Geometry/Algebra 2 Summer Math Packet

Over the summer to better to prepare you for the challenges of Algebra 2 next year, we have put together some

worksheets for you to complete over the summer. The packet will be due the first day back to school

in the fall. You will be assessed on this work. The purpose of this packet is to keep fresh in your mind the skills you have learned in mathematics so far.

There are 7 sheets to be completed and about 10 weeks to do them in. We do not suggest that you try to do all of

this in one sitting, nor should you try to complete is all the first week or last week of summer vacation!

The worksheets cover the following topics:

Review Sheet 1 – Solving equations and inequalities

Review Sheet 2 – Linear equations including slope, y = mx+b

Review Sheet 3 – Systems of equations and inequalities

Review Sheet 4 – Polynomials, adding, subtracting, distributing/FOIL, factoring

Review Sheet 5 – Quadratics

Review Sheet 6 - Radicals

These are all topics that have been taught in previous years and which should be familiar to you. If you have

forgotten the material or are unsure if you learned the material, we expect you to take the time and search for a

youtube.com video or other video which will refresh your memory about the material.

The assignment will count towards your homework average for the first quarter in your Algebra 2 class. You

will be tested on the information from the packet during the first week of school. The assignments stress

some of the more important skills you have learned to date and the foundations for what we will be working on

next year.

We hope you have a wonderful summer! See you in the fall.

Review Sheet 1: Solving Equations and Inequalities.

DIRECTIONS: Solve for x. Graph the inequalities. SHOW WORK.

1) 12 15 8 5 7(18 4 )x x x 2)

314 1

2x

3) 5

4 86

x

4) 2 14

16 25

x

DIRECTIONS: Solve for x. SHOW WORK.

5) 3 (6 15 ) 12(6 4) 3 4x x x x 6) 4 10 14 17 6(3 5)x x x

7) 2 1 2 1

(3 4 )3 7 5 4

x x 8)

3 2 6

5 11

x

x

9) 15

7x 10)

3

4(𝑥 − 9) − (4 + 5𝑥) > 11 − 7𝑥

Review Sheet 2: Linear equations including slope, standard form, slope intercept, point slope form

DIRECTIONS: For 1-4, find the slope of the line containing the given points. SHOW WORK.

1) ( 2,5),(6, 1) 2) (4, 15),( 9, 11)

3) ( 7, 11),( 7,4) 4) (8,4),( 1,4)

DIRECTION: For 5-10, write the equation of the line under the given circumstances. Write the equation of

the line in whichever form is asked in the question. SHOW WORK.

5) slope = -4, passes through (-7,5) 6) passes through (12, -4), (-6, 7)

(answer in Slope-intercept Form) (answer in Standard Form)

7) passes through (8, -3), (8, 5) 8) Is parallel to 8 3y x and passes through (5,-2)

(answer in Slope-intercept Form) (answer in Standard Form)

9) Is perpendicular to 5 2 19x y and has the same x-intercept as 6 27y x . Answer in Slope-intercept

Form.

10) Is parallel to 5 7( 1)y x and has the same y-intercept as 8 3 17x y . Answer in Standard Form.

11) The point (3, y) is on the line which passes through the points (5, - 3) and (2, 9). Find the value of y.

DIRECTIONS: For 12-15, Determine the slope and y-intercept for each line. Also, graph the line. SHOW

WORK.

12) 5

47

y x

13) (-5, 8), (-2, 2)

y

x

10

10

-10 -10

y

x

10

10

-10 -10

14) 5 4( 3)y x

15) 3 5 9x y

16) 4 – 5y = 2x + 7

y

x

10

10

-10 -10

y

x

10

10

-10 -10

Review Sheet 3: Systems of Equations and Inequalities.

DIRECTIONS: Solve the system for x & y. SHOW WORK.

1) 4 2

3 2 1

y x

y x

2) 4 2 34

10 4 5

x y

x y

3)

13

3

82 3

3

x y

x y

4)

6 4

3

2 4

y

x

y x

5) 5 3( 7) 11

18 3 4 3

x y

y x x

DIRECTIONS: Solve the system of inequalities by graphing.

SHOW WORK.

7)

25

3

3 2 6

y x

x y

8) – –1

2 + 2 10

x y

x y

9) 5

2

y

x

y

x

10

10

-10 -10

y

x

10

10

-10 -10

y

x

10

10

-10 -10

Review Sheet 4: Polynomials.

DIRECTIONS: Simplify each expression. SHOW WORK.

1) Combine like terms for 2 2 23 9 7 12x x x x

2) Multiply 3 4 2 9x x

3) Multiply 2

2 9x

4) Multiply 25 7 6 4x x x

5) Simplify 24 3 3 9 8 (3 1)(7 5)x x x x x

6) Subtract: 2 2(13 5 6) (14 3 2)x x x x

DIRECTIONS: Factor the following expressions.

7) 2 10 24x x 8) 28 29 12x x

9) 249 64x 10) 216 8 1x x

Review Sheet 5: Quadratics.

DIRECTIONS: Solve each of the following. SHOW ALL WORK.

1) 2 8 7 0x x

2) 2 25 0x

3) 23 33x x

4) 212 8 2 3x x x

5) 28 5 4x x

6) 29 6 1x x

7) 6x2 – 10x = 3x – 5 8) 3x2 + 10x + 1 = 0

9) 12𝑥2 + 7𝑥 − 10 = 325 10) (𝑥 − 5)2 = 36

11) (2𝑥 + 1)2 + 10 = 59 12) 4𝑥2 + 5𝑥 + 11 = 18

13. What is the equation of the axis of symmetry of the function 𝑓(𝑥) = 6𝑥2 − 18𝑥 − 17? ____________

14. What are the coordinates of the vertex of the graph of the function 𝑦 = −𝑥2 + 6𝑥 − 11 ? _________

15. A golf ball is driven in the air toward the hole from an elevated tee with an upward velocity of 160 ft/s.

Its height h in feet after t seconds is given by the function ℎ = −16𝑡2 + 160𝑡 + 2.

a) How long will it take for the golf ball to reach its maximum height? ___________

b) What is the ball’s maximum height? ___________

c) Find the equation of the axis of symmetry. ___________

d) What is the elevation of the ball at the elevated tee (before the ball is hit)? ___________

e) Approximately how long is the ball in the air? ___________

f) What is the range of the function? ___________

16. Find the coordinates of the x-intercepts of the following functions.

a) 𝑓(𝑥) = 𝑥2 − 196 b) 𝑓(𝑥) = 7𝑥2 − 1008

For each of the following, graph the functions. Find and label the axis of symmetry, vertex and y-intercept.

17. 𝑓(𝑥) = −1𝑥2 + 3𝑥 − 9 18. 𝑓(𝑥) =3

7𝑥2 − 12𝑥 + 11

19. A triangle and a square have the same area. The triangle has a base of 28 cm and a height of 24 cm. Find

the length of one side of the square to the nearest tenth if necessary.

20.

Review Sheet 6: Radicals

1. a. Find the perimeter of the rectangle at the right. _____________

b. Find the area of the rectangle at the right. ______________

Short Answer. Show all work.

2. The coordinates of the midpoint of segment RS is (6, - 10) and the endpoint of S has coordinates

(- 12, 15). Find the coordinates of R.

R ( , )

3. Find the length of the missing side in simplest radical form.

4. The sides of a triangle are 29, 11 and 44. Is the triangle right, acute or obtuse? _________

Explain why. ____________________________________________________________________

5. Given M(3, - 8) and N(- 17, 5)

A) Find the coordinates midpoint of MN.

B) Find the length of MN

7√2

X

5√8

3√8

7 + 2√5

3√5

6. M is the midpoint of AB. If M(-3, 12) and A(5, - 17), then find the coordinates of B.

7. Find the distance between the points ( - 4, 8) and ( -12, -10).

8. An umbrella is to be packed in a box. The box is 10 inches wide,

by 6 inches long by 8 inches high. What is the maximum length of an

umbrella that can fit in the box?

9. Find the coordinates of the midpoint of the segment with the given endpoints.

( 𝟑√𝟏𝟑 , −𝟐

𝟑) ( −𝟏𝟐√𝟏𝟑 ,

𝟏

𝟐 ). (do not give decimal answers)