Download 2. Algebra - International School of Sosua

Grade 10 Math Syllabus Algebra II
Course Description
Grade10 Algebra II has been developed taking into consideration the five standards
(strands) of Mathematics defined by NCTM: the course develops student
understanding and skills in Algebra II including numbers, operations, geometry,
measurement, data analysis, probability and problem solving. The Algebra II course
will focus on linear equations and inequalities, systems of equations and inequalities,
factoring polynomials and trinomials, matrices, quadratics, relations, functions, graphs,
roots, radicals, complex numbers and exponents and logarithms. In addition students
learn different ways to represent math, to communicate their math understanding and
to make connections to real world situations and other subject areas. Students are
assessed in a variety of ways continuously throughout the program of study to ensure
they are understanding content and are able to use and apply the knowledge and skills
they are developing.
Curricular content
APPENDIX A contains the standards. APPENDIX B contains the performance indicators
for each standard for High School, APPENDIX C contains the Mathematics Focal Points
for Grade 10 and APPENDIX D contains the Secondary Assessment Policy. Students use
the Holt McDougal – Algebra 2 textbook.
Quarter 1
Unit 0: Numeracy
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Theory behind number
Operations with intergers, fractions, decimals
Unit 1: Foundations for functions
 Classify and order real numbers (1.1)
 Simplify, add, subtract, multiply and divide square roots (1.3)
 Simplify and evaluate algebraic expressions (1.4)
 Simplify expressions involving exponents & use scientific notation (1.5)
 Identify the domain and range of functions & determine whether a relation is
a function (1.6)
 Graph functions (1.7)
Unit 2: Linear Equations and Inequalities in Two Variables
 Solving linear equations and inequalities (2.1)
 Proportional reasoning (2.2)
 Graphing linear equations on a coordinate plane (2.3)
- Graphing from slope-intercept form
- Graphing using x and y intercepts
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Writing equations of lines (2.4)
- Given slope and y-intercept
- Given slope and a point
- Given two points
- Given a point and a parallel line
- Given a point and a perpendicular line
Using linear equations and inequalities in two variables to solve real-world
problems Linear Programming (2.4)
Graphing linear inequalities in two variables on a coordinate plane(2.5)
Transforming linear functions (2.6)
Solving absolute value equations and inequalities (2.8)
Drawing absolute value functions and transforming them (2.9)
Unit 3: Systems of Linear Equations and Inequalities
 Solving systems of equations by graphing (3.1)
 Solving systems of equations with the substitution method (3.2)
 Solving systems of equations with the elimination (linear combination)
method (3.2)
 Determining number of solutions to a system of equations (3.2)
 Using systems of equations to solve real-world problems (3.2)
 Graphing systems of inequalities (3.3)
 Using systems of inequalities to solve real-world problems (3.3)
 Linear Programming (3.4)
- Finding the feasible region
- Maximizing or minimizing the objective function
- Linear problems in real world examples
 Graph points and linear equations in 3 dimensions (3.5)
 Solve linear systems in 3 variables Linear Programming (3.6)
Quarter 2
Unit 4: Matrices
 Use Matrices to display real world data, Adding & subtracting (4.1)
 Multiplying matrices (4.2)
 Computing determinants of matrices (2x2 and 3x3 matrices only) (4.3)
 Using Cramer´s rule to solve systems of equations (4.3)
 Computing inverses of matrices (2x2 only) (4.5)
 Using inverse matrices to solve systems of equations (only systems of 2
equations) (4.5)
Unit 5: Quadratic Functions (Part 1)
 Graphing quadratic functions (5.1)
 Properties of quadratic functions in standard form (5.2)
 Solving quadratic equations by factoring (5.3)
- When leading coefficient is equal to 1
- When leading coefficient is not equal to 1
- Using special patterns (difference of squares, perfect square trinomial)
 Using quadratic functions to solve real-world problems (5.3)
Semester Exam
Quarter 3
Unit 5: Quadratic Functions (Part 2)
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Solve quadratic equations by completing the square. (5.4)
Write quadratic equations in vertex form. (5.4)
Define and use imaginary and complex numbers. (5.5)
Solve quadratic equations with complex roots. (5.5)
Solve quadratic equations using the quadratic formula. (5.6)
Classify roots using the discriminant. (5.6)
Solve quadratic inequalities by using tables, graphs and algebra. (5.7)
Perform operations with complex numbers. (5.9)
Unit 6: Polynomial Functions
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Identify, evaluate, add and subtract polynomials. (6.1)
Classify and graph polynomials. (6.1)
Multiply polynomials, use binomial expansion to expand binomial expressions that are
raised to positive integer powers. (6.2)
Use long division and synthetic division to divide polynomials. (6.3)
Use the factor theorem to determine factors of a polynomial. (6.4)
Factor the sum and difference of two cubes. (6.4)
Identify the multiplicity of roots. Solve polynomials with rational and irrational roots.
(6.5)
Write a polynomial equation of least degree with given roots. (6.6)
Identify all of the roots of a polynomial equation. (6.6)
Use properties of end behavior to analyze, describe, and graph polynomial functions.
(6.7)
Identify and use maxima and minima of polynomial functions to solve problems. (6.7)
Transform polynomial functions. (6.8)
Unit 7: Exponential and Logarithmic Functions
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Write and evaluate exponential expressions to model growth and decay situations. (7.1)
Graph and recognize inverses of relations and functions. (7.2)
Write equivalent forms for exponential and logarithmic functions. (7.3)
Write, evaluate, and graph logarithmic functions. (7.3)
Use properties to simplify logarithmic expressions. (7.4)
Translate between logarithms in any base. (7.4)
Solve exponential and logarithmic equations. Solve problems involving exponential and
logarithmic equations. (7.5)
Use the number e to write and graph exponential functions representing real-world
situations. (7.6)
Solve equations and problems involving e or natural logarithms. (7.6)
Quarter 4
Unit 8: Rational and Radical Functions
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Solve problems involving direct, inverse, joint, and combined variation. (8.1)
Simplify rational expressions. (8.2)
Multiply and divide rational expressions. (8.2)
Add and subtract rational expressions. Simplify complex fractions. (8.3)
Graph rational functions. Transform rational functions by changing parameters. (8.4)
Solve rational equations. (8.5)
Rewrite radical expressions by using rational exponents. (8.6)
Simplify and evaluate radical expressions and expressions containing rational exponents.
(8.6)
Solve radical equations. (8.8)
Unit 9: Probability and Statistics
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Solve problems involving the fundamental counting principle. (11.1)
Solve problems involving permutations and combinations. (11.1)
Find the theoretical probability of an event. (11.2)
Find the experimental probability of an event. (11.2)
Determine whether events are independent or dependent. (11.3)
Find the probability of independent and dependent events. (11.3)
Find the probability of mutually exclusive or inclusive events. (11.4)
Find measures of central tendency and measures of variation for statistical data. (11.5)
Examine the effect of outliers on statistical data. (11.5)
Use the Binomial Theorem to expand a binomial raised to a power. (11.6)
Find binomial probabilities and test hypotheses. (11.6)
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**Extension: Normal Distributions.
Final exams
Grading Policy

Effort: Classwork and Homework
15%
Formative: Quizzes, projects, major HW, Accelerated Math
45%
Summative: Quarter Tests and Major portfolio projects
40%
Semester grades are developed based upon the following formula for Math:

Quarterly Grades
(average)
80%
Exam Grade or Semester Project 20%
Final grades are accrued by averaging the two semester grades.
APPENDIX A: Mathematics Standards
1. Number and Operations
Instructional programs from prekindergarten through grade 12 should enable all
students to-
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understand numbers, ways of representing numbers, relationships among
numbers, and number systems;
understand meanings of operations and how they relate to one another;
compute fluently and make reasonable estimates
2. Algebra
Instructional programs from prekindergarten through grade 12 should enable all
students to-
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understand patterns, relations, and functions;
represent and analyze mathematical situations and structures using algebraic
symbols;
use mathematical models to represent and understand quantitative relationships;
analyze change in various contexts
3. Geometry
Instructional programs from prekindergarten through grade 12 should enable all
students to-
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analyze characteristics and properties of two- and three-dimensional geometric
shapes and develop mathematical arguments about geometric relationships;
specify locations and describe spatial relationships using coordinate geometry
and other representational systems;
apply transformations and use symmetry to analyze mathematical situations;
use visualization, spatial reasoning, and geometric modeling to solve problems.
4. Measurement
Instructional programs from prekindergarten through grade 12 should enable all
students to-

understand measurable attributes of objects and the units, systems, and
processes of measurement;
apply appropriate techniques, tools, and formulas to determine measurements.
5. Data Analysis and Probability
Instructional programs from prekindergarten through grade 12 should enable all
students to-
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formulate questions that can be addressed with data and collect, organize, and
display relevant data to answer them;
select and use appropriate statistical methods to analyze data;
develop and evaluate inferences and predictions that are based on data;
understand and apply basic concepts of probability
6. Problem Solving
Instructional programs from prekindergarten through grade 12 should enable all
students to-
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build new mathematical knowledge through problem solving;
solve problems that arise in mathematics and in other contexts;
apply and adapt a variety of appropriate strategies to solve problems;
monitor and reflect on the process of mathematical problem solving.
7. Reasoning and Proof
Instructional programs from prekindergarten through grade 12 should enable all
students to-
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recognize reasoning and proof as fundamental aspects of mathematics;
make and investigate mathematical conjectures;
develop and evaluate mathematical arguments and proofs;
select and use various types of reasoning and methods of proof.
8. Communication
Instructional programs from prekindergarten through grade 12 should enable all
students to-
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organize and consolidate their mathematical thinking through communication;
communicate their mathematical thinking coherently and clearly to peers,
teachers, and others;
analyze and evaluate the mathematical thinking and strategies of others;
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use the language of mathematics to express mathematical ideas precisely.
9. Connections
Instructional programs from prekindergarten through grade 12 should enable all
students to-
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recognize and use connections among mathematical ideas;
understand how mathematical ideas interconnect and build on one another to
produce a coherent whole;
recognize and apply mathematics in contexts outside of mathematics.
10. Representation
Instructional programs from prekindergarten through grade 12 should enable all
students to-
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create and use representations to organize, record, and communicate
mathematical ideas;
select, apply, and translate among mathematical representations to solve
problems;
use representations to model and interpret physical, social, and mathematical
phenomena.
APPENDIX B: Performance Indicators Grades 9-12
1. Numbers and Operations Standard
Instructional
programs from
In grades 9 through 12 all students should—
prekindergarten
through grade 12
should enable all
students to
1.1 Understand
numbers, ways of
representing numbers,
relationships among
numbers, and number
systems
1.2 Understand
meanings of
operations and how
they relate to one
another
1.3 Compute fluently
and make reasonable
estimates
 develop a deeper understanding of very large and very small
numbers and of various representations of them;
 compare and contrast the properties of numbers and number
systems, including the rational and real numbers, and
understand complex numbers as solutions to quadratic
equations that do not have real solutions;
 understand vectors and matrices as systems that have some
of the properties of the real-number system;
 use number-theory arguments to justify relationships
involving whole numbers.
 judge the effects of such operations as multiplication,
division, and computing powers and roots on the
magnitudes of quantities;
 develop an understanding of properties of, and
representations for, the addition and multiplication of
vectors and matrices;
 develop an understanding of permutations and combinations
as counting techniques.
 develop fluency in operations with real numbers, vectors,
and matrices, using mental computation or paper-and-pencil
calculations for simple cases and technology for morecomplicated cases.
 judge the reasonableness of numerical computations and
their results.
2. Algebra Standard
Instructional
programs from
prekindergarten
through grade 12
should enable all
students to—
2.1 Understand
patterns, relations, and
functions
In grades 9 through 12 all students should—

generalize patterns using explicitly defined and recursively
defined functions;
 understand relations and functions and select, convert
flexibly among, and use various representations for them;
 analyze functions of one variable by investigating rates of
change, intercepts, zeros, asymptotes, and local and global
behavior;
 understand and perform transformations such as
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2.2 Represent and
analyze mathematical
situations and
structures using
algebraic symbols
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2.3 Use mathematical
models to represent
and understand
quantitative
relationships
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2.4 Analyze change in
various contexts
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arithmetically combining, composing, and inverting
commonly used functions, using technology to perform such
operations on more-complicated symbolic expressions;
understand and compare the properties of classes of
functions, including exponential, polynomial, rational,
logarithmic, and periodic functions;
interpret representations of functions of two variables
understand the meaning of equivalent forms of expressions,
equations, inequalities, and relations;
write equivalent forms of equations, inequalities, and
systems of equations and solve them with fluency—
mentally or with paper and pencil in simple cases and using
technology in all cases;
use symbolic algebra to represent and explain mathematical
relationships;
use a variety of symbolic representations, including
recursive and parametric equations, for functions and
relations;
judge the meaning, utility, and reasonableness of the results
of symbol manipulations, including those carried out by
technology.
identify essential quantitative relationships in a situation and
determine the class or classes of functions that might model
the relationships;
use symbolic expressions, including iterative and recursive
forms, to represent relationships arising from various
contexts;
draw reasonable conclusions about a situation being
modeled.
approximate and interpret rates of change from graphical
and numerical data.
3. Geometry Standard
Instructional
programs from
prekindergarten
through grade 12
should enable all
students to—
3.1 Analyze
characteristics and
properties of two- and
three-dimensional
geometric shapes and
develop mathematical
In grades 9 through 12 all students should—

analyze properties and determine attributes of two- and
three-dimensional objects;
 explore relationships (including congruence and similarity)
among classes of two- and three-dimensional geometric
objects, make and test conjectures about them, and solve
problems involving them;
arguments about
geometric
relationships
3.2 Specify locations
and describe spatial
relationships using
coordinate geometry
and other
representational
systems
3.3 Apply
transformations and
use symmetry to
analyze mathematical
situations
3.4 Use visualization,
spatial reasoning,
and geometric
modeling to solve
problems
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establish the validity of geometric conjectures using
deduction, prove theorems, and critique arguments made by
others;
 use trigonometric relationships to determine lengths and
angle measures.
 use Cartesian coordinates and other coordinate systems,
such as navigational, polar, or spherical systems, to analyze
geometric situations;
 investigate conjectures and solve problems involving twoand three-dimensional objects represented with Cartesian
coordinates.
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understand and represent translations, reflections, rotations,
and dilations of objects in the plane by using sketches,
coordinates, vectors, function notation, and matrices;
use various representations to help understand the effects of
simple transformations and their compositions.
draw and construct representations of two- and threedimensional geometric objects using a variety of tools;
visualize three-dimensional objects and spaces from
different perspectives and analyze their cross sections;
use vertex-edge graphs to model and solve problems;
use geometric models to gain insights into, and answer
questions in, other areas of mathematics;
use geometric ideas to solve problems in, and gain insights
into, other disciplines and other areas of interest such as art
and architecture.
4. Measurement Standard
Instructional
programs from
prekindergarten
through grade 12
should enable all
students to—
4.1 Understand
measurable attributes
of objects and the
units, systems, and
processes of
measurement
4.2 Apply appropriate
techniques, tools, and
formulas to determine
measurements
In grades 9 though 12 all students should—
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make decisions about units and scales that are appropriate
for problem situations involving measurement.
analyze precision, accuracy, and approximate error in
measurement situations;
 understand and use formulas for the area, surface area, and
volume of geometric figures, including cones, spheres, and
cylinders;
 apply informal concepts of successive approximation, upper
and lower bounds, and limit in measurement situations;
 use unit analysis to check measurement computations
5. Data Analysis and Probability Standard
Instructional
programs from
prekindergarten
through grade 12
should enable all
students to—
5.1 Formulate
questions that can be
addressed with data
and collect, organize,
and display relevant
data to answer them
In grades 9 through 12 all students should—
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5.2 Select and use
appropriate statistical
methods to analyze
data
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5.3 Develop and
evaluate inferences
and predictions that
are based on data
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understand the differences among various kinds of studies
and which types of inferences can legitimately be drawn
from each;
know the characteristics of well-designed studies, including
the role of randomization in surveys and experiments;
understand the meaning of measurement data and
categorical data, of univariate and bivariate data, and of the
term variable;
understand histograms, parallel box plots, and scatterplots
and use them to display data;
compute basic statistics and understand the distinction
between a statistic and a parameter.
for univariate measurement data, be able to display the
distribution, describe its shape, and select and calculate
summary statistics;
for bivariate measurement data, be able to display a
scatterplot, describe its shape, and determine regression
coefficients, regression equations, and correlation
coefficients using technological tools;
display and discuss bivariate data where at least one variable
is categorical;
recognize how linear transformations of univariate data
affect shape, center, and spread;
identify trends in bivariate data and find functions that
model the data or transform the data so that they can be
modeled.
use simulations to explore the variability of sample statistics
from a known population and to construct sampling
distributions;
understand how sample statistics reflect the values of
population parameters and use sampling distributions as the
basis for informal inference;
evaluate published reports that are based on data by
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5.4 Understand and
apply basic concepts
of probability
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examining the design of the study, the appropriateness of
the data analysis, and the validity of conclusions;
understand how basic statistical techniques are used to
monitor process characteristics in the workplace.
understand the concepts of sample space and probability
distribution and construct sample spaces and distributions in
simple cases
use simulations to construct empirical probability
distributions;
compute and interpret the expected value of random
variables in simple cases;
understand the concepts of conditional probability and
independent events;
understand how to compute the probability of a compound
event.
APPENDIX C: Focal Points Grade 10 Algebra II
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Students solve equations and inequalities involving absolute value.
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Students solve systems of linear equations and inequalities (in two or three
variables) by substitution, with graphs, or with matrices.
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Students are adept at operations on polynomials, including long division.

Students factor polynomials representing the difference of squares, perfect square
trinomials, and the sum and difference of two cubes.

Students demonstrate knowledge of how real and complex numbers are related
both arithmetically and graphically. In particular, they can plot complex numbers
as points in the plane.
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Students add, subtract, multiply, and divide complex numbers.

Students add, subtract, multiply, divide, reduce, and evaluate rational expressions
with monomial and polynomial denominators and simplify complicated rational
expressions, including those with negative exponents in the denominator.

Students solve and graph quadratic equations by factoring, completing the square,
or using the quadratic formula. Students apply these techniques in solving word
problems. They also solve quadratic equations in the complex number system.

Students demonstrate and explain the effect that changing a coefficient has on the
graph of quadratic functions; that is, students can determine how the graph of a
2
parabola changes as a, b, and c vary in the equation y = a(x-b) + c.

Students graph quadratic functions and determine the maxima, minima, and zeros
of the function.

Students prove simple laws of logarithms.
o Students understand the inverse relationship between exponents and
logarithms and use this relationship to solve problems involving
logarithms and exponents.
o Students judge the validity of an argument according to whether the
properties of real numbers, exponents, and logarithms have been applied
correctly at each step.

Students know the laws of fractional exponents, understand exponential functions,
and use these functions in problems involving exponential growth and decay.

Students use the definition of logarithms to translate between logarithms in any
base.

Students understand and use the properties of logarithms to simplify logarithmic
numeric expressions and to identify their approximate values.

Students determine whether a specific algebraic statement involving rational
expressions, radical expressions, or logarithmic or exponential functions is
sometimes true, always true, or never true.

Students demonstrate and explain how the geometry of the graph of a conic
section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the
quadratic equation representing it.

Given a quadratic equation of the form ax + by + cx + dy + e = 0, students can
use the method for completing the square to put the equation into standard form
and can recognize whether the graph of the equation is a circle, ellipse, parabola,
or hyperbola. Students can then graph the equation.

Students use fundamental counting principles to compute combinations and
permutations.
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Students use combinations and permutations to compute probabilities.

Students know the binomial theorem and use it to expand binomial expressions
that are raised to positive integer powers.

Students apply the method of mathematical induction to prove general statements
about the positive integers.

Students find the general term and the sums of arithmetic series and of both finite
and infinite geometric series.

Students derive the summation formulas for arithmetic series and for both finite
and infinite geometric series.

Students solve problems involving functional concepts, such as composition,
defining the inverse function and performing arithmetic operations on functions.

Students use properties from number systems to justify steps in combining and
simplifying functions.
2
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APPENDIX D: Secondary Assessment Policy
Assessment monitors the progress of student learning and produces feedback for
students, teachers, parents and external institutions. The following policy outlines
the general assessment procedures for the school. Teachers are responsible for
communicating their individual assessment policies to the students and parents at
the beginning of the school year.
Teachers are expected to communicate assessment expectations and criteria,
including major assignments and projects clearly to students prior to a chunk of
learning. Assessment should take into account the ISS diverse group of learners
and learning styles. Feedback on assignments should be positive, constructive and
prompt. Teachers should provide a wide variety of different assessment
opportunities which are relevant and motivational to students. Formative
assessments assist student in building understanding, knowledge and skills and
summative assessments assess students’ acquired understanding, knowledge and
skills.
External
Definition External
assessments are
assessments
which are
designed and
marked
externally
Primary
To measure
Purpose
growth and
progress, to
inform teaching,
to identify needs,
to collect data, to
determine level
of
understanding,
to determine
reading or math
levels against
national norms,
assessing
student learning,
providing a
qualification for
university or
Summative
Summative
assessments are
those assessments
given within a class at
the end of a chunk of
learning (such as a
unit).
To inform teaching, to
identify needs, to
determine level of
understanding, to
measure progress, to
communicate with
parents
Formative
Formative assessments are
those given regularly and
continuously throughout
the school year.
To determine prior
knowledge, to determine
student interest, to modify
teacher practice, measure
understanding, ensuring
short-term knowledge and
understanding objectives
and targets are being met, to
ensure students are
progressing
Policies
Practices
college entry.
Some external
assessments are
taken twice a
year, some are
once and some
are on-going.
STAR Math,
NWEA,
Accelerated
Math, PSAT, SAT,
AP
Assessments are
aligned to curriculum,
teachers model in
advance, authentic
assessments,
differentiated if
necessary.
Essays, projects, test,
RAFTS, portfolio,
investigations, realworld examples,
exams, oral
presentation, reports,
reflections, midtrimester reports,
mid-quarter reports
Assessments are aligned to
curriculum, differentiated if
necessary.
Observation, journal, quiz,
exit cards, peer assessment
or self-assessment (not
graded on Gradequick), role
play, conferencing, small
group discussion, debate,
create/present, note-taking,
reflection, homework,
classwork, effort, behavior,
participation, Gradequick
reporting,
Teachers will be asked to implement IEP's/ILP's in their classroom should it contain
students receiving necessary support. Teachers will be provided with the
document, as well as support in how to effectively implement the modifications in
order to ensure student success. We strongly suggest that teachers consult with the
learning specialist or principal during the design and implementation of all
summative evaluations for students with IEPs.