neiu placement test entering freshman students are given two options for placement into a math...
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NEIU Placement Test Entering freshman students are given two options for placement into a math course:
ACT scores or the Math Placement Test (MPT). The university will use the higher of the two scores for placement into a math course Since there is no penalty to taking the MPT, freshmen are strongly encouraged to do
so, particularly if they took a math course in their senior year of high school. Freshmen with Math ACT scores of 21 or less are given the Basic MPT.
The Basic MPT is one hour consisting of a thirty minute test in Elementary Algebra and a thirty minute test in Intermediate Algebra.
Students with Math ACT scores of 22 or higher are given the Advanced MPT. The Advanced MPT is one hour consisting of a thirty minute test in Intermediate
Algebra and a thirty minute test in Pre-Calculus. Freshmen who do not submit ACT scores must take the Basic MPT. Please note: Calculators are not allowed to be used during MPT testing.
NIU The math placement test consists of 40 multiple-choice
questions: 5 choices per question, no penalty for guessing. You have 75 minutes to take the test, which seems to be
sufficient for almost everyone. The questions range from Basic Algebra through Advanced
Algebra (e.g. logarithms and graphing). There is a separate portion (20 questions) on trigonometry
which is required only if you are trying to test into Math 229 (Calculus 1).
You will not need a calculator and are not permitted to bring in any electronic tools, books, or notebooks.
NEIU Sample Placement Math TestIntermediate Algebra
Type of Problem Number of ProblemsFactoring or FOIL 5
Quadratic functions (graph, vertex, x-intercepts, y-intercepts)
3
Solving quadratic equations 3
Writing equations of lines: Slope, parallel and perpendicular lines
4
Systems of equations: Substitution, elimination
3
Rational expressions: Solving equations with fractions
7
Exponent rules, radicals 5
NEIU Sample Placement Math TestElementary Algebra
Type of Problem Number of Problems
Factoring or FOIL 9
Adding/subtracting polynomials 1
Simplifying expressions: Distributive property, CLT, order of
operations, solving equations
5
Graphing inequalities 1
Basic adding/subtracting (fractions, absolute value, word problems)
8
Exponent rules, radicals 6
New unit on Exponents, Radicals & Rational Expressions
SWBAT…1. Apply and explain the rules of exponents
Zero exponent property Negative exponent property Product of powers rule Power of a power rule Power of a product rule Power of a quotient rule Quotient of powers rule
2. Simplifying radicals (square roots)
3. Simplifying rational expressions
Definition of an exponent
An exponent tells how many times a number is multiplied by itself.
34= (3)(3)(3)(3) = 81
34
BaseExponent
A = π(8cm)2
A = 64π cm2
Exponents are often used in volume problems to show the centimeters are cubed
Volume = (length)(width)(height) Length = 10 cmWidth = 10 cmHeight = 20 cm
Volume = (20cm)(10cm)(10cm) = 2,000 cm3
10
10
20
What is the exponent?
(5)(5)(5)(5) = 54
What is the base and the exponent?
(7)(7)(7)(7)(7) = 7 5
What is the answer?
53
= 125
Compute: (-4)2
Answer: (-4)(-4) = 16
Calculate: -42
Answer: -(4)(4) = -16
PEMDAS
Simplify: n2 when n = -5
Answer: (-5)2 = (-5)(-5) = 25
Simplify: -n2 when n = -5
Answer: -(-5)2 = -(-5)(-5) = -25
Simplify: (x + 3)2
Answer: (x + 3)(x + 3) x2 + 6x + 9
Compute: 02
Answer: 0
Compute: 20
Answer: 1
WHY is anything to the power zero "1"
36 = 72935 = 243 34 = 81 33 = 27 32 = 9 31 = 3
30 = 1
Laws of Exponents
nmn
m
m
mm
mmm
mnnmnmnm
nnn
n
xx
x
y
x
y
xyxxy
xxxxx
xx
orx
xx
.7
.6.5
.4.3
11.21.1 0
Zero Exponent Property (1)Words: Any nonzero number raised to the zero
power is equal to 1.
Symbols: For any nonzero number x, x0 = 1.
Examples:
1.) 120 = 1
2.)
3.)1
0
c
b
17
20
Open Ended: Create a problem that satisfies this property!
Let’s practice…
Simplify each expression:
1.) (-3.14)0
2.) -3.140
3.) (-x)0 if x = 4
4.) -54(-4)0
5. [(3x4y7z12)5 (–5x9y3z4)2]0
Negative Exponent Property (2)Words: For any nonzero number a and any integer n,
x-n is the reciprocal of xn.
Also, the reciprocal of x-n = xn.
Symbols: For any nonzero number a and any integer n,
Examples:
nnn
n xx
andx
x 11
25
1
5
15
22 3
3
1m
m
Open Ended: Create a problem that satisfies this property!
228
2
2
7
2
24
4
06 yx
OYO Problems (On Your Own)24
0)7(32 22)16(
3
2
2
5