Algebra Entering Geometry: Summer Learning

Name _________________________________________________________ Date __________

Solve the equation. Check your solution.

1. 14 5x + = − 2. 3 2 4x x− = −

Solve the equation.

3. 3 4 8 10 53n− + + = 4. ( ) ( )23 3 4 3 8 1b b− = − − − − +

Describe the values of c for which the equation has no solution.

5. 3 3 8x c x− + = − + 6. 3 x c− + =

Write the sentence as an inequality.

7. The quotient of n and 3 is less than 5.

8. 10 more than y is greater than or equal to 17.

Solve the inequality. Graph the solution.

9. ( )3 3 1 x− ≤ − − 10. 3 2 1 2x− + + ≤ −

Write and graph a compound inequality that represents the numbers that are not solutions of the inequality represented by the graph shown.

11.

12.

Determine whether the relation is a function. If the relation is a function, determine whether the function is linear or nonlinear.

13. 14. ( )21y x= − +

x −3 0 3 6 9

y −3 −4 −5 −6 −7

Write an equation in slope-intercept form of the line with the given characteristics.

15. through: ( )3, 1 , slope 2− =

16. through: ( ) 343, 4 , perpendicular to 5y x− − = − +

Name _________________________________________________________ Date __________

Write an equation in point-slope form of the line with the given characteristics.

17. through: ( ) ( )1, 3 and 2, 5− −

18.through: ( ) 164, 4 , parallel to 2y x= − +

Graph the equation and identify the intercept(s). If the equation is linear, find the slope of the line.

19. 2 5 10x y+ = 20. 2 1 4y x= − −

Graph f and g. Describe the transformations from the graph of f to the graph of g.

21. ( ) ( ); 3 2f x x g x x= = − + 22. ( ) ( ); 2 1 1f x x g x x= = − − +

Graph the function. Describe the domain and range.

23. ( )23 , if 3

6, if 3

x xf x

x

⎧− <⎪= ⎨⎪ ≥⎩

24.

, if 33, if 3 2

3 6, if 2

x xy x

x x

≤ −⎧⎪

= − − < <⎨⎪ − ≥⎩

Name _________________________________________________________ Date __________

Solve the system of linear equations using any method.

25. 2 6 142 7x yx y+ =

− = −

26. 6 194 4 12x y

x y− = − +

= − −

Graph the system of linear inequalities.

27. 13

1

3

y x

x y

≥ +

+ ≥ −

28. 4 13

x yy

− ≤ −

< −

Evaluate the expression. Round to the nearest hundredth, if necessary.

29. 6 100 30. ( )1 436 31. ( )4 327−

Simplify the expression. Write your answer using only positive exponents.

32. 3 7x x−• 33. 3 2

4 224w zw z

− −

− 34.

32

143aab

−

−

⎛ ⎞− −⎜ ⎟⎝ ⎠

Solve the equation. Check your solution.

35. 1 1416 r− − = 36. 2 364 1x− + =

Find the sum or difference. Then identify the degree of the sum or difference and classify the polynomial by the number of terms.

37. ( ) ( )2 23 6 4 8x x x x+ + − 38. ( ) ( )3 4 43 7 8x x x x+ + − − +

Find the product.

39. ( )( )5 3c c− − 40. ( )( )2 7 7 4a a+ − 41. ( )( )2 1 2 1x x+ −

Factor the polynomial completely.

42. 3 23 3b b b− + − 43. 2 20n n− + + 44. 22 17 21x x− +

Solve the equation.

45. ( )( )( )2 3 1 8 2 0x x x x− + − + = 46. 24 3 13k k+ = −

Name _________________________________________________________ Date __________

Solve the equation using any method.

47. 23 54x− = − 48. 2 8 7 0x x− + = 49. 23 2 4 0x x− − + =

Graph the function. Compare the graph to the graph of ( ) .f x x2=

50. ( ) 23 1g x x= − 51. ( ) ( )212 4h x x= +

Find the inverse of the function.

52. ( ) 142f x x= − − 53. ( ) 3 4f x x= + −

Graph the function f. Describe the domain and range. Compare the graph of f to the graph of g.

54. ( ) ( )2;f x x g x x= − + = 55. ( ) ( )3 34;f x x g x x= − =

Solve the equation. Check your solutions.

56. 8 2 16n − = − 57. 2 3 1v v= − 58. 2 4 12x x+ − =

Find the mean, median, mode, and range of the data set. Round to the nearest tenth, if necessary.

59. 60. 20.1, 30.5, 22.3, 19.7, 17.5, 32.1

Shoe Sizes

8.5 7.5 7 6

8.5 9.5 10 13

10 11.5 10 12

Topic Analysis

Item Number Skills Item

Number Skills

1 solving equations 25 solving linear systems 2 solving equations 26 solving linear systems 3 solving equations 27 graphing linear inequalities 4 solving equations 28 graphing linear inequalities

5 number sense 29 evaluating rational expressions

6 number sense 30 evaluating rational expressions

7 writing inequalities 31 evaluating rational expressions

8 writing inequalities 32 simplify exponents 9 solving inequalities 33 simplify exponents 10 solving inequalities 34 simplify exponents

11 writing and graphing inequalities 35 solving exponential equations

12 writing and graphing inequalities 36 solving exponential equations

13 understanding functions 37 simplify polynomial expressions

14 understanding functions 38 simplify polynomial expressions

15 writing linear equations 39 simplify polynomial expressions

16 writing linear equations 40 simplifying polynomial expressions

17 writing linear equations 41 simplify polynomial expressions

18 writing linear equations 42 factoring 19 graphing linear equations 43 factoring 20 graphing linear equations 44 factoring

21 comparing linear transformations 45 solving quadratics

22 comparing linear transformations 46 solving quadratics

23 graphing piecewise functions 47 solving quadratics

24 graphing piecewise functions 48 solving quadratics

49 solving quadratics

Topic Analysis

Item Number Skills Item

Number Skills

50 graphing quadratics 56 solving radical equations 51 graphing quadratics 57 solving radical equations 52 finding inverses 58 solving radical equations 53 finding inverses 59 measures of center 54 graphing radicals 60 measures of center 55 graphing radicals