3 ⋅ 2r2 4) 4n4 ⋅ 2n-6
5) 2k4 ⋅ 4k 6) 2x3 y-3 ⋅ 2x-1 y3 7) (x2)0 8) (2x2)-4
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5
9) (2x4 y-3)-1 10) 2 3
3 34 2h g h 11) 2 7
4 6 6 314a b a c
12) 36
2
r
r 13)
18 5
11 3
21
7
d e
d e 14)
4
6
3w
g
15)
342
4
d
e
16)
311 16
6 6
d f
d f
17)
1 427
18) 1 4
10
10 19)
1 55
5
6
9
20) 1
3 4 1 47 7
21.) 3 75 22.) 3 381 9 23.) 5
80
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6
Solve the following equations:
1. 8 43
t
2.
59
2
p
3. 3 2 60k k
4. 43 12 6p p 5. 28 8 13 35b b 6. 11 6 3 30j j
7. 12 5 3 2 17r 8. 3 2 5 2 16x x 9. 4 7 3x x
10. 8 2 3 12b b 11. 8 5 3 8 4h h h 12. 10 7 15 3g g g
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13. 3 4 4 5w w 14. 8 3 2 3 3 5 4 2g g g
Solve the following quadratic equations . Check your solutions.
Quadratic formula:
1. 2 6 5 0x x 2. 2 6 9 0x x 3. 2 25 0x
4. 2 4 12 0x x 5. 212 4x 6. 3x2
+ 5x = 8
7. 2 64g 8. 2
2 16y 9. 2 1 0x
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8
10. 26 4 2x x 11. 2x2 – x = 7 12. 24 3 1x x
Solve the following systems:
1. 10 2
4
y x
x y
2. 4 1
5
y x
x y
3. 11 4
3 2 0
y x
x y
4. 3 2
2 3
x y
x y
5. 4 5
3 9
x y
x y
6. 2 5 7
2 3 1
x y
x y
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9
7. 7
5 2 8
x y
x y
8. 7 6 9
5 2 19
x y
x y
9. 0
3 3 6
x y
x y
10. 2 2 8
4
x y
x y
11. 3
2 5
2 6
y
x y
x y z
Solve and check the following rational equations.
1.3 1
4 2x x
2.
4 6
2 2x x
3.
3 5
1 5
x
x x
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10
4.4 2
43 x 5.
4 1 1
5 5
x
x x x
6.
2
12 3 3
2 2x x x x
Perform the indicated operation:
1.4 2 3 2
4 5 3
54
9
x y x y
y x y 2.
3
4
2 1 3
1
x x x x
x x
3.
2 25 4 3
3
x x x x
x x
4.2 2
2 2
4 5 2 6
6 9 3 2
x x x x
x x x x
5.
4 9
7 5
28
2
x y y
y x
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6.2
4 3 3
6 3
3 6 6
x x x
x x x
7.
7 3
2 2
x
x x
8. 2
7 4
2 3x x 9.
2
14 6
7 18 9x x x
10. 2 6 1 3x x x 11. 23 11 4 1x x x
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12
Find f g x and f g x . Then evaluate f g and f g
for the given value of x.
1. 3 34 ; 9 4 ; 2f x x g x x x
2. 2 3 23 5 ; 6 4 ; 1f x x x x g x x x x
Find fg x and f
xg
. Then evaluate fg and f
g for the
given value of x.
;
4. 2 1 43 ; 5 ; 16f x x g x x x
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13
Logarithms
Rewrite the equation in exponential form.
1. 2log 8 3 2. 7log 7 1 3. 5log 25 2
Rewrite the equation in logarithmic form.
4. 24 16 5. 05 1 6. 1 16
6
Evaluate the logarithm.
7. 2log 16 8. 5log 125 9. 6log 6
10. 515
log 11. 9log 1 12. 218
log
Expand the logarithmic expression.
13. 2log 5x 14. 4log 7x 15. 6
2log
x
y
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14
Condense the logarithmic expression.
16. 7 7log 3 log 5 17. log 10 log 5
18. 3 ln 9 ln x y 19. 2 212
log 9 log y
Use the change-of-base formula to evaluate the logarithm.
20. 5log 3 21. 2log 11 22. 6log 10
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15
Solve the equation.
1. 7 2 36 6x x 2. 5 3 4x xe e 3. 1 33 9x x
4. 8 35x . 5. ln 3 8 ln 6x x 6. 3 3log 9 2 log 4 3x x
7. log 4 1 log 25x 8. 6log 5 4 2x
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16
Solve the equation. Check for extraneous solutions.
1. 2 2log log 3 2x x 2. 3 3log 3 log 2 1 2x x
3. ln ln 4 3x x 4. 26 6log 2 log 3 2x