THE PUTNEY SCHOOL
PRECALCULUS PLACEMENT TEST
Please round all decimal answers to the nearest hundredth, unless otherwise indicated.
1. What is the domain of the function: f (x) = √x−1
x2−4 ?
a.
b.
c.
d.
e.
All real numbers except 2 and -2
All real numbers greater than 1
All real numbers greater than one, except 2
All real numbers greater than or equal to 1, except 2
All real numbers greater than or equal to 1
2. Which of the following is NOT true about the function:
x−2
x2−x−6
?
a. The y-intercept of the graph of the function is (0, 13) b. The only zero of the function is x = 2
c.
There is a vertical asymptote at x = 3
d. The function has no horizontal asymptotes
3. Which of the following is the inverse of the function f (x) = x2 + 5 ?
a.
f −1(x) = √x − 5
b.
f −1(x) = 5 − √x c.
f −1(x) = √x − 5
d.
f −1(x) = √5 − x
4. If f (x) = √x + 1, g(x) = x3 − 2x, and h(x) = 4x , what is g(h(f(3))) ?
5. What is the value of log 2(16) ?
6. Solve the equation 9x = 2187
log2(25)
7. Evaluate and simplify the expression: log (17)
2
8. Give three solutions to the equation: 4x3 − 16x2 + 12x = 0
9. If P (t) is an exponential function of the form P (t) = Aekt and it is known that
P (1) = 12, P (3) = 20 , find P (4) .
10. Solve the equation: √x2 + 3 = x + 1
11. Convert
3π
4 radians to degrees.
12. Given f (x) = 3sin(π2x + 2) − 5 provide the following information:
a. What is the function’s amplitude?
b. What is the function’s period (in radians)?
c. What is the y coordinate of the function’s horizontal line of symmetry?
13. Find the length of d in the following diagram:
14. What is the sum of the infinite geometric series 27 + 9 + 3 + ... ?
15. If the third term of an arithmetic sequence is 5 and the common difference between terms is -4,
find the 450th term.
9
16. Evaluate ∑ (n2 − 1)
n=5
17. Solve the equation: 3sin 2x + 18 + 3cos2x = 39 − 6x
18. If this represents the graph of f (x ) ,
,
which of the following best represents the graph of f (x − 2) ?
A
B
C
D