Packet 1
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Math Teacher Last Year: AP Calculus Summer Review This packet is a review of the entering objectives for AP Calculus and is due the day of your first math class of the year. Have a great summer. I. Simplify. Show the work that leads to your answer. 1.
2.
3.
4.
II. Fill in the blanks with the following identities. 1. Pythagorean: 2. Double Angles:
III. Simplify each expression. 1.
2.
3.
4.
IV. Solve each equation below for z. 1.
2.
V. If determine each of the following: 1.
2.
3.
4.
5.
6.
7.
8.
VI. Miscellaneous: Follow the directions for each problem.. 1. Evaluate
2. Expand
and simplify if
3. Simplify:
4. Eliminate the parameter, t, and write a rectangular equation for
VII. Expand and simplify. 1.
2.
VIII. Simplify 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
IX. Using the point slope form
, write an equation for the line
1. with slope -2, containing the point
2. containing the points
and
3. with slope 0, containing the point
4. perpendicular to the line in problem #1, containing the point
X. Given the vectors
and
, determine
1.
2.
3.
4.
XI. Without a calculator, determine the exact value of each expression. 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
XII. For each function, determine its domain and range. 1.
2.
Domain:
Domain:
Range:
Range:
3.
4.
Domain:
Domain:
Range:
Range:
XIII. Determine the coordinates of all points of intersection of: 1.
and
2.
and
XIV. Solve all the equations below for x, where x is a real number. 1.
2.
3.
4.
in the first quadrant.
5.
6.
7.
8.
9.
10.
11.
12.
XV. Graph each equation. Give its domain and range. Scale all graphs by one unless a scale is provided. 1. Domain:
2. Domain:
Range:
Range:
3. Domain:
4. Domain:
Range:
Range:
5. Domain:
6. Domain:
Range:
Range:
7. Domain:
8. Domain:
Range:
Range:
9. Domain:
10. Domain:
Range:
Range:
11. Domain:
12. Domain:
Range:
Range:
13.
14.
Domain:
Domain:
Range:
Range:
XVI. Decompose into partial fractions. 1.
2.
XVII. Solve for x and y in the triangles below. 1.
2.
XVIII. Find the area of the figures below. 1.
2.
3.
4.
XIX. Find the volume of the solids below. 1.
2.
3.
4.
Math Teacher Last Year: AP Calculus Summer Review This packet is a review of the entering objectives for AP Calculus and is due the day of your first math class of the year. Have a great summer. I. Simplify. Show the work that leads to your answer. 1.
2.
3.
4.
II. Fill in the blanks with the following identities. 1. Pythagorean: 2. Double Angles:
III. Simplify each expression. 1.
2.
3.
4.
IV. Solve each equation below for z. 1.
2.
V. If determine each of the following: 1.
2.
3.
4.
5.
6.
7.
8.
VI. Miscellaneous: Follow the directions for each problem.. 1. Evaluate
2. Expand
and simplify if
3. Simplify:
4. Eliminate the parameter, t, and write a rectangular equation for
VII. Expand and simplify. 1.
2.
VIII. Simplify 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
IX. Using the point slope form
, write an equation for the line
1. with slope -2, containing the point
2. containing the points
and
3. with slope 0, containing the point
4. perpendicular to the line in problem #1, containing the point
X. Given the vectors
and
, determine
1.
2.
3.
4.
XI. Without a calculator, determine the exact value of each expression. 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
XII. For each function, determine its domain and range. 1.
2.
Domain:
Domain:
Range:
Range:
3.
4.
Domain:
Domain:
Range:
Range:
XIII. Determine the coordinates of all points of intersection of: 1.
and
2.
and
XIV. Solve all the equations below for x, where x is a real number. 1.
2.
3.
4.
in the first quadrant.
5.
6.
7.
8.
9.
10.
11.
12.
XV. Graph each equation. Give its domain and range. Scale all graphs by one unless a scale is provided. 1. Domain:
2. Domain:
Range:
Range:
3. Domain:
4. Domain:
Range:
Range:
5. Domain:
6. Domain:
Range:
Range:
7. Domain:
8. Domain:
Range:
Range:
9. Domain:
10. Domain:
Range:
Range:
11. Domain:
12. Domain:
Range:
Range:
13.
14.
Domain:
Domain:
Range:
Range:
XVI. Decompose into partial fractions. 1.
2.
XVII. Solve for x and y in the triangles below. 1.
2.
XVIII. Find the area of the figures below. 1.
2.
3.
4.
XIX. Find the volume of the solids below. 1.
2.
3.
4.
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