NAME________________________________
AP CALCULUS SUMMER ASSIGNMENT 2014
DIRECTIONS: Each section must be completed separately on looseleaf. All work should be
shown and done in a neat and precise manner. Any questions pertaining to the examples you
may email me on my edline account. These assignments will be graded and you will have a test
within the first two weeks of school in September. You are responsible to memorize the formulas
and definitions.
PART ONE: Solve for the missing variables. Only an algebraic solution
will be accepted.
1.
3.
3x – y = 10
2x + 3y = 3
6x – y = 1
4x + 3y = 8
2. 5x + 7y = 29
2x + 3y = 12
4. x + y – z =1
x–y +z=3
x - y - z = -5
5. If x2 – 3y = 6 when x = 3 and x + y – z = 6 find x and y and z
6.
7x – y = 6
4x + 3y = 8
PART TWO: Solve for x by factoring.
1. x2 – 8x = x + 10
6. 2x2 – x = 3
2 5x2 - x = 4
7. x3 + 11x2 + 30x = 0
3. x2 = 9x
8. 9x2 – 6x + 1 = 0
4. x3 – 5x2 – 4x + 20 = 0
9.
5. 10x( x- 2) = x(x – 1) -13x -1
10. 2x2 – 200 = 0
x3 + 3x2 – 25x - 75 = 0
PART THREE: Solve algebraically and check.
1. 4 – (x – 2) = x - 8
2. 642x = 32 x + 4
6. 25x -2 = 125 x + 3
7. log3 4 + log3 (x + 2) = 3
3. 2x-4 - 1 = 31
8. loga10+ loga (x + 1) = loga5
4. 4x ½ – 2 = 3
9. – (x – 2) - ½ ( 4 + 2x) = x – 1
5. ½ (6x – 2) – x = -10
10. 4√x - 2 = 2√x + 8
Name ________________________________
PART FOUR: Show all work on looseleaf.
1. Write the equation of the line perpendicular to 3y -x = 2 and passing through (-3, -10)
2. Write the equation of the line normal to 4y – 2x = 1 and passing through (-4, 11)
3. Write the equation of the line passing through the points (2, 4) and (-9, 15)
4. Write the equation of the circle with radius 12 and having the center (2, 1) in two different
forms.
5. Write the equation of the circle where the endpoints of the diameter are (2, 1) and ( -6, 7)
6. Write the equation of the sphere with center (2, -3, 1) and diameter 14
7. Find the x -intercepts and y -intercepts of the following in ordered pair form.
a. y = x2 – 6x – 16
b. 4x2 + 5y2 = 20 c. x = y2 – 2y – 3
8. Find to the nearest tenth the volume of a sphere that has a diameter of 40 inches.
9. Find to the nearest tenth the surface area of a sphere that has a radius of ¼
10. Find to the nearest hundredth the volume of a right cylinder with a height of 4 inches and
diameter of 6 inches.
PART FIVE: Find the following exact values:
1.
sin (150o)
6. tan (-150o )
2.. cos (330o )
3. sec ( 135o ) 4. cot (300o ) 5. csc( 480o)
7. tan (3π/4)
8. cos(-π/6)
9. csc (1020o)
10. cot(-120o)
Name _______________________
PART SIX: Answer all of the following questions. Be sure to show all
work or no credit will be given.
1. Find the exact value of sin(15o ). Using the formula for sin (A – B)
2. Find the exact value of cos(45o) by using the formula for cos (A – B)
3. Find the exact value of tan (75o ) by suing the formula for tan (A + B)
4. If the sin A = ½ and angle A lies in quadrant II, find the exact value of the following:
a. cos (2A)
b. tan (2A)
c. sin (2A)
5. If the sin x = ¼ , find the value of sin(2x) and cos (2x )
PART SEVEN: Answer all of the following questions. Be sure to show
all work or no credit will be given.
f(x) = x2 – 2x + 1
1.
g(x) = 5x – 5 and h(x) = 2 - 5x
f(g(x))
2. g(f(x))
3. f(x)/g(x) ; xǂ 1
4. f(g(h( 1/5)))
5. g(x) – f(x)
6. 2 f(x) – 3 g(x)
7. f(-2) – g(2/5) – h(-1/5)
8. f(2x – 3)
9. g(x) • h(x)
10. f(√3 + 1)
Name ___________________________
PART EIGHT: Answer the following questions. Show all work or no
credit will be given.
1. Use the quadratic formula to solve for x for the following examples. All radicals
must be in simplest form.
a. x2 – 8x + 15 = 0
b. x2 – x - 3 = 0
c. 2x(x -3) = x – 1
d. x2 – 8x – 4 = 0
2. Find the following in simplest radical form.
a. √300 - √27 + 2 √12
b. ( 5 - 2 √2)( 6 + √2)
c. (3 + 7√11)2