PENNCREST HIGH SCHOOL SUMMER REVIEW PACKET

For students ENTERING Geometry (ALL LEVELS).

Name: __________________________________________________________ Assigning Teacher: 1. This packet is to be handed in to your Geometry teacher on the first day of the school year. 2. All work must be shown in the packet OR on separate paper attached to the packet. 3. Completion of this packet is worth 50 points (or one-half of a major test) and will be counted

in your first marking period grade.

Chapter 1 Evaluate the expression for the given value of the variable. 1. 4n when n = 2 __________ 2. 4.8w when w = .06 __________ 3. 16 divided by x when x = 4 ___________ 4. 62 divided by x when x = .6 ____________ 5. 16.8n when n = 3 ___________ Evaluate the expression for the given value of the variable. 6. 3ⁿ when n = 4________ 7. (9x)2 when x = 1 ________ 8. 8 + 4a when a = 7 _________ Evaluate the expression for the given values of the variable. 9. x + y2 when x = 5 and y = 4 __________ 10. (a-b)3 when a = 5 and b= __________ Evaluate the expression. 11. 48 + 1 ÷ 7 × 7 ___________ 12. 4 ÷ 2 + 5 – 4 ___________ Check whether the given number is a solution. 13. 10x – 4 ≤ 16 ; x = 2 ___________

Chapter 2 Write the numbers in increasing order. 1. 3.5,3.6,2.6,32.5,04.5,31.5 −− 2. 02.0,2.0,0.2,0,2.0,03. −−−

3. 21,

213,6.1,6.2,8.4 −−−−

4. 214,1.5,5,1.4,4.3,

213 −−−

5. 07.6,02.6,11.6,1.6,08.6,03.6 −−−− Evaluate the expression. 6. 7 7. 5.4− 8. 66 +−

9. 1.3−− 10. 63

32 −+ 11. 01.61.6 −−

12. 3511+− 13. 146 − 14. 811−− 15. 8.95.12 −

16. 7.12.3 −− 17. )49(

43 −− 18.

41

109 −− 19. 7)4(2 −−−−

20. 3)12(8 +−−− 21. )2.16(9.35.8 −+−− 22. )81()

43(

127 −+−−

Evaluate the function for these values of x: -2, -1, 0, 1. Organize your results in a table. 23. 8−= xy 24. 1.12+−= xy Write an equation and solve. A landscaping company had a loss of $512.55 in March. It then had a profit of $294.21 in April, a profit of $498.97 in May, and loss of $187.81 in June. Did the company make a profit or loss money during the four-month period? Chapter 3 Solve the equations for x. 1. x - 12 = -3x 2. 23 + x = -35 - x 3. -21 = x (15)

4. 412

=−x 5.

615

2=x 6. 2212

23 −=−x

7. -2(4 - x) - 3 = 5 8. 16 = 2(1 - x) 9. x - 4(2 + 5x) = -2 10. 3x + 24 = -3 11. 9(-2 - x)=-10 - 2x

Solve the equations for x.

12. )6(4)93(32 +=− xx 13.

61525.425.15.2 ==+ x

Solve each equation for the indicated variable. 14. 2x + y = 4 solve for x 15. bwhV = solve for w

16. xy−=− 2

5 solve for y 17. lwP 22 += solve for w

Write an equation and solve. 18. You earn $260 in 40 hours. At this rate, how much do you earn in 75 hours? 19. Convert $240 American to Canadian. ($1 US = $1.40 Can.) 20. One tomato plant is 12 inches tall and grows 1.5 inches per week. Another tomato plant is 6 inches tall and grows 2 inches per week. When will the plants be the same height?

Chapter 5 Write an equation of the line with the given slope and y-intercept. 1. m = 1 b = -4 2. m = 2 b = -4 Write an equation of the line that passes through the point and has the given slope. 3. m = -1; (5, 2) 4. m = 2; (1, 4) 5. m = -3; (5, 4) Write the slope-intercept form of an equation of the line that passes through the points. 6. (2, 8), (-1, -1) 7. (2, -5), (-3, 6) 8. (0, -4), (3, 3) 9. (-4, -5), (1, 7) 10. (-4, 1), (6, 8) 11. (-1, -2), (2, 6) Write an equation of the line shown in the graph. 12. 13.

-10 10

10

-10

-10 10

10

-10

Chapter 6 Solve the inequality and graph its solution on a number line. 1. 72 <+x 2. 113 −≤+− x 3. 6.134.3 <x

4. 2

5 x−≤

5. 1424 ≥−− x 6. 485 <−<− x 7. 1234 −>−− xx 8. )7(23 −≤+ xx 9. 3018410 ≤−−≤− x 10. 19510 63 −<−+<− xorx 11. 12142xor 32 <+−<− x 12. A person must be at least 52 inches tall to ride to Power Tower ride at Cedar Point. Write

and inequality that describes the required heights. 13. The lowest temperature recorded was –128.6 degrees in Antarctica. The highest temperature recorded was 136 degrees. Write a compound inequality whose solution includes all of the other temperatures ever recorded.

Chapter 7 Use substitution to solve the linear system.

1. 721422

+−==+xyyx

2. 2222676

−==+

xyyx

Use linear combinations to solve the linear system.

3.2354338−=+

=+yxyx

4. 2845483

=+−=−

yxyx

Solve the following systems using any of the three methods.

5. 323434

−=+−=−

yxyx

6. 2185456

=−−=+

yxyx

7. 4264

−==+

xyyx

8. 089=+−=yxxy

Chapter 8 Simplifying Exponential Expressions Simplify the following exponential expressions so that the following terms have the smallest possible exponential expression. 1. 2x-2y3z xyz2 2. (1/(27x3))-1/3

3. (8xyz/16abc)0 4. (1/4)-3 5. (3-2x-2y)*(9xz) xyz

11

2

)2x4x-( −

− 6.

1)65( − 7.

)xx( 0

5-3x 8.

232

)xy2x( y 9.

02

3

).(yxxyy

xy3x3 −

10.

Algebra I Chapter 9 Test Simplifying radicals. 1. 98 2. 40 3. 175 4. 287

5. 9052 6. 32

41 7. 28 ⋅ 8. 6128 ⋅

9. 510 ⋅ 10. 1919 ⋅ 11. 327 ⋅ 12. 3635 ⋅

13. 6441 14. 1213 15. 232 16. 6124

17. 9322 18. 5210 19.

25 20. (2 50 )(3 2 )

Solve the equation by finding square roots. Solve for x. 21. 9009 2 =x 22. 531116 2 =−x 23. 9688 2 =x Use the vertical motion model to answer the following.

24. Jimmy is trying to play basketball after school one day. He decides to try and dunk the ball, but he needs to jump 2.2 feet. If his initial velocity is 15.5 feet per second…..

a. Set up the equation. b. See how much hang time he has. c. Can he dunk the ball?

25. If Rob takes a face-off in Monday night’s game, he may need to take a face-off. If the official drops the puck from 3 feet, how long will it take to hit the ice?

a. Set up the equation. b. Solve.

Chapter 10 Add or subtract the following polynomials to combine all like terms. 1. (x2 − 4x + 3) + (3x2 − 3x − 5) 2.(−x2 + 3x − 4) − (2x2 + x − 1) 3. (x3 + 5x2 − 4x) − (3x2 − 6x + 2) 4. (4x3 + x2 − 1) + (2 − x − x2)

Find the product. 5. 4x3(−x2 + 2x − 7) 6. (x + 3)(x − 11) 7. (4x − 1)(3x + 8) 8. (2x − 5)(x + 5) 9. (x + 5)(x + 3) 10. (x + 6)(x2 − 6x + 2) Solving special products. 11. )3)(3( +− xx 12. 2)5( +x 2)43( +x 13. )56)(56( +− xx

14. 2)54( −x Use the zero product property to solve the equation. 16. 0)1)(4( =−+ xx 17. 0)3( 2 =+x

18. 0)126)(84( =+− xx Use the zero product property to solve the equation. 19. 0)123)(82( =++ xx 20. 0)43)(93(7 =−+ xx 21. You are designing a calendar as fund-raising project. The cost of printing is $750, plus $4.50 per calendar. You sell the calendars for $7.00. a) Write an equation to model the total cost of printing the calendars. b) Write an equation to model the total income for selling the calendars. c) Graph both equations and state the significance of their intersection. Factor the trinomials. 22. x2 − 6x + 9 = 0 23. x2 − 13x + 40 = 0 Factor the trinomials. 24. x2 − 3x − 4 = 0 25. 012132 =++ xx 26. x2 − 29x = 170 27. x2 + 26x = −25

28. x2 − 11x = −18 Factor the trinomials. 29. x2 − 20x = −51 30. x2 − x − 8 = 82 31. 5x2 − 9x = 2 32. 05163 2 =++ xx 33. 02116 2 =−− xx 34. 0295 2 =−− xx 35. 035274 2 =++ xx 36. 010116 2 =−− xx 37. 044373 2 =+− xx Chapter 11 Solve the proportion.

1. x12

416 = 2.

37

24 =x

3. 18

36

−+= x

4. 25

36 −=+ xx 5.

1010

42 +=− xx 6.

xx

x1

32 −=

Solve the proportions.

7. xx

x4

15 =+

8. 22

4196

2 +−=xx

Solve the percent problems. 9. What number is 25% of 80? 10. 18 is what percent of 60? 11. 14% of 220 is what number? 12. 42 feet is 50% of what length? 13. 85% of 300 is what number? 14. 55 years is what percent of 20 years? 15. 9 people are what percent of 60 people?