I. Trigonometry Review · Summer Packet (from Honors Analysis to AP BC Calculus). I. Trigonometry...
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Summer Packet (from Honors Analysis to AP BC Calculus). I. Trigonometry Review Convert to radian measure without a calculator: 1. 2. 3. Find the exact value without a calculator: 4. 5. 6. 7. 8. 9. Find the exact value without a calculator: 10. ( ) 11. () 12. ( √ ) 13. 14. √ 15. ( ())
Transcript of I. Trigonometry Review · Summer Packet (from Honors Analysis to AP BC Calculus). I. Trigonometry...
Summer Packet (from Honors Analysis to AP BC Calculus).
I. Trigonometry Review
Convert to radian measure without a calculator:
1. 2. 3.
Find the exact value without a calculator:
4.
5. 6.
7.
8.
9.
Find the exact value without a calculator:
10. (
) 11. ( ) 12. (
√
)
13. 14. √ 15. ( ( ))
Use the calculator to find each value. Round values to 4 decimal places.
16. 17.
Without using a calculator, find the following:
18. Given
, find all values of .
Without using a calculator, solve the following, :
19. 20. √
21. √
22. √
23.
24.
Use the calculator to solve the following, :
25. 26.
Graph the following by hand through transition(s) of the respective
parent graph. State the domain, range, period and amplitude:
27. (
) 28.
29. 30. ( )
Algebra Review:
Factor completely:
1. 2.
Solve each inequality by hand:
4. √ 5.
Find the real roots:
6. ( ) ( )
7. ( ) ( ) ( )( ) =0
Simplify:
8.
( )
( )
9.
√ √
10. (
( )
) 11.
( ) ( )
Given two points ( ) and ( ), find the following(12 – 14):
12. Slope of line segment PQ
13. An equation in standard form of the line containing and .
14. Distance between and .
15. Find an equation of a line in point slope form perpendicular to
through the point ( ).
Graph the following by hand:
16. ( ) {
17. ( ) {
18. Write ( ) | | as a piecewise function.
Without a calculator test analytically for symmetry with respect to the
x axis, y axis, origin and y=x. State whether the function is even, odd or
neither (19 – 21).
19. ( )
20. ( )
21.
22. Graph the function ( ) on the calculator.
State the interval(s) on which ( ) is increasing or decreasing.
Round to three decimal places.
23. Sketch the function ( ) by hand. State the interval(s)
on which ( ) is increasing or decreasing.
Series:
Quickly determine if the following series are convergent or divergent:
1. ∑ ( )
2. 2. ∑ (
)
3. ∑ ( )
4. ∑
5. ∑
6. If the infinite geometric series with and converges to
6 (the sum is 6), find the numeric value of the ratio.
7. Use the ratio test to determine if the following series converges or
diverges: ∑
( ) .
Polar Graphs:
1. Identify . Place the polar equation in standard
rectangular form.
2. Graph the polar point
. Find the rectangular form of the
point.
Without a calculator, identify the following polar graphs:
3.
4.
5.
6.
Use a calculator to determine the number of radians it takes to trace
each polar graph one time only:
7.
8.
Limits:
Without the use of a calculator determine the following limits:
1.
2. ( )
( )
3. | |
| |
| |
4.
5.
6.
7. √
9.
10. ]]
Answers:
Trig:
1.
2.
3.
4.
5. √
6. Undefined
7. √
8. √
9. √
10.
11.
12.
13.
14.
15. √
16. -1.2521
17. -1.0154
18.
19.
20.
21.
22.
23.
24.
25.
26.
27. Reflection over the x axis, right
,
domain:
range:
period:
amplitude: 1
28. No translation
domain:
range:
period:
amplitude: none
29. Vertical stretch, up 2
domain:
range:
period:
amplitude: 2
30. Horizontal shrink
domain:
range:
period:
amplitude: none
Answers
Algebra
1. ( ) ( ) ( )
2. ( ) ( )
3. ( ) ( )
4. or
5.
6.
7.
8.
( )
9.
√
10. ( )
( )
11.
( )
12.
13.
14. √ units
15.
( )
18 . ( ) {
or ( ) {
19. y axis, even
20. origin, odd
21. origin, y=x, odd
22. Increasing ( ) ( )
Decreasing ( )
23. Increasing ( )
Decreasing ( )
Series:
1. Converges
2. Converges
3. Diverges
4. Converges
5. Diverges
6.
7. , converges
Polar:
1. Circle ( )
3. Archimedes Spiral
4. Rose
5. Cardioid
6. Limacon
7.
8.
Limits:
1. 5
2. 1
3. 1, -1, does not exist
4.
5.
6.
7.
8. 4
9. -1
