Name:______Date:______

Calculus Pretest

I. Linear Equations

  1. Find the point-slope form of the equation of the line passing through the points (-1, 2) and (1, -2).

II. Solving Equations, finding zeros, roots of functions, factoring.

  1. Factor by grouping: 5cos2(x) – 5sin2(x) + sin(x) + cos(x)
  1. Factor over the set of real numbers: x2 + 5x + 5.
  1. Factor the polynomial:
  1. Solve for .

a.

b.

c.

  1. Solve the system for x and y:
  1. Solve for : (x + 1)1/2 + (x – 1)1/2 = 2

III. Families of Functions (Domain, Range, Asymptotes, Intercepts, Max, Min, Etc)

1.  Given the graph of , determine the domain, range, asymptotes and intercepts.

2.  Given the graph of g(x) = cos(2x + π /3), determine the domain, range, period, frequency, amplitude, and phase shift.

IV. Rules of Logs and Exponentials

1.  Solve for .

a.  3x+1 = 15

b. log(x-2) + log(2x-3) = 2log(x)

c. -14 + 3ex = 11

d. 5 + 2ln(x) = 4

2. If 55 is approximately equal to 3000, then approximate the value of 510?

V. Algebraic Substitution

1.  If , find .

2. Given , find the difference quotient, , and simplify completely.

VI. Solve Inequalities/Polynomial/Absolute Value

1.  |x – 2| +3 < 7

2.  x2 – 25 > 0

VII. Composition of Functions/ Inverse Functions

1.  If r(x) = x2 – 4 and s(x) = x1/2, find s(r(x)) and specify its domain.

2.  Given the graph of an inverse function f-1, sketch a graph of the function f.

VIII. Simplifying Rational Expressions/ Rationalizing Algebraic Expressions

1.  Reduce the expression to lowest terms: (x + 1)3(x – 2) + 3(x + 1)2

(x + 1)4

2. Reduce the expression to lowest terms: x1/2 – x1/3

x1/6

3. Simplify: x1/2 – 51/2

x – 5

3.  Simplify: x4 + x – 2

x - 1

IX. Represent Geometric Parameters with Algebraic Expressions

1.  The length of a rectangle is 3 meters more than twice its width. What is the width if the perimeter of the rectangle is 186 meters?

2.  A square picture is mounted on a larger rectangular sheet of poster paper leaving a border around the picture of 2 inches on the bottom and 1 inch on each of the remaining sides. The sheet of poster paper has an area of 42 square inches. If x represents the length of a side of the square picture, then write the equation that can be used to determine the value of x and solve it.

X. Trigonometric Functions and Solving Trigonometric Equations.

1. Prove: csc2(x) – cot2(x) = 1

2. If f(x) = cos(3x), then find f(π/6).

3. For which values of x is sec(x) not defined?

4. Simplify the following expression: sec(θ)cot(θ)sin2(θ)

5. Given that cos(θ) = ½, and θ terminates in quadrant I, evaluate all six trigonometric functions of θ.

6. Solve the following equation for x: 2sin(x) – 1 = 0.