Math 252 – Pre-Requisite Skill Review
Selected Topics to review:
• Trigonometry
o Know unit circle values backwards and forwards
o Convert between radians and degrees
o Use right-triangle trigonometry (SOH-CAH-TOA) to find missing angles and side
lengths
o Convert between polar and rectangular coordinates
• Differentiation/Integration formulas and techniques
o Know all formulas (formula list provided for review)
o Apply integration techniques, such as completing the square, long division, integration by
parts, etc.
• Evaluate limits using algebraic techniques as well as L’Hopital’s Rule
I. Trigonometry
A. Trigonometric Function Values (unit circle). Without a calculator, and without looking at a unit
circle diagram, evaluate each of the following:
1. cos(π )
2. sin(π )
3. tan 45°
4. cos 
π 

2
 2π 

 3 
6. sin 
 3π 

 4 
8. sin150°
9. tan 
π 

6
10. cot 
11. sec 240°
12. csc 
5. tan 
7. cos 
 4π 

 3 
 5π 

 3 
π 

2
 2π 

 3 
14. sin 
 π

 2
16. cos( −270°)
13. cos  −
15. tan  −
 −π 

 4 
Math 252 – Pre-Requisite Skill Review
B. Radian/Degree Conversion. You should know the special angle conversions by heart, but also be able
to convert non-standard angles. Recall: 180° = π radians.
1. Convert between radians and degrees without the use of a calculator.
a. 60° = ________ radians
b.
2π
radians = ___________ degrees
3
c. 210° = ________ radians
d.
7π
radians = ___________ degrees
4
2. Use a calculator to convert between radians and degrees. Give answers rounded to the nearest tenth.
π
a. 80° = ________ radians
b.
c. 195° = ________ radians
d. −2.4 radians = ___________ degrees
7
radians = ___________ degrees
C. Use SOH-CAH-TOA to find the measures of angles A and B in each situation. Give answers in
degrees, as exact values or rounded to the nearest tenth, as appropriate.
1.
2.
D. Convert from rectangular (i.e. (x, y)) coordinates to polar (i.e. (r ;θ ) ) coordinates. DRAW a diagram
to help, as you need to know what quadrant you are in to determine the appropriate angle. Give your
answer in degrees.
1. (2, -2)
2. (− 3,1)
3. (-2, -5)
Math 252 – Pre-Requisite Skill Review
II. Differentiation and Integration.
A. Find each derivative, in simplest form.
4
1. f ( x) = π 2
2. f ( x ) =
4. g ( x) = x 2 sin(2 x)
5. h( x) = e −5 x ln(10 x + 1)
3
3. f ( x) =
x2
x3 + 4 x 2 − 2
2x + 5
6. P (t ) = arcsin(t 3 )
x

2
7. y = x 4 arctan 
B. Evaluate each integral.
4x
cos x
1.
∫ cos(4x + 7)dx
2.
∫ x + 9 dx
3.
∫ 1 + sin x dx
4.
−5 x
∫ xe dx
5.
x2 + 2 x + 5
∫ x + 3 dx
6.
∫ 4 x + 9 dx
2
x+7
2
III. Limits.
A. Evaluate each limit using algebraic or analytical techniques – NOT L’Hopital’s Rule!
x 2 − 3x + 2
x →1
5x − 5
2. lim
1. lim
θ →0
sin(2θ )
θ cos θ
B. Evaluate each limit using L’Hopital’s Rule:
x 2 − 3x + 2
x →1
5x − 5
1. lim
sin(2θ )
θ → 0 θ cos θ
2. lim
ex − 1
x →0
x3
3. lim