Calculus Review

Trig (Sum/Dif/Laws)

100

cos45 cos15 + sin45 sin 15

√ 3/2

200

Sin105

(√6 + √2) / 4

300

A local airline does not offer direct connection from city A to city B. Rather, the flight travels 40 miles from city A to City C, the 70 miles from city C to city B. If m<ACB = 110, find the distance between city A and city B to the nearest mile.

92miles 

400

In triangle ABC, angle A= 30, angle C=45, and c=10. Find the exact value of "a" in simplest radical form. 

5√2

500

In Triangle ABC, a=12, c=8, m<B=60. Find the exact area of Triangle ABC.

48√ 3

Lines and Quadratics

100

Write the equation of the line parallel to the line 2x+3y=12 that passes through the point (4,-3).

2x+3y+1=0

200

Write the quadratic equation given the roots 7 and -4.

f(x)=x^2-3x-28

300

What is the equation of the line that passes through the point (-4,5) and is perpendicular to the line 4x+7=7? 

x-4y+24=0

400

Solve by using the quadratic formula and put solutions in a a+bi form. 5x^2-2x=-1

x=1/5±2/5i

500

Solve the given equation by completing the square method. x^2-8x=9

x=-1,9

Complex Fractions and Rational Equations

100

Simplify the following monomial divided by a monomial:    3x⁵y⁶/6x⁸y³

y³/2x³

200

Simplify the following monomial divided by a monomial:    20x¹⁰y⁸/4x²

5x⁸y⁸

300

Simplify the following monomial divided by a monomial:     7x³y/21x⁵y⁸

1/3x²y⁷

400

Simplify the following rational expression:  

x²+5x-14/x²-4

x+7/x+2

500

Simplify the following rational expression

4x²-1/10x-5

2x+1/5

Derivatives

100

Find the average rate of change over the stated interval. Given y=x^2+3

1 ≤x ≤3

4

200

Find the average rate of change over the stated interval. Given h(t) = 39.2t-4.9t^2

2 ≤x ≤4

9.8

300

Find an expression for the derivative of the function which is given: f(x)=3x^2-10x+3

6x-10

400

Find an expression for the derivative of the function which is given: f(x) = -10/x

10/x^2

500

Identify the critical points of each polynomial function f. Determine whether each critical points is a relative maximum or minimum. f(x)=2x^3-3x^2-12x

Max : (1,-13)

Min : (2,-20)

Properties of Exponents and Logs

100

Simplify the following:

(5x⁵)(-3x²)

-15x⁷

200

Simplify the following:

3x⁵/(2x)⁴

3x/16

300

Solve the following exponential equation:

4^2x+3=1

x=-3/2

400

Calculate the following log without a calculator:

log₂64

6

500

Solve the following log equation:

log(4x-2)=log(-5x+5)

7/9