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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# OBJECTIVES FOR THE MMPT

 NO CALCULATORS ARE ALLOWED ON THE MMPT. PRACTICE THE FOLLOWING EXERCISES WITHOUT A CALCULATOR.

. Hierarchy of Operations

Be able to:
• apply the proper order of operations when evaluating an arithmetic expression
Ex. Evaluate: −32 − (−52) − (−10)2 = ;

• apply the proper order of operations when working with algebraic expressions.
Ex. Simplify: ;

B. Factoring

Be able to factor polynomials over the integers:
1. By factoring the GCF

Ex. 25x (2x − 3)2 − 5x (2x − 3) = ;

2. By regrouping of the terms
Ex. Factor completely: 16x3 − 4x2 − 36x + 9 = ; x2 − 2xy + y2 − 4z2 =;

3. By applying the basic identities:

• A2 ± 2AB + B2 = (A ± B)2
Ex. Factor: x2 − 6xy + 9y2 =
• A2 − B2 = (A + B)(A − B)
Ex. Factor: 16x4 − 81y4 =
• A3 ± B3 = (A ± B)(A2 AB + B2)
Ex. Factor: 27a3 − 64b3 =

C. Rational Expressions

Be able to:
• Simplify, multiply, divide, add and subtract rational expressions • Simplify complex fractions. Be able to:
• Apply the laws of exponents to simplify, multiply and divide expressions involving
integer and/or rational exponents • Evaluate numbers raised to rational exponents and which result in a rational number Write in radical form expressions containing rational exponents and simplify the (Answer : )

• Write in exponent form a radical expression and simplify the answer. (Answer : )

expressions • Rationalize numerators or denominators.

Ex. 1. Rationalize the numerator: ;
2. Rationalize the denominator and simplify: E. Equations

Be able to solve:

• linear equations

Ex. Solve for x: Ex. Solve for x: x2 − 5x + 6 = 0 ;

Ex. Solve for x: 3x2 − 2x +1 = 0 ;

• polynomial equations over the complex numbers by factoring

Ex. Solve for x: x3 − 27 = 0 ;

• rational equations
Ex. Solve for x: ;
• absolute value equations

Ex. Solve for x: |2x − 3|= 5;

Ex. Solve for x: (2x + 3)2 − 3(2x + 3) + 2 = 0 ;

Ex. Solve for x: ;

• exponential equations
Ex. Solve for x: ;

• logarithmic equations

Ex. Solve for x: • literal equations

Ex. Solve for W: S = 2LW + 2LH + 2HW;

• systems of equations in two variables

Ex. Solve the system: • trigonometric equations
Ex. Solve for x: , for 0 ≤ x ≤ 2π

F. Inequalities

Be able to solve:

• linear inequalities in one variable

Ex. Solve for x: • compound inequalities

Ex. Solve for x: −4x ≤ 8 and 2(x − 3) > 4 ;

−4x ≤ 8 or 2(x − 3) > 4; −3 < 5 − 2x ≤ 10;

• absolute value inequalities

Ex. Solve for x: |2x – 3|< 5; |5x + 7| + 8 > 11;

Ex. Solve for x: .