## AP Calculus

## Placement Test

## (3729, 241)

Placement tests are posted in the Course Catalog to help students plan their own placement,
**not for study purposes. Placement tests are intended to be taken in one sitting with no prior **
**study, books, notes or outside help, or the results will be invalid and the student may be **
inappropriately placed in a course where he will struggle or fail.

Visit the TPS Enrollment FAQ - Prerequisites, Placement and Matriculation, visit Live Chat, or email TPS Support (support@pottersschool.org) for additional information.

The student must be enrolled in the TPS course to submit a placement test for the course.

1

**Welcome to AP Calculus! **

### Placement Questionnaire and Test

Student name _____________________________

1. Give the curriculum and course of your math program from the last two years.

2. How are you testing and what is the average test grade in your current math course?

3. What is your child's general attitude toward mathematics? What is your plan for future study in mathematics?

4. How old is your student and what is the grade level (9, 10, 11, 12)?

5. Take the placement test. This test is used for both AB and BC, so certain problems distinguish the BC. You may either highlight the answers in the document, or just list the problem numbers and the answers below. For example,

2

### The Potter’s School AP Calculus Placement Test

Please answer the following without using any resources other than your knowledge and a scientific calculator. You may not use a graphing calculator.

1. Solve and round answers to the nearest hundredth: x2 + 3x – 7 = 0 a. 1.54, -4.54

b. 3, -7 c. 1.28, -1.28 d. 3.08, -9.08

2. Let f(x) = 2−*x*. Give the domain.
a. − *x*2*and*2*x*

b. −*x*2*or*2*x*

c. *x*2
d. *x*2

3. Solve the equation with exact answers: -x2 – 3x + 10 = 0
a. {-5, 2}
b. {-2, 5}
c.
2
31
*3 i*
d. {-3, 10}
4. Let f(x) = 3x2 – 5 and g(x) =
*x*
2

. Find the function f g (x).
a. 12_{2} −5
*x*
b.
*x*
*x* 10
6 −
c.
5
3
2
2 −
*x*
d. 0

5. Describe the graph defined by the parametric equation: x = 3 – t2, y = 1 + 2t a. Parabola opening down

3

6. Describe the shape of the graph and how the graph of y = (2(x +1))2_{ can be }

obtained from the graph of y = x2.

a. Parabola with a horizontal shift right 2 units

b. Parabola with a horizontal stretch of 2 and a horizontal shift left 2 units c. Line with a slope of 2

d. Parabola with a horizontal shift left 1 unit and a vertical stretch of 4
7. Describe the graph y = 3x_{ – 4 and how the graph can be obtained from the graph }

of y = 3x.

a. Parabola with a horizontal stretch of 3 and vertical shift down 4 units b. Exponential growth with a growth factor of 3 and a vertical shift down 4

units

c. Exponential decay with a horizontal stretch of 3 and a vertical shift up 4 d. Line with a slope of 3 and a y-intercept of -4

8. Find the equation for the line passing through the point (5,4) and parallel to the line 10y – 6x = 11.

a. 10x – 6y = 4 b. 6x – 10y = 5 c. 3x – 5y = -5 d. 3y – 5x = -4

9. A graph of a parabola has a line of symmetry x = 3 and contains the points (1,0) and (4,-3). Determine an equation for the parabola.

a. ( 3)2
9
1 _{−}
= *x*
*y*
b. *y= x*3( −4)2 +3
c. *y= x*( −3)2 −4
d. *y= x*( −4)2 −9

10. Write the expression in standard form:

*i*
*i*
4
3
3
8
−
+
a. *i*
25
41
25
12 +
b. *i*
4
3
3
8 −
c. 36 −23*i*
d. 24 +12*i*

11. Identify all asymptotes and zeros of the function g(x) =

4

12. Find the vertex of the parabola y = 2x2_{ – 12x + 23. }

a. (3,5)
b. (6, 13)
c. (6, 23)
d. (3,14)
13. Solve for x:
2
1
3
log*x* =
a.
2
3
b. 3
c. 6
d. 9

14. Find the slope of the line determined by the points (-1, 3) and (4, 7). a. 5 4 b. 4 5 c. 3 10 d. 2

15. Find the equation of the line passing through the point (3, -2) and perpendicular to the line 3x + 2y = 5. a. 3x + 2y = 5 b. 3x + 2y = 13 c. 2x + 3y = 0 d. 2x – 3y = 12

16. Which of the following is an odd function?
a. y = x3_{ – 5 }

b. y = x2 + 3x – 5 c. y = 2x3 – x d. y = 3

5

18. Given the functions f(x) = x + 3 and g(x) = x2_{ + 1, find f(g(x)). }

a. x2 + 4 b. x2 + x + 4 c. x2 + 6x + 10 d. x3 + 3x2 + x + 3

19. Give the domain and range of the graph y = 3 cos(4x).
a. − *x*,− *y*

b. − *x*,−1 *y*1
c. −4*x*4,−3 *y*3
d. − *x*,−3 *y*3

20. Identify the period and amplitude for f(x) = 3 sin(2x + π/3) + 4 a. 2 and 1

b. 2 and 3 c. and 3 d. and 4

21. Find an expression equivalent to sin x in terms of cos x.
a. 1 −cos2 *x*

b. 1 – cos x
c. 1 + cos x
d. 1 +cos2 *x*

22. Find an expression equivalent to tan2 x in terms of cos x.
a.
*x*
*x*
cos
cos
1 +
b.
*x*
*x*
2
2
cos
cos
1 −
c. cos x + 1
d.
*x*
*x*
2
2
cos
cos
1 +

6 24. Evaluate: tan (tan-1 ( 3))

a. 2
b.
3
c. 3
d.
3
3
25. Solve for x: 23*x*−1 =16
a. 1
b.
3
2
c.
3
5
d. no solution

26. Solve the equation 8 – 2 lnx = 12. a. -2

b. 1_{2}

*e*

c. e2

d. no solution

27. Find an equation for the ellipse whose major axis endpoints are (-7 -6) and (-7,12) and minor axis length is 2.

a. 81(x + 7)2 + (y – 3)2 = 81
b. 4(x – 7)2_{ + 81(y + 3)}2_{ = 1 }

c. (x + 7)2 + (y – 3)2 = 18 d. (x – 7)2 + 81(y + 3)2 = 81

28. Find the sum of the first 12 terms of the sequence: 28, 22, 16, 10, …. a. 0

b. 86 c. -80 d. -60

29. Find the remainder when 3x4_{ – 2x}2_{ – 3x + 7 is divided by x + 1. }

7 30. Expand the binomial (2x + y)5

a. 2x5 + 5x4 + 10x3 + 10x2 + 5x + y

b. 2x5 + 10x4y + 20x3y2 + 20x2y3 + 10xy4 + y5 c. 32x5 +16 x4y +8 x3y2 + 4x2y3 + 2xy4 + y5 d. 32x5 + 80x4y + 80x3y2 + 40x2y3 + 10xy4 + y5

31. Find a Cartesian equation for a curve that contains the parametric curve given by x = 4 cos t and y = 3 sin t

a. 9x2 + 16y2 = 144 b. 3x + 4y = 1 c. 4x + 3y = 1 d. 16x2 + 9y2 = 1

32. In the right triangle shown, find tan 𝜃 a. 𝑥

b. 𝑥√𝑥2 _{− 1 }

c. 𝑥2 + 1
d. √𝑥2 _{− 1 }

33. What is the area of the rectangle in the figure shown below? (the figure is not drawn to scale)

a. 3 b. 39 c. 31 d. 27

34. Solve the inequality: (𝑥−1)