Honors Mathematics

Main Objective: Students will explore the key concepts and theories that provide a foundation for further study of Honors Geometry and Honors Algebra II. Our goal is to increase students’ mathematics literacy, problem solving, and critical thinking skills.Students will be tested on Algebra I concepts on 2nd or 3rd day of

school.

I-VI:

Order of operations, simplifying radicals, evaluating algebraic

expressions, properties of exponents, solving linear equations, operations

with polynomials.

VII-XI.

Factoring polynomials, linear equations with two variables, graphing linear functions, solvingsystems of equations, linear inequalities and absolute value inequalities, solving literal equations.

I. Order of Operations (PEMDAS)

  • Parenthesis and other grouping symbols.
  • Exponential expressions.
  • Multiplication & Division.
  • Addition & Subtraction.

Simplify each numerical expression.

1)6 + 2 x 8 – 12 + 9 32)

II. Simplifying Radicals

An expression under a radical sign is in simplest radical form when:

  • there is no integer under the radical sign with a perfect square factor,
  • there are no fractions under the radical sign,
  • there are no radicals in the denominator

Express the following in simplest radical form.

1) 2) 3) 4) 5)

III. Evaluating Algebraic Expressions

To evaluate an algebraic expression:

  • Substitute the given value(s) of the variable(s).
  • Use order of operations to find the value of the resulting numerical expression.

Evaluate.

1) 2)

3) . Evaluate

IV. Properties of Exponents

Property / Example
Product of Powers / am an = am + n / x4 x2 =
Power of a Power / (am)n = amn / (x4)2 =
Power of a Product / (ab)m = ambm / (2x)3 =
Negative Power / a-n = (a0) / x-3 =
Zero Power / a0 = 1 (a0) / 40 =
Quotient of Powers / = am – n (a0) / =
Power of Quotient / = (b0) / =

Simplify each expression. Answers should be written using positive exponents.

1) (3x7)(-5x-3) 2) (-4a-5b0c)2 3) 4)

V. Solving Linear Equations

Solve for the indicated variable:

1) 2[x + 3(x – 1)] = 182) 2x2 = 50 3) 5 + 2(k + 4) = 5(k - 3)+ 10

4) 6 + 2x(x – 3) = 2x25) 6)

VI. Operations With Polynomials

  • To add or subtract polynomials, just combine like terms.
  • To multiply polynomials, multiply the numerical coefficients and apply the rules for exponents.

Perform the indicated operations and simplify:

1) -2x(5x + 11)2) (7x - 3)(3x + 7)3) (n2 + 5n + 3) + (2n2 + 8n + 8)

4) (5x2 - 4) – 2(3x2 + 8x + 4)5) (5x – 6)26) . Find

VII. Factoring Polynomials

Examples:

Factoring out the GCF Difference of Squares Perfect Square Trinomial

1) 6x2 + 21x / 2) x2 - 64 / 3) x2 - 10x + 25
Trinomial
4) x2- 2x – 63 / Trinomial
5) 2x2– 13x + 15 / Trinomial
6) 6x2 + x – 1

VIII. Linear Equations in Two Variables

1) Find the slope of the line passing through the points (-1, 2) and (3, 5).

2) Graph f(x) = 2/3 x - 43) Graph 3x - 2y - 8 = 0

4) Write the equation of the line with a slope of 3 and passing through the point (2, -1).

5) Write an equation of a line that is perpendicular to x - 2y = - 12 and passes through the point (-2,-5).

IX. Solving Systems of Equations(Answers should be written as ordered pairs.)

1) y = 2x + 4 2) 2x + 3y = 6 3) x – 2y = 54) 3x + 7y = -1 -3x + y = - 9 -3x + 2y = 17 3x – 5y = 8 6x + 7y = 0

X. Linear Inequalities and Absolute Value Inequalities

1) 2) 3) 4)

XI. Literal Equations

1) Solve for h.2) Solve for x.3) Solve for a.

A= 4ab – 2 = 3a

Students,

Please find extra practice problems on the school’s website under summer assignments. We highly recommend you review, practice, and UNDERSTAND ALL topics outlined above. Students will be tested on Algebra I concepts on 2nd or 3rd day of school.You are EXPECTED to know these Algebra 1 concepts prior to the test!