Northern York County School District
Mathematics
Submittal for Board Approval
Course of Study: SAT I, SAT II, ACT Math Preparation 2255
Submitted by: William Witt ___________________________________
Approval Signature and Date
___________________________________
Approval Signature and Date
Approved by: _____________________________________ Date: ______________
(Building Administrator)
Approved by: ____________________________________ Date: ______________
(Assistant Superintendent)
Approved by: ____________________________________ Date: ______________
(Chair, Curriculum Committee)
SAT I / ACT Prep Page #1
Northern York County School District
Mathematics
NORTHERN YORK COUNTY SCHOOL DISTRICT
SAT I, SAT II, ACT Math Preparation
2255
May 2004
SAT I / ACT Prep Page #2
Northern York County School District
Mathematics
SAT I, SAT II, ACT Math Preparation
PHILOSOPHY
The Mathematics Program will provide students the opportunity to develop proficiency in basic mathematical
skills according to their capabilities. Inductive and deductive thought patterns will be presented at the different
levels of the mathematics curriculum. This instruction will encourage the evaluation, analysis and comparisons
of different mathematical relationships. This will enable students to become aware of the usefulness and the
necessity of mathematics and how it relates to their daily lives.
SAT I / ACT Prep Page #3
Northern York County School District
Mathematics
COURSE OF STUDY
A. Course Title: SAT I, SAT II, ACT Math Preparation
B. Grade Level: 11 & 12
C. Length of Course:
1. Frequency –6 days per 6 day cycle
2. Duration – 43 minutes per period
3. Length – 90 school days
D. Academic Level: Middle / High / Honors (WV 1.06)
1
E. Credits:
2
F. Prerequisites: Algebra II or concurrently.
G. Textbooks:
1. The Princeton Review SAT – Primary Text
2. The Princeton Review ACT – Primary Text
3. The Princeton Review SAT II: Math – Primary Text
4. Mastering the PSAT / SAT 1 – Supplementary Text
5. SAT Math Workout – Supplementary Text
6. Learning Express: Algebra Success in 20 Minutes a Day – Supplementary Text
7. Learning Express: Geometry Success in 20 Minutes a Day – Supplementary Text
H. Course Description:
SAT I / ACT Prep Page #4
Northern York County School District
Mathematics
This course is a semester elective developed to help either prepare or improve their math performance on SAT I/ACT and SAT
II tests. The SAT I/ACT is taken at the earliest in the spring of the junior year. Therefore, this course would provide the
greatest benefit if taken in a student's fall or junior year or later. This course covers comprehensive topics and practice test
questions in the areas of algebra, geometry, probability, statistics, problem solving, and test taking tips (including calculator
use) for the math SAT I/ACT test. The math SAT II test is recommended for students who have completed Trigonometry or
Pre-calculus. Additional study and practice materials will be available for students who wish to pursue preparation for this test.
It is important to realize that each testing organization determines its own administration schedule.
SAT I / ACT Prep Page #5
Northern York County School District
Mathematics
Expected Levels of Achievement
93% - 100% =A
85% - 92% =B
77% - 84% =C
70% - 76% =D
SAT I / ACT Prep Page #6
Northern York County School District
Mathematics
SAT I, SAT II, ACT Math Preparation
Content : SAT I, SAT II, ACT Math Preparation - Overview
STUDENT PERFORMANCE/ PROCEDURES FOR
NUMBER CONCEPT/TOPIC LEARNING EXPERIENCES ASSESSMENT RESOURCES
NA Study Skills, Calculator Use, Test Students will investigate recommended skills in Teacher Princeton Review
Taking Strategies, and Grid In calculator use and test taking strategies by observation Workbooks
Forms practicing sample test questions and exploring Worksheets Web site
recommendations provided by the testing Quizzes Calculator Guide
services. Tests
NA Pre Testing Students will complete a pretest for the SAT I/ Test Workbook
ACT to help identify strengths and weaknesses
in content areas.
NA Math Subject Reviews Students will complete a series of subject Daily Work Log Workbook
reviews which involve a variety of mathematical Quizzes Web sites
areas (listed in detail) to reinforce and deepen Tests Calculators
their understanding of test content.
NA Glossary of Terms Students will discover and match commonly Completed Word bank and
used terms with their meanings. matching exercise List of definitions
from word bank
NA Post Test Students will complete assessment test designed Teacher
to predict performance on both ACT/ SAT I utilization of
exams student test -
Princeton Review
Assessment Test
SAT I / ACT Prep Page #7
Northern York County School District
Mathematics
Content : Arithmetic
PROCEDURES
STUDENT PERFORMANCE/
NUMBER CONCEPT/TOPIC FOR RESOURCES
LEARNING EXPERIENCES
ASSESSMENT
2.1A, Number Sets – Identify and Students will classify real numbers through Teacher Princeton
2.2A, classify real numbers and visualization and comparison. observation Review
2.2C, subcategories and prime. Daily Work Log Workbook
2.3C Following this exercise, students will compare Worksheets Web site
Mixed Number Conversions rational numbers with their decimal equivalents on Quizzes Calculator
a calculator to further enhance their classification Tests Guide
skills.
Sets – Union, Intersection, Students will use the Real Number family tree to
Elements investigate the concepts of how sets of numbers
may be used to illustrate set concepts of union,
intersection and elements.
Fractional Arithmetic, Decimal Students will review and integrate arithmetic skills
Arithmetic, Order of Operations, through practice problems, both generic and
Comparing Fractional Values, application. These skills will involve fraction,
Percent Conversions and decimal, percent, percent conversions as well as
Applications review orders of operations. The calculator will be
a tool in checking work and conversions.
Additionally, the formal vocabulary will be
appropriately assigned to solutions.
Distributive Property, Exponent Students will model, visualize, compare and apply
Rules and Radicals concepts of prime, composite, perfect squares and
cubes as they relate to factors and exponents.
Integer and Rational Exponents Students will combine knowledge of rational
SAT I / ACT Prep Page #8
Northern York County School District
Mathematics
PROCEDURES
STUDENT PERFORMANCE/
NUMBER CONCEPT/TOPIC FOR RESOURCES
LEARNING EXPERIENCES
ASSESSMENT
numbers and radicals to expand their
understanding of radicals as rational exponents.
They will also reinforce exponent rules by
applying them to rational exponents.
Absolute Value Students will investigate the idea of absolute value
by connecting the concept of distance between two
points with absolute value.
Ratio & Proportions Students will combine fraction skills to set up
descriptive ratios, use these to model a proportion,
and then solve.
Average Students will use an “Average Pie” to organize
information and solve problems dealing with
averages.
SAT I / ACT Prep Page #9
Northern York County School District
Mathematics
Content : Algebra
STUDENT PERFORMANCE/ PROCEDURES FOR
NUMBER CONCEPT/TOPIC RESOURCES
LEARNING EXPERIENCES ASSESSMENT
NA Test Taking Techniques Students will investigate test taking techniques for Teacher observation Princeton Review
solving multiple choice questions by plugging in Worksheets Workbook
answers; testing own numbers. Quizzes Web site
Tests Calculator Guide
Daily Work Log
2.8A Evaluate Expressions Students will be able to evaluate expressions by
substituting real numbers and computing the results.
2.8A Simplify Expressions Students will symbolically simplify a series of
expressions.
2.8A Polynomial Students will reinforce binomial multiplication skills
Multiplication utilizing the FOIL method.
2.8A Factoring Students will review factoring techniques for
Difference of Squares, Perfect Square Trinomials and
ax 2 bx c 0,
polynomials of the form .
a 1
2.8K Solving Linear Students will be able to solve linear as well as apply
Equations the concepts of equations.
2.8 F, H Solving 2 x 2 systems Students will demonstrate ability to organize and
solve systems by substitution, variable elimination
and graphing, while being able to describe solution
sets with appropriate vocabulary.
SAT I / ACT Prep Page #10
Northern York County School District
Mathematics
STUDENT PERFORMANCE/ PROCEDURES FOR
NUMBER CONCEPT/TOPIC RESOURCES
LEARNING EXPERIENCES ASSESSMENT
2.8 E Solving Quadratic Students will organize and find solutions of quadratic
Equations equations through factoring, quadratic formula, and
graphing calculator.
2.8 K Solving Inequalities Students will be able to solve simple linear
inequalities and represent solutions on a number line
and in interval notation.
2.5 B Symbol Recognition Students will be able to match a vocabulary list to a
set of appropriate mathematical symbols.
2.8 S Absolute Value Students will demonstrate correct notation,
expression simplification, equation solution and
graphs of absolute value.
2.5 B Negative and Rational Students will demonstrate the rules and solution
Exponents techniques connected with negative and rational
exponents.
2.8 O Domain and Range Provided with a function either symbolically or
graphically, students will be able to describe the
domain and range.
2.2F Functions Students will be able to define a function, utilize
2.8 A, C, functions as models and identify functions as graphs.
Q, R, T
2.11 B
2.8 D Function Notation Students will be able to represent functions using
Slope and Linear appropriate notation, slope and y – intercept, for
Equations linear equations.
SAT I / ACT Prep Page #11
Northern York County School District
Mathematics
STUDENT PERFORMANCE/ PROCEDURES FOR
NUMBER CONCEPT/TOPIC RESOURCES
LEARNING EXPERIENCES ASSESSMENT
2.8 S Rational Equations Students will correctly solve rational equations while
communicating any exclusion from the solution set.
2.8 S Rational Inequalities Students will integrate knowledge of solving linear
inequalities and rational equations to find solutions
for rational inequalities.
2.8 S Radical Equations While drawing on previous knowledge of rational
exponents, students will demonstrate techniques for
solving radical equations both algebraically and
graphically.
2.8 B, P Direct y kx and Students will be able to represent written expressions
as direct or inverse variation functions and solve.
k
Inverse y
x
Variations
2.4 E Applications Students will formulate equations from a variety of
2.8 G, N written applications; demonstrate solutions by
graphing, table of values and algebraic methods.
SAT I / ACT Prep Page #12
Northern York County School District
Mathematics
Content : Geometry
PROCEDURES
STUDENT PERFORMANCE/
NUMBER CONCEPT/TOPIC FOR RESOURCES
LEARNING EXPERIENCES
ASSESSMENT
2.3 B Angle Types Students will classify angle types using Teacher Princeton Review
appropriate symbols and compare their degree observation Workbook
measure with radian equivalent. Worksheets Web site
Quizzes Calculator Guide
Tests
Daily Work Log
2.3 B Vertical Angles Students will solve algebraic problems by
identifying vertical angles and applying their
properties.
2.9 I Angle Sum Properties Students will investigate and apply properties of
angle sums for straight angles, triangles and other
figures.
2.9 I Polygon Students will be able to sketch and determine the
angle sum of any polynomial by method of
triangulation.
2.9 I Parallel Lines and Students will be able to apply congruence and
Transversals angle sum properties of parallel lines cut by a
transversal to algebra based problems.
2.10 B Triangles Students will be able to identify and apply side
length proportions for two common, special
triangles 30 60 90 & 45 45 90 .
SAT I / ACT Prep Page #13
Northern York County School District
Mathematics
PROCEDURES
STUDENT PERFORMANCE/
NUMBER CONCEPT/TOPIC FOR RESOURCES
LEARNING EXPERIENCES
ASSESSMENT
2.10 B Triangle Types Provided with information, either by sketch or
written form, students will be able to classify
triangles and their properties as Equilateral,
Isosceles, Right, Scalene, and Equiangular.
2.9 D Area and Perimeter Students will be able to apply triangle properties
in a pursuit of area and perimeter.
2.9 C Quadrilaterals Students will be able to connect triangle Rectangle Family and
principles to rectangles for the purpose to Trapezoid
determining perimeter and area.
2.9 C Volume of a Regular Solid Students will be able to extend their knowledge
of area into three dimensions by finding volume
of rectangular solids.
2.10 B Pythagorean Theorem Students will be able to apply the Pythagorean
Theorem to find missing lengths of a right
triangle.
2.9 I, J Right Triangle Students will be able to apply Angle/Side Students will utilize a
2.10 B Trigonometry relationships of right triangle to solve triangles memory device
and related application problems. SOHCAHTOA to
assist with their
progress.
2.9 J Identities Students will review fundamental trigonometric Reciprocal Identities
identities and their applications. Quotient Identities
SAT I / ACT Prep Page #14
Northern York County School District
Mathematics
PROCEDURES
STUDENT PERFORMANCE/
NUMBER CONCEPT/TOPIC FOR RESOURCES
LEARNING EXPERIENCES
ASSESSMENT
2.9 E Circles Students will be able to identify and apply Tangent line
properties of chords, tangents, and arcs of a relationship to
circle, as well as define subtends. diameter and radius is
a specific emphasis.
2.9 E Circumference and Area Students will be able to apply formulas for
circumference and area to open ended questions.
2.8K, Graphing and Coordinate Students will demonstrate their ability to graph
2.9 G Geometry and identify graphs using accepted notation for
segment, segment length, line and ray.
2.9 G Slopes of parallel and Students will be applying relationships of lines Example: given a
perpendicular lines that are parallel or perpendicular to equation point find a line that is
generation. parallel/perpendicular
to a given line.
2.8 J, L Equations of Lines, Students will be able to determine equations of
Midpoints, Distance lines, midpoints or distance between points from
Between Points given information or graph.
2.10 A Graph Analysis Students will be able to determine qualitative
2.11 A behavior from a graph (i.e. Number of values of x
for which f(x)=3.)
2.9 H Transformations of Graphs Students will be able to represent vertical and
horizontal transformations for a graph and
identify how these shifts algebraically affect
function notation.
SAT I / ACT Prep Page #15
Northern York County School District
Mathematics
PROCEDURES
STUDENT PERFORMANCE/
NUMBER CONCEPT/TOPIC FOR RESOURCES
LEARNING EXPERIENCES
ASSESSMENT
2.10 A Amplitude, Period, Phase Students will be able to solve problems involving
Shift formulas for amplitude, period, and phase shift of
sine, cosine and tangent functions.
2.9 H Graph Applications for Students will use graphing utilities to display and
2.10 A Amplitude, Period, Phase explain effects of amplitude, period and phase
Shift shift for sine, cosine and tangent functions.
SAT I / ACT Prep Page #16
Northern York County School District
Mathematics
Content : Data Analysis, Statistics and Probability
STUDENT PERFORMANCE/ PROCEDURES FOR
NUMBER CONCEPT/TOPIC RESOURCES
LEARNING EXPERIENCES ASSESSMENT
2.6 C Data Interpretation Students will be able to estimate a line of best fit from a Teacher observation Princeton Review
2.8 M given scatter plot or set of data by its general Worksheets Workbook
characteristics relating to slope and y-intercept. Quizzes Web site
Tests Calculator Guide
Daily Work Log
2.6 D Data Interpretation Provided with a graph, students will be able to interpret
2.7 D concepts from graphs to make judgments about various
outcomes in uncertain situations.
2.7 A, C, Probability Students will be able to determine geometric probability of
D, E an event using a
formula Probability Event
# of Favorable Outcomes
, a
# Of Possible Outcomes
graph, or diagram with shaded region.
2.5 A, B Sequences Students will find a Common Ratio and General Form of a
2.8 A, B Geometric (Exponential) Sequence; and, find a Common
Difference and General Form of an Arithmetic Sequence.
SAT I / ACT Prep Page #17