Objectives for Precalc/Trig Summer Packet



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ACC PreCalculus & Trigonometry

Summer Review Packet

2017-2018

Name __________________

Supplies Needed For ACC PreCalc/Trig:

1. Graph Paper Composite Notebook

2. Folder

3. Graphing Calculator TI 83 or TI 84

4. Pencils

Objectives for ACC PreCalc/Trig Summer Packet

2017-2018

I. Equations and Inequalities ( Problems: # 1 – 10 )

[pic] Using properties of equality

[pic] Solve equations involving radicals

[pic] Identify identities, conditional, and inconsistent equations

[pic] Solving equations involving rational expressions

[pic] Solving equations involving absolute value

II. Equations and Graphs in two variables ( Problems: # 11 – 15 )

[pic] Using the distance and midpoint formulas

[pic] Using a graph to solve equations and show the intercepts

III. Quadratic Equations ( Problems: # 16 – 23 )

[pic] Solving quadratics by factoring

[pic] Using the quadratic formula

IV. Linear and Absolute Value Inequalities ( Problems: # 24 – 32 )

[pic] Using interval notation when solving linear inequalities

[pic] Solving compound inequalities

[pic] Solving absolute value inequalities

V. Functions ( Problems: # 33 – 38 )

[pic] Determining domain and range

[pic] Using function notation

VI. Solving quadratics by graphing ( Problem # 39)

• Graphing quadratic equations

• Finding zeros from a graph.

VII. Operations with Functions ( Problems # 40 – 44 )

[pic] Evaluating functions

[pic] Applying the sum, difference, product, and quotient functions

[pic] Calculating the composition of functions

VIII. Linear Functions ( Problems # 45 – 46 )

[pic] Writing equations in standard form given two points

[pic] Using the point-slope form of a line

[pic] Writing equations parallel and perpendicular to given lines

Directions: Complete each problem showing all work. You must show work

or explain your solution in order to receive credit for the

answer.

QUESTION HINT

Solve for x.

1. [pic] Multiply through by the common denominator.

2. [pic] Multiply through by the common denominator.

Solve each equation. Identify each equation as an identity, an inconsistent

equation, or a conditional equation.

3. [pic] If the variables cancel out and

the statement is true - identity

Solution: all real numbers

4. [pic] Clear fractions

5. [pic] Cross Multiply

QUESTION HINT

6. [pic] Multiply by common

denominator

7. [pic] Multiply all terms by the Common denominator

8. [pic] Mult. by common denominator

then distribute

Solve each absolute value equation. Write your answer as a solution set.

9. [pic] Isolate the absolute value

Remember two cases

10. [pic] Isolate the absolute value

Remember two cases

QUESTION HINT

For each pair of points, find the distance and midpoint between them.

11. [pic] Use the distance and midpoint

formulas

12. [pic] Use the distance and midpoint

formulas

Sketch the graph of each linear equation. Please find the x and y

intercepts.

13. [pic] Set x and y equal to 0

[pic]

QUESTION HINT

14. [pic] Set x and y equal to 0

[pic]

15. Graph y = 3 and x = -2 on the same graph.

[pic]

Solve each equation by using the square root property

Find all real solutions.

16. x[pic]-9 = 0 Isolate x[pic] and take the

Square root of both sides

17. (x-1)[pic] = 9 Take the sq. root

18. (x-3)[pic] + 8 = 0 Move 8 to other side and

Take the square root

Solve each equation by factoring.

19. [pic] Set quadratic equal to 0,

then factor.

20. [pic] A times C long factoring

Or use “slipe and slide"

21. [pic] A times C long factoring

Or use “slipe and slide"

Solve each equation using the quadratic formula. Simplify radical answers.

22. [pic] [pic]

23. [pic] [pic]

QUESTION HINT

Solve and graph each inequality. Write your answer in interval notation.

24. [pic] Clear fractions

25. [pic] Change the inequality

When multiplying by a negative

26. [pic]

Solve and graph each inequality. Write your answer in interval notation.

27. [pic] Solve each inequality

separately

28. [pic] “ and “ intersection of

Both

“ or “ include all answers

29. [pic] “ and “ where graphs overlap

QUESTION HINT

Solve and graph each inequality. Write your answer in interval notation.

30. [pic] Two cases; [pic] Solve for x.

31. [pic] Two cases; [pic]

32. [pic]

.

QUESTION HINT

[pic]

33. [pic] Plug (-4) into the “ f “ function

34. [pic] Evaluate the “ g “ function 1st, then use its value in the “ k “ function

35. [pic] Evaluate the “ g “ function first then use its value in the “f” function

Determine the domain and range. Write your answer in interval notation.

36. [pic]

[pic]

37. [pic] Remember domain lists all the

possible values for “ x “

38. [pic] Range lists all possible values

for “ y “

QUESTION HINT

Solve the quadratic equation by graphing.

39. [pic] Find the vertex ([pic] )

Make a table and graph.

Find the zeros from the

x-axis.

[pic]

Find the following functions.

a) f + g b) f – g c) f [pic] g d) f/g

40. [pic] Add, subtract, multiply,

and divide the functions

41. [pic]

QUESTION HINT

Suppose that [pic]

42. [pic] Substitute 1 into the f function

then use this calculated value in

the g function

43. [pic] Work right to left

44. [pic]

QUESTION HINT

45. Find an equation for the line that contains the point ( 2, -3 ) and is

parallel to the line 2x + y = 6 .

Use y = mx + b

46. Find an equation of the line that contains the point ( 1, -2 ) and is

perpendicular to the line x + 3y = 6 .

Graph the two lines on the graph below.

HINT – Change to y = mx + b

Then use the negative reciprocal

Slope along with the given point to

Substitute for x, y, and m

[pic]

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