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1
THE CALCULUS I PLACEMENT TEST - Fall, 1999
The test consists of three parts: Basic Algebra, Intermediate Algebra and Trigonometry, one
page for each part. Please read the following instructions before starting the test.
INSTRUCTIONS:
(1) For each question provide only one answer.
(2) Do not use a calculator.
(3) NA stands for none of the above.
1 Basic Algebra:
1: 12 + 23 , 43 =
(a) 23
2. ( ), is equal to
1
2
3.
4.
5.
6.
7.
4
(b) 54
5
(c) 12
5
(d) , 12
(e) NA
1
1
(e) , 16
(a) , 16
(b) 16
(c) , 8
(d) 16
Let C be a constant. If 2x + 7 = C , 3x, then x =
(a) C , 7
(b) , 2x + 7 , C
(c) C , 3x , 7
(d) 7 , C
(e) NA
5
3
2
5
The slope of the line: 2x , 3y + 8 = 0 is
(a) , 23
(b) 32
(c) 32
(d) , 4
(e) , 23
One of the solutions of the equation: x , 3x , 10 = 0 is
(a) 2
(b) 10
(c ) 5
(d) , 5
(e) 13
The domain of the function y = x x, x, is a set which contains all real numbers except
(a) 2
(b) 4
(c) , 1
(d) , 1 ; 4
(e) 2; , 1 ; 4
3
3
3
One of the solutions of the equation: (2x + 1)(x + 4) = 0 is
(a) , 12
(b) 12
(c) 2
(d) , 2
(e) 0
2
2
(3 +1)(
4)
2
p
8. If f (x) = ,6 , 3(x , 4) and g(x) = x + 1, then f (2) + g(8) =
(a) , 21
(b) , 9
(c) 9
(d) , 3
(e) 3
9. The equation of the line passing through points (1,-2) and with a slope is
(a) 4x + 3y , 10 = 0 (b) y = ,2 (c) 4x , 3y , 10 = 0 (d) 3x , 4y , 11 = 0
10. The sum of the two solutions of 4x , 3x = 2 is
p
13
3
3
+
3
41
(b)
(c)
(d)
(e) NA
(a)
4
4
8
4
4
3
2
(e) NA
Intermediate Algebra
2
2 Intermediate Algebra:
11. If x,x = 5, then x is equal to
10
10
5
5
(
b
)
(
c
)
(
d
)
(
e
)
(a) 13
4
3
2
3
p7
12. Let a and b be nonzero real numbers. Then a + b =
(a) a + b
(b) (a + b)
(c) a b
(d) (a b)
(e) NA
13: The least common denominator of x 2, 4 + x ,1 2x is
(a) x , 4
(b) x , 2x
(c) (x , 4)(x , 2x)
(d) x(x , 4)
(e) NA
,
=
14. (16) is equal to
(a) 81
(b) 8
(c) , 8
(d) , 18
(e) NA
15. If log x = 2 and log y = 3, then log (x y) is equal to
(a) 24
(b) 10
(c) 9
(d) 11
(e) NA
16. If 9x = , then x =
(a) , 32
(b) 23
(c) , 23
(d) 32
(e) NA
17. ln( e2 ) =
1
(a) 2
(b) , 2
(c) ln(,e )
(d) ln 2
(e) 27
18. If 5 = 1 , 4 ln x, then x =
(a) e
(b) 1
(c) , 1
(d) 1
(e) NA
2
(
2)
2
2
2
2
2
2
2
2
2
3 4
10
10
10
3
5
1
27
1
2
e
19: (2x y) (xy ) =
(x) (16x y )
2
2 3
6
5
( b) y
(c) 1
(d) 1
(e) NA
(a) y
8x
8x
8yx
8
p
20. If f (x) = 1 , x and g(x) = x + 3, then f (g(0)) =
(a) , 6
(b) , 2
(c) 10
(d) 6
(e)NA
21: Simplify x x+ 2,x 1+ 1 :
(a) , 1
(b) x , 1
(c) x , 1
(d) x , 1
(e) NA
2x + 1
x + 2x + 1
x+1
22. The length of a rectangular garden is 8 feet longer than its width. If the total perimeter of
the garden is 52 feet, then the width of the garden is:
(a) 9 feet
(b) 22 feet
(c) 14.77 feet
(d) 8 feet
(e) NA
2
2
2
2
2
2
2
2
Trigonometry
3
3 Trigonometry:
23. The two shorter legs of a right triangle have lengths 3 and 4, respectively. Let A be the
smallest angle of this right triangle. Then cos(A) is
(b) 54
(c) 35
(d) 34
(e) NA
(a) 43
24. [sin(45)] =
p
2
(a) 1
(b ) 2
(c) 0
(d) 12
(e) 22
25. If sin(A) = a and cos(A) = b, then tan(A) is equal to
(b) ab
(a) ab
(c) p a
a +b
2
2
(d) p b
a +b
2
(e) NA
2
26. If sin () = 0:55, then cos () =
2
2
(b) 0:155
(a) 90 , 0:55
(c) 0:45
(d) 1:45
(e) NA
27. The period of y = 5 cos(6x) is
(a) 3
28. sin(,330) is equal to
p
(a) 23
(b) 6
(c) 2
(d) 30
(c) 12
(d) , 12
p
(b) , 23
(e ) 6
p
(e) , 22
29. If is an acute angle such that cos = , then sin( , ) =
(a) , 32
p
(b) 35
2
3
(c) 32
2
p
(d) , 35
(e) , 23
30. If sin = and is acute, then sin(2) =
3
5
(a) 65
(b) 10
3
8
(c) 25
6
(d) 25
(e) 24
25
Answers
4 Answers:
4
Basic Algebra
Intermediate Algebra
Trigonometry
1. (c)
2. (b)
3. (a)
4. (b)
5. (c)
6. (d)
7. (a)
8. (e)
9. (c)
10. (a)
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
(b)
(e)
(d)
(a)
(c)
(a)
(b)
(d)
(a)
(b)
(d)
(a)
(b)
(d)
(b)
(c)
(a)
(c)
(c)
(e)