# 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: −3^{2} − (−5^{2}) − (−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: 16x^{3} − 4x^{2} − 36x + 9 = ; x^{2}
− 2xy + y^{2} − 4z^{2} =;

3. By applying the basic identities:

• A^{2} ± 2AB + B^{2} = (A ± B)^{2}

Ex. Factor: x^{2} − 6xy + 9y^{2} =

• A^{2} − B^{2} = (A + B)(A − B)

Ex. Factor: 16x^{4} − 81y^{4} =

• A^{3} ± B^{3} = (A ± B)(A^{2}
AB + B^{2})

Ex. Factor: 27a^{3} − 64b^{3} =

**C. Rational Expressions**

Be able to:

• Simplify, multiply, divide, add and subtract rational expressions

• Simplify complex fractions.

**D. Exponents and Radicals**

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.

(Answer :)

• Write in exponent form a radical expression and simplify the answer.

(Answer :)

Apply the laws of radicals to simplify, add, subtract,
multiply and divide radical

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:

• quadratic equations by factoring

Ex. Solve for x: x^{2} − 5x + 6 = 0 ;

• quadratic equations over the complex numbers using the quadratic formula

Ex. Solve for x: 3x^{2} − 2x +1 = 0 ;

• polynomial equations over the complex numbers by factoring

Ex. Solve for x: x^{3} − 27 = 0 ;

• rational equations

Ex. Solve for x:

;

• absolute value equations

Ex. Solve for x: |2x − 3|= 5;

• equations in quadratic form

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

• equations that involve radicals

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;

• quadratic inequalities

Ex. Solve for x : x^{2} − 5x + 6 ≥ 0;

• easily factorable or already factored polynomial inequalities

Ex. Solve for x: 2x^{3}(x − 2)(x + 4)^{2}(x +1) ≥ 0 ;

• rational inequalities

Ex. Solve for x: .