Trigonometry
Central Bucks Math Department
Pre-Calc/Trig 3: Course Prerequisite Packet
I. Solving Equations.
Solve each of the following equations.
1) [pic] 2) [pic]
3) [pic] 4) [pic]
II. Solve the following proportions. Use the “cross product” method [pic]
5) [pic]
III. Use the coordinate plane to graph the following lines.
6) [pic] 7) [pic]
[pic] [pic]
IV. Writing Equations of Lines.
8. Write the equation of the line in slope-intercept form which has a slope of [pic] and passes through (6,4).
9. Write the equation of the line in slope-intercept form which passes through (6,1) and (8,-4).
10. Write the equation of the line (in slope-intercept form) that passes through (-2,0) and is perpendicular to the line whose equation is [pic].
V. Solve each system of equations using the substitution method or linear combination method:
11) [pic] 12) [pic]
VI. Factoring
A. Common monomial factor [pic]
B. Difference of Squares [pic]
C. Quadratic Trinomial (coefficient of [pic]equal to 1)
[pic]
D. Quadratic Trinomial (coefficient of [pic]not equal to 1)
[pic]
E. Sum/Difference of Cubes [pic]
F. Factoring by Grouping [pic]
Factor.
13) [pic] 14) [pic]
15) [pic] 16) [pic]
17) [pic] 18) [pic]
19) [pic] 20) [pic]
21) [pic] 22) [pic]
VII. Solve by factoring
A. Example: [pic]
Solution: First rewrite the equation so that one side is 0. Then factor.
[pic]
[pic]
Then set each factor to zero and solve (Zero Product Property)
[pic], therefore x = 6 and x = -1
Solve each equation by factoring:
23) [pic] 24) [pic]
25) [pic] 26) [pic]
27) [pic] 28) [pic]
VIII. FOIL
[pic]
Multiply:
29) [pic] 30) [pic]
31) [pic]
IX. Combining Like Terms
Combine like terms:
32) [pic] 33) [pic]
34) [pic] 35) [pic]=
X. Simplifying Radicals.
Express in simplest radical form(no decimal approximations). Remember: the expression cannot have a radical in the denominator!
36) [pic] 37) [pic] 38) [pic]
39) [pic] 40) [pic] 41) [pic]
IX. Using Properties of Exponents
[pic] [pic] [pic]
Simply each expression using properties of exponents:
42) [pic] 43) [pic] 44) [pic]
X. Complex Numbers
Multiply: Rationalize:
45) [pic] 46) [pic] 47) [pic]
XI. Solve each equation by using the quadratic formula: [pic]
48) [pic] 49) [pic] 50) [pic]
Piecewise Functions
[pic]
[pic]
Evaluate the piecewise function above:
51) [pic] 52) [pic] 53) [pic]
Sketch a piecewise function given the following:
54) [pic]
[pic]
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