1. No category

Birzeit University- Mathematics Department
Mathematics Mini-Sample Placement Exam
Name(Arabic):.........................................................
Circle the correct answer
(1) The graph of f (x) = (x + 2)2 − 3 is the graph of f (x) = x2 shifted.
(a) right 2,up 3.
(b) left 2, down 3.
(c) right 2, down 3.
(d) left 2, up 3
(2) The parametric equations x(t) = cos t, y(t) = sin t on the interval 0 ≤ t ≤ 2π represent
(a) A half of the circle starting at (0,1) and ends at (0,-1) clockwise
(b) A circle clockwise and end points (1,0)
(c) A circle counter clockwise and end points (1,0)
(d) A half of the circle starting at (1,0) and ends at (0,-1) counterclockwise
(3) The solution of
1
x
< 2 is
(a) (1, 2).
(b) x < 2.
(c) x > 12 .
(d) none.
(4) If y(t) = 100e0.1t then the doubling time is
(a)
ln2
.
10
(b) 10ln2
(c)
(d)
0.1
ln2
10
ln2
(5) The parametric equations x(t) = t, y(t) = t + 1 on the interval 1 ≤ t ≤ 3 represent
(a) A line through (1,2).
(b) A line segment starting at (1,2) and terminal point (3,4)
(c) A line whose equation y = x + 1
(d) An array
(6) The domain of f (x) =
√ 1
1−x2
is
(a) [0, 1] .
1
(b) [−1, 1]
(c) x ≥ 0
(d) (−1, 1)
(7) The range of f (x) =
√ 1
1−x2
is
(a) [0, 1].
(b) [−1, 1]
(c) y ≥ 1
(d) none of the above
(8) The domain of the function f (x) =
√
x2 − 1 is
(a) [−1, 1].
(b) (−∞, 1].
(c) [1, ∞).
(d) (−∞, −1] ∪ [1, ∞).
(9) The range of f (x) =
1
1+x2
is
(a) [1, ∞).
(b) (−∞, ∞).
(c) (0, 1].
(d) (0, ∞).
(10) The range of f (x) =
1
ex +1
(a) (0, 1).
(b) (0, ∞).
(c) (1, ∞).
(d) [1/2, ∞).
√
(11) limx→∞ (x − x2 + x − 1) is
(a) 0.
(b)
1
.
2
(c) ∞.
(d)
(12)
−1
.
2
d
(eln 2x )
dx
=
(a) x.
(b) 2.
2
(c) 1.
ln 2x
(d) 2 e x .
√
(13) A particle is moving on the curve f (x) = 25 − x2 . If the distance between the partice
and the origin is changing at the rate 2 units per second. Find the rate of change of the
distance between the particle and the X-axis when x = 4
(a) 5
(b) 10
(c) 8
(d) none.
(14) Given xy 2 − xy = y + 1. Then
dy
dx
at (0, −1)
(a) −1
(b) 1
(c) 0
(d) none.
(15) The equation of the normal to the graph of f (x) = x2 + x − 5 at x = 1 is.
(a) 3y = −x + 10.
(b) y = 3x + 6.
(c) y = 31 (x − 1) + 3.
(d) none.
(16) If P = {0, 0.2, 0.7, 0.9, 1} is a partition of the interval [0, 1] then the norm of P is
(a) 1.
(b) 0.5.
(c) 0.9.
(d) 0.4.
R
(17) x(2 − x2 )5 dx =
(a) −10x2 (2 − x2 )4
(b) x2 (2 − x2 )4
(c)
−1
(2
12
− x2 )6 + c
(d) −12x2 (2 − x2 )6 + c
(18)
d
(e3 )
dx
=
3
(a) 3e2 .
(b) 1.
(c) 3e3 .
(d) 0
(19)
R1
0
3x dx =
(a) 3.
(b) 2.
(c) 2 ln 3.
(d)
2
.
ln 3
(20) The derivative of the function f (x) = x cos(x2 ) at x = 0 is
(a) 1.
(b) 0.
(c) −1.
(d) 2.
(21) lim sin(2θ)
=
3θ
θ→0
(a) 1.
(b) 0.
(c)
(d)
3
.
2
2
.
3
(22) The function f (x) = x3 − x − 1 has a root in the interval
(a) [1, 2].
(b) [0, 1].
(c) [−1, 1].
(d) [−2, −1].
(23) The area enclosed between the curve y =
(a)
(b)
(c)
(d)
√
x and the lines y = 0 and x = 1 is
2
.
3
3
.
2
1
.
2
1
.
3
(24) The area of the largest triangle that we can draw inside the upper semicircle x2 + y 2 = 9
is
4
(a) 9.
(b) 3.
(c) 27.
(d) 18.
√
(25) The area bounded from above by the graph of y = x and the X-axis on the interval
[0,2] in the first quadrant is revolved about the X−axis. The volume of the solid of
revolution is
(a) π
(b) 2π
(c)
π
2
(d) none
5
Sample Math Placement Exam 2014
Name _____________________
Application Number_________
Tawjihi Average ______________
Math Tawjihi Grade _________
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