Download PreCalculus

Welcome to AP Calculus!
Placement Process and Test
Please answer a few questions by inserting your answers below and copy and paste into an email to your instructor so that we can make sure the correct placement is made in our
mathematics program. One of our goals is to place all students in classes where they will
experience success.
Student name _____________________________
1. Pre-Calculus is a pre-requisite for this course. What mathematics course and what
curriculum are you using currently (please indicate if it is with TPS)?
2. How are you testing? What is the average course grade currently?
3. What is your child's general attitude toward mathematics?
4. What percentage of your child's learning is done independently?
5. If your student is not currently taking TPS PreCalculus, then please have them
complete the following AP Calculus Placement Test. Please send me your answers in the
body of an email and in the following format. If your student has never seen a concept
before please have them write “Guess” and then do their best job of guessing. The
placement test is to be taken with no notes, no outside help, but a scientific calculator
may be used.
1. a
2. b
3. guess – c etc.
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.
Determine by visual inspection the type of linear correlation, if any, that exists
between the x and y quantities in the following data:
x
5
10
12
13
15
20
y
16
33
40
39
40
59
a.
b.
c.
d.
strong positive
strong negative
weak positive
weak negative
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}
 3  i 31 
c. 

2


d. {-3, 10}
2
4. Let f(x) = 3x2 – 5 and g(x) = . Find the function f  g (x).
x
12
5
a.
x2
10
b. 6 x 
x
2
c.
3x 2  5
d. 0
5. Describe the graph defined by the parametric equation: x = 3 – t2, y = 1 + 2t
a. Parabola opening down
b. Parabola opening left
c. Line with a negative slope
d. Parabola opening up
6. Describe the shape of the graph and how the graph of y = (2x + 2)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 units 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.
1
a. y  ( x  3) 2
9
b. y  3( x  4) 2  3
c. y  ( x  3) 2  4
d. y  ( x  4) 2  9
8  3i
10. Write the expression in standard form:
3  4i
12 41
 i
a.
25 25
8 3
 i
b.
3 4
c. 36  23i
d. 24  12i
x5
11. Identify all asymptotes and zeros of the function g(x) = 2
.
x  x6
a. (-3,0), (2,0), (5,0)
b. x = -3, x = 2, (5,0)
c. x = -1, x = 6, (5,0)
d. x = 3, x = -2, x = 5
12. Find the vertex of the parabola y = 2x2 – 12x + 23.
a. (3,5)
b. (6, 13)
c. (6, 23)
d. (3,14)
1
13. Solve for x: log x 3 
2
3
a.
2
b.
3
c. 6
d. 9
14. Find the slope of the line determined by the points (-1, 3) and (4, 7).
4
a.
5
5
b.
4
10
c.
3
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
17. Find the inverse of the function y = x2 – 3.
a. y = x2 + 3
1
b. y  2
x 3
c. y  x  3
1
d. y  2  3
x
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 cos 2 x
b. 1 – cos x
c. 1 + cos x
d.  1 cos 2 x
22. Find an expression equivalent to tan2 x in terms of cos x.
1  cos x
a.
cos x
1  cos 2 x
b.
cos 2 x
c. cos x + 1
1  cos 2 x
d.
cos 2 x
23. Solve for x: 2sin x  3 
a.  , 
4 4 
  
b.  , 
6 3
   
, 
c. 
 4 4
  
d.  , 
2 4
2=0
24. Evaluate: tan (tan-1 ( 3 ))
a. 2

b.
3
c.
3
3
3
25. Solve for x: 2 3 x 1  16
a. 1
2
b.
3
5
c.
3
d. no solution
d.
26. Solve the equation 8 – 2 lnx = 12.
a. -2
1
b.
e2
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. 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
30. 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