Objectives for Precalc/Trig Summer Packet
[pic]
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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