Practice Problems and Solutions (in pdf)

for Review of The Placement Test for Calculus I/Precalculus

M. Chen

Part

Topics/Practice Problems/Solutions

 

 

1.

1. Fraction computation with numbers and letters
2. Common factors with numbers and letters
3. Use of parentheses
4. Express a statement with symbols and numbers and some commonly used formulas

 

practice problems for Part 1     solutions

 

 

2.

1. Integer exponents, radicals and rational exponents
2. Polynomial algebra: +,-,x

 

practice problems for Part 2     solutions

 

 

3. 

1. Solution of a linear equation: (equations with numbers and letters
2. Solution of a quadratic equation: factoring, quadratic formula


practice problems for Part 3     solutions

 

 

4.

1. Solution of a polynomial equation: factoring, grouping
2. Definition of function and function operations

 

practice problems for Part 4     solutions

 

 

5.

1. Linear functions: graph, slope, x,y-intercepts

2. Equation of a line: slope-intercept, point-slope
3. Applications of linear function and linear equations


practice problems for Part 5     solutions

 

 

6.

1. Quadratic functions: graph, zeros, vertex


practice problems for Part 6     solutions

 

 

7.

1. Polynomial functions: zeros, graph

2. Rational functions: zeros, domain

 

practice problems Part 7     solutions

 

 

8.

1. Exponential functions: growth, decay, graph


practice problems Part 8     solutions

 

 

9.

1. Degree and radian angle measures
2. Right triangle trigonometry: sin(x), cos(x), tan(x), cot(x), csc(x), sec(x)
3. Identities: sin2(x) +cos2(x) =1
4. Values of trigonometric function at special angles
5. Trigonometric functions of general angles


practice problems for Part 9     solutions

 

 

10.

1. Trigonometric functions: sin(x), cos(x), tan(x), domain, period and graph
2. Amplitudes, periods, graphs of Asin(b x), Acos(b x)
3. Identities: sin(2x), cos(2x)


practice problems for Part 10     solutions