Download Calculus Pretest (Bobby Revised)

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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)
2. Factor over the set of real numbers: x2 + 5x + 5.
3. Factor the polynomial: x 3  8
4. Solve for x .
a. x 3  x  2 x 2  2  0
b. x 2  x  4  0
c.
3x 2  8 x  3
0
x4
2 x  y  0
5. Solve the system for x and y:  2
 x  y  1
6. Solve for x : (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 f ( x)  log 4 ( x) , 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 x .
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
4x  2
1. If f ( x) 
, find f (b  1) .
x4
1
f ( x  h)  f ( x )
2. Given f ( x)  2 , find the difference quotient,
, and simplify completely.
h
x
VI. Solve Inequalities/Polynomial/Absolute Value
1. |x – 2| +3 < 7
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Calculus Pretest
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
1/2
1/3
2. Reduce the expression to lowest terms: x – x
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.