Math Placement Test Format and Topics
Effective May 2013
The Math placement test at Khalifa University includes 40 questions that should be solved within
75 minutes. The test is divided into two parts: Part 1 consists of 20 questions in Arithmetic and
Basic Algebra and Part 2 consists of 20 questions in College Algebra and Pre-Calculus
questions. No calculator is allowed.
The topics that are included in the test are described in the following table:
Number of questions
Topics covered
Part 1: (30 Minutes)
Arithmetic
&
Basic Algebra
20
• Arithmetic: fractions,
decimals, etc.
• Operations with real
numbers: absolute
value, powers and
radicals, rationals &
irrationals, etc.
• Linear equations.
• Linear inequalities.
• Simplifying rational
expressions, etc.
• Geometry: angles,
perimeter & area of
plane figures,
Cartesian
coordinates, lines,
Pythagorean
Theorem, etc.
• Polynomials: degree
2 at most.
Part 2 (45 Minutes)
College Algebra
&
Precalculus
20
• Geometry (advanced).
• Polynomials (advanced).
• Trigonometry: identities,
equations, graphs.
• Exponential functions.
• Logarithmic functions.
• Equations involving
exponentials and/or
logarithms.
• Quadratic equations.
• Quadratic inequalities.
• Equations and
Inequalities involving
absolute value.
• Rational functions.
• Composition of functions.
Sample Questions
Part 1
1. The quantity 5 ·
√
16 − 32 · 20 is equal to
(a) 2.
(b) 14.
(c) 11.
(d) 8.
2. Subtract and simplify:
2 1
− = ···
5 3
3
.
15
1
(b) .
2
2
(c) .
5
1
(d)
.
15
(a)
3. The decimal form of
78
is
1000
(a) 7.8.
(b) 0.78.
(c) 780.
(d) 0.078.
4. |2 − 3| + |5 + 2| = · · ·
(a) 6.
(b) 8.
(c) −2.
(d) 0.
5. Solve
3
1
=x− .
2
4
(a) x = 2.
5
(b) x = .
4
(c) x = −1.5.
(d) x = 4.
1
6. Solve −4x + 7 ≥ −5.
(a) x ≤ 3.
(b) x ≥ 2.
(c) x ≤ −1.
(d) x ≥ 5.
7. Find the numerical value of
3x − 2
when x = 2.
2x + 3
3
.
4
9
(b) .
7
4
(c) .
7
2
(d) .
9
(a)
8.
52 · 34
= ···
32 · 5 · 7
1
.
7
15
.
(b)
7
45
(c)
.
7
7
(d)
.
45
(a)
9. A circle with area 4π has a radius of
(a) 2.
√
(b) 2.
(c) 4.
(d) π.
10. Which of the following polynomials has x = 2 as root?
(a) x2 + x + 100.
(b) 3(x − 2)4 + 1.
(c) x2 − x − 1.
(d) (3x − 6)(x + 1).
2
Sample Questions
Part 2
1. Find the area of a right triangle having a hypothenuse of length 5 and a base of
length 4.
(a) 10.
(b) 12.
(c) 6.
(d) 20.
2. Which polynomial of degree 3 has the following roots: −1, 0, 1?
(a) x3 − x.
(b) x3 + x.
(c) x3 − x − 1.
(d) x3 + x + 1.
h πi
such that cos2 x − 3 sin2 x = 0.
3. Find x ∈ 0,
2
π
(a) .
6
π
(b) .
2
π
(c) .
3
π
(d) .
4
4. Simplify log10
1
.
1000
(a) 3.
(b) −3.
(c) 100.
(d) −100.
5. Simplify
e3x
· ln ex .
(e2x )2
(a) xe−x .
(b) xex .
(c) −xe−x .
(d) −xex .
3
6. Solve e2x − 2ex + 1 = 0.
(a) x = 1.
(b) x = 2.
(c) x = e.
(d) x = 0.
7. A quadratic function has a double root at x = 3. Find the coordinates of the vertex.
(a) (0, 0).
(b) (3, 3).
(c) (3, 0).
(d) (0, 3).
8. Solve (x − 1)(x + 3) ≤ 0.
(a) x ∈ (−3, 1).
(b) x ∈ [−3, 1].
(c) x ∈ (−∞, −3).
(d) x ∈ (1, ∞).
9. Solve |x − 2| ≤ 4.
(a) x ∈ [−6, −2).
(b) x ∈ [−2, 6].
(c) x ∈ [2, 6].
(d) x ∈ [−6, −2].
10. If f (x) = x2 and g(x) = 2x − 1, then f (g(0)) = · · ·
(a) 1.
(b) −1.
(c) 0.
(d) 2.
4