NEIU Placement Test n n n n Entering

NEIU Placement Test n n n n 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 n n n 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 Test Intermediate Algebra Type of Problem Number of Problems Factoring or FOIL Quadratic functions (graph, vertex, x-intercepts, y-intercepts) 5 3 Solving quadratic equations Writing equations of lines: Slope, parallel and perpendicular lines Systems of equations: Substitution, elimination Rational expressions: Solving equations with fractions 3 4 Exponent rules, radicals 5 3 7

NEIU Sample Placement Math Test Elementary Algebra Type of Problem Number of Problems Factoring or FOIL Adding/subtracting polynomials Simplifying expressions: Distributive property, CLT, order of operations, solving equations Graphing inequalities Basic adding/subtracting (fractions, absolute value, word problems) Exponent rules, radicals 9 1 5 1 8 6

New unit on Exponents, Radicals & Rational Expressions n 1. SWBAT… 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. 3. Simplifying radicals (square roots) Simplifying rational expressions

Definition of an exponent n An exponent tells how many times a number is multiplied by itself. 4 Base 4 3 Exponent 3 = (3)(3) = 81

A= 2 π(8 cm) A = 64π 2 cm

Exponents are often used in volume problems to show the centimeters are cubed Volume = (length)(width)(height) Length = 10 cm Width = 10 cm Height = 20 cm 20 10 10 3 Volume = (20 cm)(10 cm) = 2, 000 cm

What is the exponent? (5)(5) = 5 4

What is the base and the exponent? (7)(7)(7) = 7 5

What is the answer? 5 3 = 125

2 Compute: (-4) Answer: (-4) = 16

PEMDAS 2 Calculate: -4 Answer: -(4)(4) = -16

2 Simplify: n when n = -5 Answer: 2 (-5) = 25

2 Simplify: -n when n = -5 Answer: 2 -(-5) = -25

Simplify: (x + 2 3) Answer: (x + 3) 2 x + 6 x + 9

2 Compute: 0 Answer: 0

0 Compute: 2 Answer: 1

WHY is anything to the power zero "1" 36 = 729 5 3 = 243 4 3 = 81 33 = 27 2 3 = 9 31 = 3 0 3 =1

Laws of Exponents

Zero Exponent Property (1) Words: Any nonzero number raised to the zero power is equal to 1. Symbols: For any nonzero number x, x 0 = 1. Examples: 1. ) 120 = 1 2. ) 3. ) 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. [(3 x 4 y 7 z 12)5 (– 5 x 9 y 3 z 4)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: Open Ended: Create a problem that satisfies this property!

OYO Problems (On Your Own)