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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