-
Summer Math Packet (revised 2017)
In preparation for Honors Math III, we have prepared a packet of
concepts that students should know how to
do as 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 on some of
the problem sets where it is noted. Honors Math
III builds on the concepts in this packet, and we start teaching
Math III 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 Honors Math III. Although
you do not have to complete every problem in this packet, you
will be held responsible for knowing how to
complete them all and the content/skills used.
Answer keys are included at the end of this packet to check your
understanding. If you are struggling with any
content from this packet, get help from a friend, parent, peer,
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 or from Reagan’s
Student Services’ website. Keep in mind these tutors may charge
a fee. You can also go to youtube.com and
type in the name of the concept and watch videos of math
teachers and tutors explain the concepts for FREE!!!!
You will have a graded assignment within the first two weeks of
school. The graded assignment will cover the
concepts/skills in the packet, but will not have the exact same
problems. The graded assignment will contain a
calculator inactive part so be prepared by following
instructions where calculators are not allowed. You will be
able to use your packet with completed problems as a resource on
the assessment at the beginning of the year so
it is in your best interest to complete as needed. The packet’s
answer key section may not be used on the graded
assessment.
TABLE OF CONTENTS:
1) Vocabulary & Important Things to Remember page 1 (KEY p.
19-20)
2) Operations with Fractions page 2 (KEY p. 21)
3) Solving Equations & Inequalities page 3 (KEY p. 22)
4) Linear Equations page 4 (KEY p. 23)
5) Graphing Linear Equations & Inequalities page 6 (KEY p.
25)
6) Systems of Equations page 8 (KEY p. 27)
7) Laws of Exponents page 10 (KEY p. 29)
8) Polynomial Operations page 11 (KEY p. 30)
9) Radicals & & Rational Exponents page 12 (KEY p.
31)
10) Using Function Notation (with numbers & variables; word
problems) page 13 (KEY p. 32)
11) Solving Quadratic Equations (Quadratic Formula, Factoring,
page 14 (KEY p. 33)
Square Root Property & Completing the Square)
12) Using Midpoint & Distance Formulas page 15 (KEY p.
34)
13) Proving Congruent Triangles page 16 (KEY p. 35)
14) Transformations (using absolute value graphs) page 17 (KEY
p. 36)
15) ANSWER KEYS page 18
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1
1) Vocabulary/Know the Difference Review
1. Proportions vs. multiplying fractions
Proportion Multiplying Fractions
12
82
x vs.
12
8
3
2
2. x * x = ? vs. x + x = ?
3. order of operations: don’t be tricked by these common
“mistaken identities”
a. 5 * 23 vs. (5 * 2)3 b. 5 + 3(x + 4) c. -82 vs. (-8)2
4. (x – 9)2 vs. (x + 9)2 vs. (x – 9)(x + 9) a. (x – 9)2 = b. (x
+ 9)2 = c. (x – 9)(x + 9) =
5. know the difference between a term, expression, equation, and
inequality term –
expression –
equation –
inequality –
6. know the difference between solve, evaluate and simplify
simplify –
evaluate –
solve –
7. know the difference between rational and irrational
rational –
irrational –
8. know the > and < symbols by name:
9. know coefficient –
10. know factor –
11. reduce factors not individual terms
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2
2) Operations with Fractions DO NOT USE A CALCULATOR
1) 9
4
3
2
2) 5
4
4
7
3) 6
1
4
3
4) 9
4
3
2
5) 5
4
4
7
6) 6
1
4
3
7) 9
4
3
2
8) 5
4
4
7
9) 6
1
4
3
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3
3) Solve Equations and Inequalities DO NOT USE A CALCULATOR
Clear out fractions.
1) 574
x
2) 7
32
x 3)
7
8
1
4
3
4
1
16a a a
Variables on both sides.
4) 3( x – 8 ) + 3( 2x + 4 ) = 15 5) 8 + 3( a – 3 ) = 4( a + 5 )
6) 6 – 2x + 5x = 7 + 7x – 15
Solve inequalities and graph your answer.
When you multiply or divide both sides by a negative remember to
flip the inequality. Get variable on the left.
7) 6 2 4x x
8) 2 6 6x x
Word Problems - You must be able to write the equation or
inequality first. Then solve for the variable.
9) The greater of two numbers is 6 more than 4 times the
smaller. Their sum is 41. Find the numbers.
10) Find three consecutive integers whose sum is 105.
11) Find three consecutive even integers whose sum is 138.
12) The length of a rectangle is 2 feet more than its width. If
its perimeter is 40 feet, find the length & width.
13) The second angle in a triangle is 3 less than twice the
first angle. The third angle measure 8 more than
twice the first angle. Find each angle.
14) Jeffery has grades of 93 and 81 on the 1st 2 tests of the
quarter. Progress reports go home after the 3rd test.
If Jeffery does not have an A average on his progress report, he
cannot go to the football game that week.
Jeffery will have to make at least what grade on the third test
to be allowed to go to the football game?
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4
4) Linear Equations: Slope, Writing Linear Equations, Horizontal
& Vertical, Parallel & Perpendicular
Find the slope (rate of change) of the following problems.
1. 8,3 , 1,5 2. 3.
4. The cost of museum tickets is $48 for four people and $78 for
10 people. What is the cost per person?
Write the equation of the line in slope-intercept form &
standard form given the following.
5. 2,5 3m 6. 5
4,2 7
m 7. 2, 6 1, 2 8. m = –2
1, b = 2
9. (2, -3) m = 0 10. (4, -1) m = undefined 11.
12. The cost for 7 dance lessons is $82. The cost for 11 lessons
is $122. Write a linear equation to find the
total cost C for L dance lessons. Then use the equation to find
the cost of 4 lessons.
Day Temperature
( F )
1 60
2 62
3 64
4 66
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5
13. Write the equation for a vertical line that goes through the
point (2, 4).
14. Write the equation for a horizontal line that goes through
the point (-1, 3).
Solve the equation for y if necessary, and find the slope. Then,
find the slope of a line parallel and
perpendicular to the original line.
SLOPE PARALLEL PERPENDICULAR
15. 2x + 6y = 8
16. x = 3
17. y = -2
Write the answers for 18-20 in slope intercept and standard
forms.
18. Write the equation for the line parallel to the given line
4x – 3y = 9 and and through the point (3, –1).
19. Write the equation for the line perpendicular to the given
line 4x – 3y = 9 and through the point (8, –3).
20. Given a line through (–2, 4) and (8, –1), find the equation
of the line perpendicular to that line through the
midpoint of those points.
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6
5) Graphing Linear Equations and Inequalities DO NOT USE A
CALCULATOR Graph each of the following lines.
1) slope:3
4 , through 5, 1 2) slope: 2, through 3, 4 3) slope:
1
4, y-intercept: – 5
4) slope: 3 , x-intercept: 4 5) 2
43
y x 6) 5 2y x
7) 5
63
y x 8) 3 5y x 9) 2
7y x
10) 5 2x y 11) 6 3 12x y 12) 4 2 0x y
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7
13) 3 15x y 14) 3 7 21x y 15) 3y
16) 4y 17) no slope; through (2, 5) 18) slope: 0 through (3,
–7)
Write each of the following in slope-intercept form: ( y mx b
)
19) A computer technician charges $75 for a consultation plus
$35 per hour.
20) The population of Pine Bluff is 6791 and is decreasing at
the rate of 7 per year.
21) A video store charges $10 for a rental card plus a $2 per
rental.
Graph each inequality. Remember to use either a solid or dotted
line, then SHADE.
22) y < x – 5 23) x > 3y 24) x < 4
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8
6) Systems of Equations
IF THE LINES INTERSECT ONCE, ANSWER IS THE ORDERED PAIR.
IF THE LINES DO NOT INTERSECT (PARALLEL), ANSWER IS .
IF THE LINES ALWAYS TOUCH (ARE THE SAME LINE), ANSWER IS
INFINITLY MANY.
Solve by graphing.
1)
62
42
1
xy
xy 2)
02
53
yx
yx
3) 5
843
y
yx 4)
2
425
x
yx
5) 1
2
yx
yx 6)
1864
932
yx
yx
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9
Solve using Substitution or Elimination.
7) x y
y x
4
2 1 8)
x y
y x
1
4 2
9) y x
y x
2 5
3 5 10)
yx
yx
22
2
11) x y
x y
3 4
2 7 12)
x y
x y
6
2
13) 642
32
yx
yx 14)
1534
023
yx
yx
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10
7) Laws of Exponents (negative exponents should always be
simplified)
(Remember: baba xxx ,
abba xx )( , ba
b
a
xx
x , 10 x and a
a
xx
1 )
1) 4 7 33 5a b a b 2) 2 2 2 43 5y y z yz 3) 3 2 2 2 3 4a b b c a
c 4) 04
5) 23 42 cc 6) 2 43 2 5x x x 7) abbcac 8) 04
9) 106
208
25
40
ba
ba 10)
710
1210
yx
yx 11)
313
63
14
22
yx
yx 12)
0)4(
13) 12 2
5 7
a b
a b 14)
1015
28
21
28
ba
ba
15)
3 15
13 6
27
9
x y
x y
16)
04x
17) 7
3x 18) 4
23x 19) 6
42x y 20) 3
42x
21) 9
6a 22) 3
84x 23) 3
5 74x y 24) 50 )2( x
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11
8) Polynomial Operations
Simplify.
1) 25 (6 3 2)x x x 2) 4 2 24 3 5ab ab a b 3) 2 26 (2 7 1)x x
x
4) 3 8x x 5) 2 4 2 3x x 6) 34 5 6x x
7) 2
5 2x 8) 2 23 1 8 8n n 9) 2 26 11 4 7w w w
10) 2 28 3 4 5 3x x x x 11) 2 2 2 25 2 6 3 5m mp p m mp p
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12
9) Radical & Rational Exponents
Simplify.
1. 100 2. 36 3. 121 4. 49 5. 8
6. 50 7. 45 8. 28 9. 80 10. 450
11. 400 12. 983 13. 236x 14.
27x 15. 218a
16. yx 220 17. 2100a 18.
272a 19. zyx 10620 20. 6201275 zyx
21. 125x 22. 5x 23. 35 x
Rational Exponents DO NOT USE A CALCULATOR
See these as examples of rational exponents: 1
225 = 25 31
125 = 3 125 1
481 = 4 81
Simplify the following. 24. 21
16 25. 31
27 26. 41
256 27. 21
36
Write as a rational exponent: 28. 121 29. 3 64 30. 4 16
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13
10) Using Function Notation
State whether each set is a function. Answer yes or no. Find the
domain and the range.
1) {(2, 5), (5, 6), (2, -6), (3, 8)} Domain: ______ Range:
______
2) {(1, -2), (8, -4), (-3, 8), (-1, 2)} Domain: ______ Range:
______
Use the vertical line test to determine whether each graph is
the graph of a function. Answer yes or no.
3) 4) 5) 6)
Use 2 3f x x and 4 1g x x to find each value.
7) 3f 8) 7g 9) 4
3f
10) 5 8f
11) 3f c 12) 7g w 13) 2 3f m 14) 2 3g x
15) The temperature of the atmosphere decreases about 5oF for
every 1000 feet increase in altitude. Thus, if
the temperature at ground level is 77oF, the temperature t at a
given altitude is found by using the equation
77 .005t h , where h is the height in feet.
a) Write the equation in function notation where t is a function
of h [f(x) is meant as f is a function of x].
b) Find t(100) and explain its meaning in this problem.
16) The function 160 1.5g x x models the weight gain of a
basketball player as he starts a workout program where g is the
weight in pounds after x weeks.
a) Explain the meaning of 160 in the context of this
problem.
b) Explain the meaning of 1.5 in the context of this
problem.
c) Evaluate 6g and explain its meaning.
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14
11) Solving Quadratic Equations Should be able to use: Square
Root Property
Factoring
(Remember when equation must be set = 0 before solving)
Completing the Square
[ ax2 + bx + c = 0 ] Quadratic Formula
Solve using Square Root Property: (best when only x2 term is
present or polynomial is squared)
1) 273 2 x 2) 9)23( 2 x
Solve using Factoring: (best when equation can be easily
factored; equation must be set = 0 to begin)
3) 9)3)(5( xx 4) 20)1)(8( xx
5) 72)1( xx 6) 524)5(2 xx
Solve using Complete the Square: (best when “b” is even but “a”
must be = 1 before using)
7) 01742 xx 8) xx 16562 2
Solve using Quadratic Formula: (this method always works but is
time consuming; set equation =0)
a
acbbx
2
42 9) 02263 2 xx 10) 0534 2 xx
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15
12) Using Midpoint & Distance Formulas
Midpoint Formula:
(𝑥1 + 𝑥2
2,𝑦1 + 𝑦2
2)
Find the midpoint of the segments with endpoints at the given
coordinates.
1) 1,10 and 15,4 2) 6,10 and 8,22
3) 20,30 and 10,3 4) 3.1,11 and 7.1,9
Distance Formula: 𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
Find the distance between each pair of points with the given
coordinates. Simplify radicals.
5) 4,1 and 7,3 6) 4,3 and 2,5
7) 9,16 and 5,11 8) 1,4 and 3,0
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16
13) Proving Congruent Triangles
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17
14) Transformations khxaxf ||)( DO NOT USE A CALCULATOR
How does the graph of || xy change to produce each of the
following graphs?
1. 5|| xy 1. _________________________________
2. |2| xy 2. _________________________________
3. |9| xy 3. _________________________________
4. ||4 xy 4. _________________________________
5. 3|| xy 5. _________________________________
6. ||3
1xy 6. _________________________________
7. 3|1| xy 7. _________________________________
8. |4|2 xy 8. _________________________________
9. 1||2
1 xy 9. __________________________________
Write the equation of the absolute value functions with the
following shifts:
10. Up 7 and left 3 10. ________________________________
11. Down 2, Reflects over x-axis, Vertical shrink of
3
1 11. _________________________________
12. Right 6, Vertical stretch of 2 12.
________________________________
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18
ANSWER
KEYS
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19
1) Vocabulary/Know the difference Review KEY
1. Proportions vs. multiplying fractions (cross multiplying for
a proportion vs. multiplying numerators and multiplying
denominators when
multiplying fractions)
Proportion Multiplying Fractions
12
82
x vs.
12
8
3
2
24 = 8x 9
4
36
16
)123(
)82(
3 = x
2. x * x = x2 vs. x + x = 2x
3. order of operations: don’t be tricked by these common
“mistaken identities”
a. 5 * 23 vs. (5 * 2)3 b. 5 + 3(x + 4) c. -82 vs. (-8)2 5 * 8 =
40 103 = 1000 5 + 3x + 12 not 8(x + 4) -1 * 64 = 64 (-8)(-8) =
64
4. (x – 9)2 vs. (x + 9)2 vs. (x – 9)(x + 9) a. (x – 9)2 = x2 –
9x – 9x + 81 = x2 -18x + 81 b. (x + 9)2 = x2 + 9x + 9x + 81 = x2
+18x + 81 c. (x – 9)(x + 9) = x2 + 9x – 9x – 81 = x2 – 81
5. know the difference between a term, expression, equation, and
inequality term – number, variable, or product of numbers and
variables (ex: 2, x, or 2x)
expression – terms with mathematical symbols (ex: 2x, 2x – 3, x2
– 4x + 3, 2
x)
equation – expressions set equal to one another (ex: x = 2, 4x +
3 = 12 – 5x)
inequality – expressions not equal to one another (ex: x > 2,
4x + 3 12 – 5x)
6. know the difference between solve, evaluate and simplify
simplify – to rewrite an expression in simplest form possible where
nothing else can be performed
(includes no parentheses or negative exponents; all fractions
have been reduced)
evaluate – to find the value of (once the value has been found,
the final result should be written in
simplest form) solve – to work out the solution to the
problem
7. know the difference between rational and irrational
rational – real number that can be written as a fraction (ex:0,
1, 3
1, 121 , 0.25) [repeating or
terminating decimals]
irrational – real number that can’t be written as a fraction
[nonrepeating, nonterminating decimals]
(ex: ...478192.2,,12 )
8. know the symbols by name: > as “greater than” vs. < as
“less than”
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20
9. know coefficient – numerical factor of a monomial [number
being multiplied by a variable]
10. know factor – two or more numbers that multiply to produce
another number [2 and 5 are factors of 10]
11. reduce entire factors not parts of a factor (individual
terms)
- you can reduce 12
510
x
x by rewriting the numerator in factored form first:
12
510
x
x=
5
12
125
x
x
- you can’t reduce 12
510
x
xby trying to reduce just
12
510
x
x
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21
2) Operations with Fractions DO NOT USE A CALCULATOR KEY
1) 9
4
3
2 =
9
10
2) 5
4
4
7 =
20
19
3) 6
1
4
3 =
12
11
4) 9
4
3
2 =
27
8
5) 5
4
4
7 =
5
7
6) 6
1
4
3 =
8
1
7) 9
4
3
2 =
2
3
8) 5
4
4
7 =
16
35
9) 6
1
4
3 =
2
9
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22
4
3) Solve Equations and Inequalities DO NOT USE A CALCULATOR KEY
Clear out fractions.
1) 574
x
2) 7
32
x 3)
7
8
1
4
3
4
1
16a a a
x = – 48 x = 17 a = 1/2
Variables on both sides.
4) 3( x – 8 ) + 3( 2x + 4 ) = 15 5) 8 + 3( a – 3 ) = 4( a + 5 )
6) 6 – 2x + 5x = 7 + 7x – 15
3x 21a 7
2x
Solve Inequalities and graph your answer.
When you multiply or divide both sides by a negative remember to
flip the inequality. Get variable on the left.
7) 6 2 4x x
8) 2 6 6x x
10x 4x -10
Word Problems - You must be able to write the equation or
inequality first. Then solve for the variable.
9) The greater of two numbers is 6 more than 4 times the
smaller. Their sum is 41. Find the numbers.
4164 xx 7 and 34
10) Find three consecutive integers whose sum is 105. 10521 xxx
34,35,36
11) Find three consecutive even integers whose sum is 138. 13842
xxx 44, 46, 48
12) The length of a rectangle is 2 feet more than its width. If
its perimeter is 40 feet, find the length and width.
22240 ww Length: 11 Width: 9
13) The second angle in a triangle is 3 less than twice the
first angle. The third angle measure 8 more than
twice the first angle. Find each angle.
1808232 xxx 35, 67, 78
14) Jeffery has grades of 93 and 81 on the first two tests of
the quarter. Progress reports will go home after the
third test. If Jeffery does not have an A average on his
progress report, he cannot go to the football game
that week. Jeffery will have to make at least what grade on the
third test to be allowed to go to the football
game?
105
933
8193
x
x
-
23
4) Linear Equations - Slope, Writing Linear Equations,
Horizontal & Vertical, Parallel & Perpendicular
KEY
Find the slope (rate of change) of the following problems.
1. 8,3 , 1,5 2. 3.
8
7
2 2
3
4. The cost of museum tickets is $48 for four people and $78 for
10 people. What is the cost per person?
$5 per person
Write the equation of the line in slope-intercept form &
standard form given the following.
5. 2,5 3m 6. 5
4,2 7
m 7. 2, 6 1, 2 8. m = –2
1, b = 2
13 xy 7
34
7
5 xy 24 xy 2
2
1 xy
13 yx 3475 yx 24 yx 42 yx
9. (2, -3) m = 0 10. (4, -1) m = undefined 11. 12
3 xy
3y 4x 223 yx
12. The cost for 7 dance lessons is $82. The cost for 11 lessons
is $122. Write a linear equation to find the
total cost C for L dance lessons. Then use the equation to find
the cost of 4 lessons.
52$
1210 LC
Day Temperature
( F )
1 60
2 62
3 64
4 66
-
24
13. Write the equation for a vertical line that goes through the
point (2, 4). x = 2
14. Write the equation for a horizontal line that goes through
the point (-1, 3). y = 3
Solve the equation for y if necessary, and find the slope. Then,
find the slope of a line parallel and
perpendicular to the original line.
SLOPE PARALLEL PERPENDICULAR
15. 2x + 6y = 8
3
4
3
1 xy
3
1
3
1 3
16. x = 3 undefined/none undefined/none 0
17. y = -2 0 0 undefined/none
Write the answers for 18-20 in slope intercept and standard
forms.
18. Write the equation for the line parallel to the given line
4x – 3y = 9 and through the point (3, –1).
53
4 xy 1534 yx
19. Write the equation for the line perpendicular to the given
line 4x – 3y = 9 and through the point (8, –3).
34
3 xy 1243 yx
20. Given a line through (–2, 4) and (8, –1), find the equation
of the line perpendicular to that line through the
midpoint of those points.
2
92 xy 924 yx
-
25
5) Graphing Linear Equations and Inequalities DO NOT USE A
CALCULATOR KEY
-
26
19) 35 75y x 20) 7 6791y x 21) 2 10y x
22) 23) 24)
-
27
6) Systems of Equations KEY
1)
62
42
1
xy
xy 2)
02
53
yx
yx
2,4 1,2
3) 5
843
y
yx 4)
2
425
x
yx
5,4 7,2 5)
1
2
yx
yx 6)
1864
932
yx
yx
infinitely many
-
28
7) x y
y x
4
2 1 8)
x y
y x
1
4 2 KEY
3,1 2,1
9) y x
y x
2 5
3 5 10)
yx
yx
22
2
3,4
11) x y
x y
3 4
2 7 12)
x y
x y
6
2
3,5 4,2
13) 642
32
yx
yx 14)
1534
023
yx
yx
infinitely many 45,30
-
29
7) Laws of Exponents KEY
1) 4 7 33 5a b a b 2) 2 2 2 43 5y y z yz 3) 3 2 2 2 3 4a b b c a
c 4) 04
41115 ba 6515 zy
646 cba 1
5) 23 42 cc 6) 2 43 2 5x x x 7) abbcac 8) 04
58c
730x 222 cba 1
9) 106
208
25
40
ba
ba 10)
710
1210
yx
yx 11)
313
63
14
22
yx
yx 12)
0)4(
14
10
5
8
a
b
5y 10
9
7
11
x
y 1
13) 12 2
5 7
a b
a b 14)
1015
28
21
28
ba
ba
15)
3 15
13 6
27
9
x y
x y
16)
04x
5
7
b
a 8
7
3
4
b
a 10
93
x
y 4
17) 7
3x 18) 4
23x 19) 6
42x y 20) 3
42x
21x
881x 62464 yx
128x
21) 9
6a 22) 3
84x 23) 3
5 74x y 24) 50 )2( x
54a
2464x 211564 yx 32
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30
8) Polynomial Operations KEY
Simplify.
1) 25 (6 3 2)x x x 2) 4 2 24 3 5ab ab a b 3) 2 26 (2 7 1)x x
x
3 230 15 10x x x
2 6 3 512 20a b a b 234 64212 xxx
4) 3 8x x 5) 2 4 2 3x x 6) 34 5 6x x
2 11 24x x
24 2 12x x 4 34 5 24 30x x x
7) 2
5 2x 8) 2 23 1 8 8n n 9) 2 26 11 4 7w w w
225 20 4x x 711
2 n 46182 ww
10) 2 28 3 4 5 3x x x x 11) 2 2 2 25 2 6 3 5m mp p m mp p
3842 xx
22 778 pmpm
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31
9) Radicals & Rational Exponents KEY
1. 100 2. 36 3. 121 4. 49 5. 8
10 6 11 i7 22
6. 50 7. 45 8. 28 9. 80 10. 450
25i 53 72i 54 215
11. 400 12. 983 13. 236x 14.
27x 15. 218a
20 221 x6 7x 23a
16. yx 220 17. 2100a 18.
272a 19. zyx 10620 20. 6201275 zyx
yx 52 a10 26a zyx 5253
353106 zyx
21. 125x 22. 5x 23. 35 x
6)5( x xx2
xx5
Rational Exponents
See these as examples of rational exponents:
1
225 = 25 31
125 = 3 125
1
481 = 4 81
Simplify the following. 24. 21
16 4 25. 31
27 3 26. 41
256 4 27. 21
36 6
Write as a rational exponent: 28. 121 2
1
121 29. 3 64 31
64 30. 4 16 41
16
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32
10) Using Function Notation KEY
State whether each set is a function. Answer yes or no. Find the
domain and the range.
1) {(2, 5), (5, 6), (2, -6), (3, 8)} no Domain: 5,3,2 Range:
8,6,5,6
2) {(1, -2), (8, -4), (-3, 8), (-1, 2)} yes Domain: 8,1,1,3
Range: 8,2,2,4
Use the vertical line test to determine whether each graph is
the graph of a function. Answer yes or no.
3) no 4) yes 5) yes 6) no
Use 2 3f x x and 4 1g x x to find each value.
7) 3f 8) 7g 9) 4
3f
10) 5 8f
6 29 911
30
11) 3f c 12) 7g w 13) 2 3f m 14) 2 3g x
392 c 294 w 6124
2 mm 88 x
15) The temperature of the atmosphere decreases about 5oF for
every 1000 feet increase in altitude. Thus, if
the temperature at ground level is 77oF, the temperature t at a
given altitude is found by using the equation
77 .005t h , where h is the height in feet.
a) Write the equation in function notation where t is a function
of h. [f(x) is meant as f is a function of x]
hht 005.77)(
b) Find t(100) and explain its meaning in this problem. 5.76
16) The function 160 1.5g x x models the weight gain of a
basketball player as he starts a workout program where g is the
weight in pounds after x weeks.
a) Explain the meaning of 160 in the context of this problem.
Starting/initial weight (y-intercept)
b) Explain the meaning of 1.5 in the context of this problem. #
of pounds added per week (slope)
c) Evaluate 6g and explain its meaning. 169; weight 6 weeks
after starting
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33
11) Solving Quadratic Equations Should be able to use: Square
Root Property KEY
Factoring
(Remember when equation must be set = 0 before solving)
Completing the Square
[ ax2 + bx + c = 0 ] Quadratic Formula
Solve using Square Root Property: (best when only x2 term is
present or polynomial is squared)
1) 273 2 x 2) 9)23( 2 x
x = 3, –3 3
1,
3
5x
Solve using Factoring: (best when equation can be easily
factored; equation must be set = 0 to begin)
3) 9)3)(5( xx 4) 20)1)(8( xx
4,6 x 4,3x
5) 72)1( xx 6) 524)5(2 xx
8,9x 3,9 x
Solve using Complete the Square: (best when “b” is even but “a”
must be = 1 before using)
7) 01742 xx 8) xx 16562 2
132 ix 324 ix
Solve using Quadratic Formula: (this method always works but is
time consuming; set equation =0)
a
acbbx
2
42 9) 02263 2 xx 10) 0534 2 xx
3
353
6
3106
x
8
713 ix
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34
12) Using Midpoint & Distance Formulas KEY
Midpoint Formula:
(𝑥1 + 𝑥2
2,𝑦1 + 𝑦2
2)
Find the midpoint of the segments with endpoints at the given
coordinates.
1) 1,10 and 15,4 2) 6,10 and 8,22
(7, 8) (6, −1)
3) 20,30 and 10,3 4) 3.1,11 and 7.1,9
(33
2, −15) (−10,
3
2 )
Distance Formula: 𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
Find the distance between each pair of points with the given
coordinates. Simplify radicals.
5) 4,1 and 7,3 6) 4,3 and 2,5
5 10
7) 9,16 and 5,11 8) 1,4 and 3,0
√41 4√2
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35
13) Proving Congruent Triangles KEY
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36
14) Transformations khxaxf ||)( DO NOT USE A CALCULATOR KEY
How does the graph of || xy change to produce each of the
following graphs?
1. 5|| xy 1. __________ up 5___________________
2. |2| xy 2. ________ left 2 ___________________
3. |9| xy 3. ________ right 9 ___________________
4. ||4 xy 4. ___ reflect over x-axis; vertical stretch _
5. 3|| xy 5. _________down 3 __________________
6. ||3
1xy 6. _______ vertical shrink ______________
7. 3|1| xy 7. ______ left 1; down 3 _______________
8. |4|2 xy 8. ___ vertical stretch; right 4 __________
9. 1||2
1 xy 9. _ reflect over x-axis; vertical shrink; up 1
Write the equation of the absolute value functions with the
following shifts:
10. Up 7 and left 3 10. _____ 7|3|)( xxf __
11. Down 2, Reflects over x-axis, Vertical shrink of
3
1 11. _ 2||3
1)( xxf __
12. Right 6, Vertical stretch of 2 12. _____ |6|2)( xxf
_____