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

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

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

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?

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

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.

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

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

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

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

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

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

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 3

1

125 = 3 125 1

481 = 4 81

Simplify the following. 24. 2

1

16 25. 3

1

27 26. 4

1

256 27. 2

1

36

Write as a rational exponent: 28. 121 29. 3 64 30. 4 16

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.

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

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

16

13) Proving Congruent Triangles

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. ________________________________

18

ANSWER

KEYS

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”

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

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

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 2

7x

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

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 4618 2 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

384 2 xx 22 778 pmpm

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 52 53 35 3106 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 3

1

125 = 3 125

1

481 = 4 81

Simplify the following. 24. 2

1

16 4 25. 3

1

27 3 26. 4

1

256 4 27. 2

1

36 6

Write as a rational exponent: 28. 121 2

1

121 29. 3 64 3

1

64 30. 4 16 4

1

16

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 9

11

30

11) 3f c 12) 7g w 13) 2 3f m 14) 2 3g x

39 2 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

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

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

35

13) Proving Congruent Triangles KEY

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 _____