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, solving systems 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  3
2)
15 - [8 - (2 + 5)]
18 - 52
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) 24
2) 147
3)
6
27
4)
3
6
5) Find the distance between
(50, 4) and (40, -6)
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.
y

1
1) x  + 3z 2  - 2x if x = , y = 4, z = -2
2
2

3)
2)
-b + b2 - 4ac
if a = 1, b = - 4, c = -21
2a
. Evaluate
IV. Properties of Exponents
PROPERTY
Product of Powers
a  an = am + n
x  x2 =
Power of a Power
(am)n = am  n
(x4)2 =
Power of a Product
(ab)m = ambm
(2x)3 =
Negative Power
1
a = n
a
a0 = 1
x-3 =
Zero Power
m
(a  0)
-n
(a  0)
Quotient of Powers
am
= am – n
an
Power of Quotient
am
a
=
 
bm
b
EXAMPLE
4
40 =
(a  0)
x3
=
x2
3
m
(b  0)
x
  =
 y
Simplify each expression. Answers should be written using positive exponents.
7
-3
1) (3x )(-5x )
-5 0
2
2) (-4a b c)
-15x 7 y -2
3)
25x -9 y5
 4 x9 
4) 
4 
 12 x 
3
V. Solving Linear Equations
Solve for the indicated variable:
1) 2[x + 3(x – 1)] = 18
2) 2x2 = 50
4) 6 + 2x(x – 3) = 2x2
5)
3) 5 + 2(k + 4) = 5(k - 3)+ 10
2
x
x -18 =
3
6
6)
x - 2 2x + 1
=
3
4
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)
4) (5x2 - 4) – 2(3x2 + 8x + 4)
5) (5x – 6)2
3) (n2 + 5n + 3) + (2n2 + 8n + 8)
6)
. Find
VII. Factoring Polynomials
Examples:
Factoring out the GCF
1) 6x2 + 21x
Trinomial
4) x2 - 2x – 63
Difference of Squares
2)
x2 - 64
Perfect Square Trinomial
3) x2 - 10x + 25
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 - 4
3) 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
1)
y = 2x + 4
-3x + y = - 9
(Answers should be written as ordered pairs.)
2) 2x + 3y = 6
-3x + 2y = 17
3) x – 2y = 5
3x – 5y = 8
4) 3x + 7y = -1
6x + 7y = 0
X. Linear Inequalities and Absolute Value Inequalities
1)
2) 4  7  2 x  10
3)
5  2 x  11
4) 2 x  5  11
XI. Literal Equations
1) Solve for h.
A=
2) Solve for x.
3) Solve for 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!