Valley Stream Central HS District
CAP Project
August 2009
SAT Math
Scope and Sequence
Curriculum Writers
David Aguado – Project Supervisor, North High School
Rebekah Williams – Central High School
Caryn Simon – South High School
Administration
Dr. Marc F. Bernstein, Superintendent of Schools
Dr. Thomas Troisi, Assistant Superintendent of Curriculum and Instruction
Mrs. Jill Vogel, District Director of Guidance
Ms. Maureen Henry, South High School, Principal
Mr. Cliff Odell, North High School, Principal
Dr. Joseph Pompilio, Central High School, Principal
Dr. Kathleen Walsh, Memorial Junior High School, Principal
Table of Contents
I.
Rationale
II. Resources
III. Course Outline
IV. Daily Lesson Plans
V. Assessments
VI. Works Cited
Rationale
In the past, the Valley Stream Central High School District offered an SAT Preparation
course as an elective to its 11th and 12th graders in conjunction with the Princeton
Review. After the Spring 2009 semester, the High School District cut ties with the
Princeton Review. This curriculum represents the new elective offered to the 11th and
12th grade students and will be implemented in September 2009.
The purpose of this CAP was to review several SAT Math Preparation tools and prepare
an outline for the new elective. In this process, teachers also reviewed numerous new
SAT Preparation review books in order to select a workbook for the course. The
committee chose the SAT Math Workbook by Kaplan.
This document contains the Scope and Sequence that will be used throughout the course.
Also included is an outline of each chapter and the suggested number of days for each
topic. Daily lesson plans have been prepared. Although it is the individual teacher’s
responsibility to prepare assessments for this course, sample quizzes are provided.
Resources
The workbook chosen for this course contains all topics listed in the outline. However,
teachers may find it necessary to supplement some topics. The College Board workbook,
The Official SAT Study Guide, is a good resource for additional practice problem. This
book not only contains review material but contains 8 full – length practice examinations.
Another good resource for teachers to use is the Math Workout for the SAT by Cornelia
Cooke. Although this covers most of the same topics as the Kaplan book, it gives the
teacher another tool to prepare the students for the SAT.
Teachers should also use the College Board website (http://www.collegeboard.com) for
additional information related the SAT examination.
Additional information may be found on the following websites:
http://www.petersons.com/testprepchannel/new_sat.asp?sponsor
http://www.act-sat-prep.com/
http://www.kaptest.com
http://education.yahoo.com/college/essentials/practice_tests/sat/
http://www.rocketreview.com/
http://www.princetonreview.com
http://www.barronstestprep.com/
http://www.testprepreview.com/sat_practice.htm
http://www.syvum.com/sat/
http://www.tamingthesat.org/practice.html
Daily Lesson Plans
Chapter (NA); Sub - Topic (Course Introduction) (Day 1 of 1)
Aim: What is expected of us in the SAT Math elective?
Objectives:
1. Understand the course requirements
2. Be aware of the due dates of the signed contract and SAT registration
3. Realize that the quarter grade is a combination of a Math score and a Verbal
score
Anticipatory Set / Do Now:
Various students will be asked to read paragraphs from the syllabus aloud. The students
will learn that they will be asked to read quite a bit in this class. The students must read
clearly and loud enough for everyone in the room to hear them.
Guided Practice:
Students are always concerned with the grading policy for a course they are taking and
this one is no different. The grading policy is as follows:
 One grade is submitted each quarter by the SAT Math and Verbal teachers.
 70% of each student’s quarter grade is based upon class work quizzes, homework,
participation and attendance
Quizzes
Homework
Class Participation and
Attendance
20%
20%
30%

30% of each student’s quarter grade is based upon the completion of one take
home diagnostic exam and proof of registration for the SAT.
Diagnostic 1
Registration for the SAT



20%
10%
The score that you earn on each diagnostic exam does NOT affect your quarter
grade.
Fall Semester:
o If you are a senior, you must register for the December SAT exam
o If you are a junior, you must register for the January SAT exam
Spring Semester:
o You must register for the June SAT exam
Closure:
Students will receive their materials for this class. They will receive two books. The
SAT Math Workbook by Kaplan will be brought to class every day. The Official SAT
Study Guide by the College Board will stay in the classroom as it contains full length
practice SAT examinations.
Homework:
Students will be required to sign the bottom of the syllabus and have a parent do the
same. This will be collected next class.
Chapter (1); Sub - Topic (How to Prepare for the SAT) (Day 1 of 1)
Aim: How do we prepare for the SAT?
Objectives:
1. Understand the format of the SAT exam
2. Differentiate between the Regular Math questions and the Grid – Ins
3. Realize that the math questions will be arranged in order of difficulty
4. Apply the 7 general SAT strategies for approaching each section
Anticipatory Set / Do Now:
Various students will be asked to read paragraphs from pages 3 and 4 aloud. This brings
us to the 7 General SAT Strategies.
Guided Practice:
We will discuss each of the 7 General SAT Strategies:
1. Think About the Question First
2. Pace Yourself
3. Know When a Question is Supposed to be Easy or Hard
4. Move Around Within a Section
5. Be a Good Guesser
6. Be a Good Gridder
7. Two – Minute Warning: Locate Quick Points
Closure:
Students will read the Chapter 1 Summary to themselves. They will be given an
opportunity to ask any questions they may have. Students will also hand in their signed
forms from the syllabus.
Homework:
Students will read the pages ix and x in their workbook. These pages educate the
students on how to use the book to improve their SAT Math score.
Chapter (2); Sub - Topic (Introduction to SAT Math) (Day 1 of 2)
Aim: What should we expect on the SAT?
Objectives:
1. Utilize the 5 step method for solving SAT Math questions
2. Solve problems using the “Picking Numbers” technique (Plugging In)
3. Solve problems using the “Backsolving” technique (PITA)
Anticipatory Set / Do Now:
Various students will be asked to read pages 9 and 10 aloud. This introduces us to the
first four steps.
Guided Practice:
Picking numbers is one of the most valuable tools that can be used to solve SAT Math
Questions. The first example on page 11 is the students first opportunity to use this. We
will often refer to this strategy as “Plugging In”.
After solving the problem, this should be put in the students’ notebook.
How to Recognize a Plugging – In Question
 There are variables in the answer choices
 The question says something like in terms of…
 Your first thought is to write an equation
 The question asks for a percentage or fractional part of something, but doesn’t
give you any actual amounts
How to Solve a Plugging – In Question
 Don’t write an equation
 Pick an easy number and substitute it for the variable
 Work the problem through and get a target score then circle it
 Plug in your number – the one you chose in the beginning – to the answer
choices and see which choice produced your correct answer
With some math problems, it’s easier to work backward from the answer choices then to
try the problem using methods from traditional math classes. Students can use this
“Backsolving Strategy” which we often call PITA (Plugging In the Answers).
The first example on page 12 will be completed as a class. The students should
understand that they should always start by plugging in choice (C) because the answers
are displayed in order. This often helps eliminate answer choices.
Independent Practice:
 The students will get an opportunity to plug in on the second problem on page 11
 The students will get an opportunity to use PITA on the second problem on page
12
Closure:
The students will answer the following Plugging – In question.
Jill spent x dollars on pet toys and 12 dollars on socks. If the amount Jill spent was twice
the amount she earns each week, how much does Jill earn each week in terms of x.
A) 2(x +12)
B) 2x + 24
𝑥
C) 2 + 12
D)
E)
𝑥+12
2
𝑥−12
2
Homework:
Students will be required to bring in a calculator next class and for the remainder of the
course.
Chapter (2); Sub - Topic (Introduction to SAT Math) (Day 2 of 2)
Aim: How do we solve Grid – In Questions?
Objectives:
1. Successfully grid in questions on the SAT
2. Understand which calculators are permitted on the SAT
Anticipatory Set / Do Now:
Students will attempt the following Easy level question by using PITA.
If 4 less than the product of b and 6 is 44, what is the value of b?
A) 2
B) 4
C) 6
D) 8
E) 14
Guided Practice:


The students will read pages 13 – 15 aloud on Grid – In questions. The directions
for this section of the SAT are the same on every test. If you understand how to
grid – in correctly, you do not have to waste valuable time reading the directions.
Pages 15 – 17 discuss how calculators can help improve your SAT score. We will
read these allowed and the students will ask questions.
Independent Practice:
The students will answer each of the following Grid – In Questions. Whatever they do
not complete will be finished for homework.
1) What value of x satisfies both of the following equations?
2) Of the 6 courses offered by the music department at her college, Kay must choose
exactly 2 of them. How many different combinations of 2 courses are possible for
Kay if there are no restrictions on which 2 courses she can choose?
3) Of the 6 courses offered by the music department at her college, Kay must choose
exactly 2 of them. How many different combinations of 2 courses are possible for
Kay if there are no restrictions on which 2 courses she can choose?
4) If
1)
, what is one possible value for x ?
2)
3)
4)
Closure:
The students will read the section on page 17 entitled “Wrapping it Up”. This will
introduce the students to the SAT Math Practice sections which focus on individual
topics.
Homework:
Students will complete the remaining Grid – In Questions
Chapter (3); Sub - Topic (Number Operations) (Day 1 of 1)
Aim: How do we answer questions on the SAT concerning Number Operations?
Objectives:
1. Solve problems using the order of operations (PEMDAS)
2. Recall and apply the properties of numbers
3. Add, subtract, multiply and divide signed numbers
Anticipatory Set / Do Now:
1) 5 × (9 − 7)2 + 6 ÷ 2
2) −12 ÷ 3 − 33
3) 12 + [15 ÷ (−17 + 12)] − 42
Guided Practice:
After reviewing the order of operations questions from the “Do Now”, we will review the
basic properties of number operations:
 Distributive Property
 Commutative Property
 Associative Property
Independent Practice:
Students will answer questions 1, 2, 7, 8, and 15 on pages 23 – 24. We will go over these
together.
Closure:
Students will answer questions 9 – 11 on pages 23 – 24. If time permits, we will review
these as a class. If not, the answers are displayed with explanations on page 26.
Homework: Complete practice set on pages 23 – 24.
Chapter (4); Sub - Topic (Number Properties) (Day 1 of 1)
Aim: How do we answer questions on the SAT concerning Number Properties?
Objectives:
1. Apply the definitions of integers, prime numbers, factors and multiples
2. Solve problems involving a remainder
3. Differentiate between the union and intersection of sets
Anticipatory Set / Do Now:
Students will review what was covered in the last class by reviewing some of the “100
Essential Math Concepts”. They will read pages 214 and 216 silently.
Guided Practice:
As a class, we will review the definitions of integers, prime numbers, factors and
multiples. An understanding of these concepts is essential to solving SAT questions.
We will complete pages 31 – 33 # 1 – 3, 7 – 8, 15 – 17.
Independent Practice:
Students will complete pages 31 – 33 # 4, 9 – 12, 18, 20.
Closure:
Students will complete page 32 # 14. Students who can correctly answer this question
have a solid understanding of what an integer and remainder is.
Homework: page 31 – 33 # 6, 13, 19, 21
Chapter (5); Sub - Topic (Averages) (Day 1 of 2)
Aim: How do we use the average pie chart to answer SAT questions concerning average?
Objectives:
1. Use the average pie chart to solve problems concerning arithmetic mean
2. Differentiate between the mean, median and mode and calculate each
3. Determine the missing number when given a group of numbers and the mean
of them
Anticipatory Set / Do Now:
The students will become familiar with the average pie chart:
This line running horizontally represents where the students should divide to find the
missing value. The line running vertically represents where the students should multiply
to find the missing number.
Guided Practice:
We will answer the following easy level question together using the chart:
6) The average of 3 numbers is 22, and the smallest of these numbers is 2. If the
other two numbers are equal, each of them is
A) 22
B) 30
C) 32
D) 40
E) 64
Independent Practice:
Students will answer following medium and hard level questions using the chart:
12) Caroline scored 85, 88, and 89 on the three of her four history tests. If her
average score for all tests was 90, what did she score on her fourth test?
A) 89
B) 90
C) 93
D) 96
E) 98
14) The average of 8, 13, x, and y is 6. The average of 15, 9, x, and x is 8. What is
the value of y?
A) –1
B) 0
C) 4
D) 6
E) 8
Closure:
Students will answer page 39 # 6 and 7. This will ensure they can successfully use the
chart before attempting the homework.
Homework: Page 39 # 1 – 5, 9 – 11
Chapter (5); Sub - Topic (Averages) (Day 2 of 2)
Aim: How do we solve SAT questions concerning arithmetic mean, median and mode?
Objectives:
1. Differentiate between the mean, median and mode and calculate each
2. Solve hard level average questions
Anticipatory Set / Do Now:
The students will complete Page 39 # 8, 12 – 15. They should be using the average pie
chart.
Guided Practice:
We will review the definition of median and mode. The students will use these
definitions to solve problems on the SAT.
Together, we will complete Page 39 # 16 – 20, 24.
Independent Practice:
The students will complete Page 39 # 21 – 23, 25.
Closure:
They will be working on the independent practice until the bell. Whatever they do not
complete will be done for homework.
Homework: Read Page 219 # 37 – 41 from the “100 Essential Math Concepts”. They
will also complete any remaining problems from Page 39 – 41.
Chapter (6); Sub - Topic (Ratios and Rates) (Day 1 of 2)
Aim: How do we solve SAT problems concerning rates?
Objectives:
1. Set up a ratio and express in simplest form
2. Find the average rate when given two units of measure
3. Convert one unit of measure to another (ie – How many minutes is 3.5 hours?)
Anticipatory Set / Do Now:
The students will read page 218 of the “100 Essential Math Concepts”. This should give
them the necessary tools to solve rate questions.
Guided Practice:
As a class, we will complete Page 49 # 4.
Independent Practice:
Students will complete Page 49 – 50 # 1 – 3, 5 – 10.
Closure:
Students will display and explain their solutions to Page 49 – 50 # 1 – 3, 5 – 10.
Homework: Page 50 – 51 # 11 – 15
Chapter (6); Sub - Topic (Ratios and Rates) (Day 2 of 2)
Aim: How do we solve SAT problems concerning ratios?
Objectives:
1. Use ratio box to solve SAT questions
Anticipatory Set / Do Now:
The students will complete Page 50 – 51 # 16 – 18. Number 16 and 17 give the students
an opportunity to Plug – In on rate and ratio questions.
Guided Practice:
We will use the ratio box to solve the following question:
John has red marbles and blue marbles in a ratio of 1:2. If he has a total of
24 marbles, how many red and blue marbles does he have?
Independent Practice:
Students will practice using the ratio box by completing Page 51 # 19 – 21.
Closure:
Students will attempt a hard level question on ratios. They will complete page 51 # 22.
We will go over this together.
Homework: Page 52 – 53 # 23 – 32
Chapter (7); Sub - Topic (Percents) (Day 1 of 2)
Aim: How do we solve math problems that involve percents?
Objectives:
1. Apply the percent equation to solve simple percent problems
2. Use the percent translation technique to answer difficult percent problems.
3. Plug appropriate values into percent problems to make problems easier.
Anticipatory Set / Do Now:
Students will be asked to complete the following question: What percent of 5 is 6?
After, I will ask the students to explain how they arrived at their answers. I expect that
is
%

some students will say they used the percent proportion, of 100 . We will review the
proportion together as a class. Then, I will teach the students another percent method
where they translate percent proportions into fraction problems. Students will fill in the
following chart:
English
% (percent)
of
what
is, are, were, did, does
Math Equivalents
Divide by 100
Multiply
Variable
Equals
We will try the same problem as earlier using the percent translation technique. Students
will see that the two methods are the same, however, many will find the translation
technique easier. By showing both techniques, students will be allowed more flexibility
to solve a percent problem.
Guided Practice:
As a class, we will complete two easy, and one medium question from the workbook.
Easy: p.65 – 68 # 1, 4 (Plug-in)
Medium: p65-68 #14
Independent Practice:
Students will complete p.65 – 68 #8 (easy), 18 (medium)
Closure:
Students will answer question 16 on p. 67 in their workbooks. This question includes the
need for plugging in and tests their percent application technique. I will poll the class for
the correct multiple-choice answer.
Homework:
Students will complete p.65 – 68 #1-15 (exclude numbers 3,7,10)
Chapter (7); Sub - Topic (Percents) (Day 2 of 2)
Aim: How do we solve math problems that involve a percent of change or a profit or
loss?
Objectives:
% of Change =
1. Use the percent of change formula.
Amount of Change
100
Original Amount
2. Differentiate profit/loss questions from percent of change questions.
3. Apply the idea that a percent increase/decrease is really an increase or
decrease of that number from 100%.
Anticipatory Set / Do Now:
Represent a profit of 25% as a decimal.
Represent a loss of 25% as a decimal.
100% + 25% = 125% or 1.25
100% - 25% = 75% or .75
Students will then be asked to complete the following question:
After getting a 20 percent discount, Jerry paid $100 for a bicycle. How much in dollars
did the bicycle originally cost? (p.67 #20)
Hint: What percent of the original price of the bike did Jerry pay? Rewrite the question
using the percent translation technique.
Translation: $100 is 80% of the original cost of the bike.
80
100 
x
100
Application:
Guided Practice:
After going over the “Do Now” we will complete question #21 on page 67 in the
workbook.
Then, I will introduce the percent of change formula. As a class, we will look at
questions 7 and 10 on p. 65-66.
Independent Practice:
Students will complete p.65 – 68 #19 (medium), 21 (hard)
Closure:
Students will answer question 7 on p. 242 in their workbooks. This question includes the
need for plugging in and tests their knowledge on percent of change, and profit/loss. I
will poll the class for the correct multiple-choice answer.
Homework:
Students will complete p.67 – 68 #17, 23, 24, and 25
Chapter (8); Sub - Topic (Powers and Roots) (Day 1 of 1)
Aim: What are the laws of exponents?
Objectives:
1. Formulate the basic power rules including multiplying, dividing, adding and
subtracting powers with the same base.
2. Build rules for fractional powers, the power of zero, the power of one, and
negative
powers (supplemental).
3. Solve radical equations with the use of the calculator and the “PITA”
technique.
Anticipatory Set / Do Now:
Students will complete the following examples:
x6
2
2
3
1. 2  2
2. x
x 
2 3
3.
After reviewing the power rules, I will ask the students to complete the following
acronym and chart in their notebook.
Laws of Exponents
Multiply
Special Rules
14,356
9240
05
3 2
Add
Divide
Subtract
Power
Multiply
=
=
=
=
1
16 2
=
Guided Practice:
After going over the “Do Now” we will complete questions 5,7,17 on page 77-78 in the
workbook.
Then, I will review radical operations with the students. They will be asked to write the
following examples in the “Do Now” section:
1. 3 5  2 5 
3.
3 12 
2. 8 2  2 
48

3
4.
3 32 8

12
5.
Independent Practice:
Students will complete p.77-79 # 1, 2, 6, and 11.
Closure:
The students will answer the following medium ranked question. I will poll the class for
their answers.
3
If w is a positive integer, then (2w) 
a )2 w3
b)4 w2
c)8w
d )8w3
e)16 w
If time allows, students will also be asked to solve question 7 on p.236 in their
workbooks.
Homework:
Students will complete all of the remaining questions from pages 77 – 79 in their
workbooks.
Chapter (9); Sub - Topic (Graph- Data Analysis) (Day 1 of 1)
Aim: How do we interpret data on the SAT?
Objectives:
1. Draw on prior knowledge such as the average pie, percent applications, and
percent of change to answer questions regarding charts.
Anticipatory Set / Do Now:
Work with your designated partner to answer question 2 on p.87 in your workbook.
Challenge yourselves to find a fast method to answer this question. Remember that it is
an “easy” question, and therefore it should not eat up all of your time.
Guided Practice:
After going over the “Do Now” we will complete questions 1,4, and 6 from pages 87-88
in the workbook. Each of these questions reviews a strategy from the past such as the
average pie, the percent application or the percent of change formula.
Independent Practice:
Students will answer the questions 3 – 11 odd on pages 87 – 89 in their workbooks.
After they are finished, they should check their answers with their designated partners
from the “Do Now” activity.
Closure:
Students will answer question 12 on p.237 and question 14 on p.275 in their workbooks.
Homework:
Students will complete the remaining questions from p.87 –89 for homework.
Chapter (10); Sub - Topic (Basic Algebra) (Day 1 of 1)
Aim: How do we answer algebra questions on the SAT?
Objectives:
1. Solve problems using polynomial operations.
2. Factor polynomials using the greatest common factor, the difference of two
perfect
3. squares or reverse foil.
4. Solve absolute value questions with the use of “PITA” or the isolation of the
absolute
5. value expression and the branching off of two equations.
Anticipatory Set / Do Now:
In your workbook, turn to p.95 and answer questions 1, 3, and 12.
Guided Practice:
After reviewing the basic algebra questions from the “Do Now”, we will complete
questions 6, 17 and 20 from pages 95-96 to review the necessary methods used to solve
function and absolute value questions.
Independent Practice:
Students will answer questions 4, 13, 15, 18, 21 and 24 on p.95-96 in their workbooks.
Closure:
Students will answer question 26 on p.97 in their workbooks.
Homework: Complete questions 1 – 29 on pages 95- 97 in the workbook.
Chapter (11); Sub - Topic (Advanced Algebra) (Day 1 of 2)
Aim: How do we use the “Plugging In” technique to solve complicated algebra
problems on the SAT?
Objectives:
1. Use the “Plugging In” technique to answer questions with variables.
2. Choose variables that satisfy the conditions for each “Plugging In” question.
3. Check all five answer choices and adjust their assigned values for each
variable should they find more than one correct answer choice.
Anticipatory Set / Do Now:
Students will answer question 1 on p.107 in their workbooks. We will review the basics
of the “Plugging In” method together.
Plugging In:
1. Assign values for variables.
2. Establish a target value.
3. P.O.E. down!
Guided Practice:
As a class, we will continue to solve questions that use the “Plugging In” method (p.107
#4).
We will also look at questions that may have more than one correct answer depending on
the values that the students choose to plug in. It is for this reason that students must be
reminded to always check all five answers before selecting their final answer. If the
students should find that more than one answer choice works within a given problem,
they must change their assigned values and try the problem again until they have only
one correct answer.
p.107 #5 is a good example practice where the students may find more than one correct
answer.
We will also complete question 10 on p.107.
Independent Practice:
Students will answer questions 3, 11, and 22 on p.107-109 in their workbooks.
Closure:
Students will answer question 11 on p.237 in their workbooks.
Homework: Complete questions 1 – 11 on pages 107-108 in the workbook.
Chapter (11); Sub - Topic (Advanced Algebra) (Day 2 of 2)
Aim: To review solving function questions, quadratics equations, and direct and
indirect variation questions.
Objectives:
1. Factor and solve quadratic equations.
2. Find the solution set of absolute value and quadratic inequalities.
3. Distinguish the difference between the direct variation and indirect variation
method to solve word problems.
Anticipatory Set / Do Now:
Students will answer the three following (medium ranked) questions.
x3  x 2
8
4
3
7) If x  x
, what is the value of x?
1
A) 16
1
B) 8
C) 4
D) 8
E) 16
7) If 2  4x  10 , all of the following are possible values of x EXCEPT
A) –3
B) –2
C) 0
D) 2
E) 3
9) If
3 x  5
, which of the following is NOT a possible value of x?
A) –10
B) –5
C) –3
D) 5
E) 10
Guided Practice:
After reviewing the “Do Now”, the class will discuss the differences between direct and
indirect variation. I will ask the class to make a chart under their “Do Now” section to
compare and contrast the different ways that two variables can be related. I will ask the
students to supply an example for each type of variation.
Direct Variation
Def: When one variable increases
(decreases), the other variable increases
(decreases).
Indirect Variation
Def: When one variable increases, the
other variable decreases (vice-versa).
Example:
Example:
X1 X 2

Y
Y2
1
Formula:
Formula:
X 1Y1  X 2Y2
Next, the class will complete the following two medium ranked questions.
7) The volume of hydrogen in a balloon varies inversely with the applied pressure. At
an applied pressure of 200 tons, the volume of hydrogen in the balloon is 3 cubic feet.
What is the applied pressure in tons, when the volume of hydrogen in the balloon is
40 cubic feet?
A) 0.6
B) 13.3
C) 15
D) 163
E) 237
2
12) If x varies directly as y , and x = 4 when y = 3, then what is the value of x when y =
12?
A) 8
B) 16
C) 36
D) 48
E) 64
Also, question 12 on p.108 in the workbook.
Independent Practice:
Students will answer questions 14,15,19, and 25 on pages 108-109 in the workbook.
Closure:
Students will answer question 11 and 15 on page 271 in their workbooks.
Homework: Complete questions 13 – 26 on pages 108-109 in the workbook.
Chapter (12); Sub - Topic (General Word Problems) (Day 1 of 2)
Aim: What are the different approaches that can be used to solve SAT word problems?
Objectives:
1. Apply the different vocabulary terms for multiplication, division, addition, and
‘
subtraction to translate the word problem information from English to algebra.
2. Use the “ PITA” charting technique to answer word problems.
Anticipatory Set / Do Now:
Students will answer question 2 and 6 on p.119 in their workbooks. Question 2
challenges students to translate words into math. Question 6 is a word problem that
requires very careful reading.
After the students answer the “easy” level questions, I will poll them for their answers. I
expect most students to answer question 6 incorrectly. This will hopefully alert the
students to the trickiness of the problem. I will remind the students at this time that SAT
Math isn’t tough because it tests tough concepts; its tough because ETS can be pretty
tricky. More than half of all math errors are caused by misreading the question, so be
sure to READ CAREFULLY.
Guided Practice:
As a class, we will complete questions 18, 8 and 22. As we work on question 18, we will
review operation vocabulary. I will stress “special cases” where the order of the numbers
must be switched. For example: 3 less than 5 translates to 5 – 3; 3 subtracted from 5
translates to 5 – 3.
Question numbers 8 and 22 both involve the “PITA” charting technique. After the class
decides that the questions will best be completed using this technique, we will review the
“PITA” steps.
Plugging In The Answer (PITA)
1) Label Answer Choices
2) Start with “C”
3) P.O.E. down!
Independent Practice:
Students will answer questions 3, 7, and 14 on p.119-120 in their workbooks.
Closure:
Students will answer the following “easy” level question:
5) Elvis gives his chauffeur a gold suit and gives his cook a diamond ring. If the suit is
worth
one fifth of what the ring is worth, and if the two items together are worth $4,800,
then how
much is the ring worth?
A) $800
B) $960
C) $3,840
D) $4,000
E) $4,200
Homework: Complete questions 1 – 18 on pages 120-121 in the workbook.
Chapter (12); Sub - Topic (General Word Problems) (Day 2 of 2)
Aim: To practice the “PITA” technique (day 2).
Objectives:
1. Use the “ PITA” charting technique to answer word problems.
Anticipatory Set / Do Now:
Students will be asked to complete question 26 on p.121 in their workbook with a
designated partner. The “hard level” question requires the use of the “PITA” charting.
Some lower scoring students will need the help of their partners to complete the question,
while other higher scoring groups can use their partner to check their answers.
Guided Practice:
As a class, we will work on a few word problems that incorporate different mathematical
topics and/or different SAT strategies. These topic/strategies include percents, direct/
indirect variation, plug-in, and PITA.
Practice Problems: p.121-122 # 19, 24, 25 and 29
Independent Practice:
Students will answer questions 20, and 33 on p.121-122 in their workbooks.
Closure:
Students will answer the following “medium” level question:
8) Lori is 15 years older than Carol. In 10 years, Lori will be twice as old as Carol. How
old is Lori now?
A) 5
B) 12
C) 20
D) 25
E) 30
Homework: Complete questions 19 – 33 on pages 121-122 in the workbook.
Chapter (13); Sub - Topic (Logic Word Problems) (Day 1 of 2)
Aim: To review probability.
Objectives:
1. Explain the definition of probability.
2. Review the counting principle, tree diagrams, and combinations.
Anticipatory Set / Do Now:
Students will complete question 3 and question 12 on pages 133-134. After the “Do
Now” we will define probability as the likelihood that a certain event will occur.
Guided Practice:
As a class, we will work on different word problems that incorporate the counting
principle, reasoning strategies, and the nCr formula.
Students will also be given a handout that contains two questions that answer the question
“How many different ways is it possible to arrange a group of items?
Practice Problems:
12) Four chefs are available to cook four different meals. If each chef is to cook one
of the meals, in how many ways could the four chefs be assigned to the four
meals?
A) 4
B) 8
C) 16
D) 24
E) 64
16) Six children, one boy and five girls, must stand in a line. If the boy cannot stand
first or last in line, how many different ways could the children be arranged?
A) 720
B) 480
C) 360
D) 240
E) 120
The class will also complete p.133-135 # 4, 6, and 9 in the workbook.
Independent Practice:
Students will answer question numbers 2, 5, 14 and 15 on pages 133 – 135 in their
workbooks.
Closure:
Students will complete question 18 on p.266 and question 6 on p.273 in the workbook.
Homework: Complete questions 1-15 on pages 133 – 135 in the workbook (omit number
7 and 11).
Chapter (13); Sub - Topic (Logic Word Problems) (Day 2 of 2)
Aim: To continue to review probability and work on pattern questions.
Objectives:
1. Use the “Plugging In” technique to simplify probability and logic questions.
2. Identify a pattern within a pattern to solve a question in less time.
Anticipatory Set / Do Now:
Students will complete question 18 on p. 136 in their workbooks. In order for the
students to solve this question, they must use the “plugging in” method. After the class is
finished, we will review the “plugging in” method and apply it to a few more practice
problems.
Guided Practice:
As a class, we will use the plugging in method to complete p. 136 # 21. We will also
look at question 22 on p.136 together. This question requires the use of a Venn Diagram.
After, I will guide the students through a pattern question. The students will write down
the following question in their workbooks.
9) A craftsman creates necklaces out of beads. He uses colored beads in a repeating
pattern of gray, lime, opal, ruby, clear, white, black and so on. If the first bead on a
necklace is gray, what is the color of the 86th bead?
A) Gray
B) Lime
C) Opal
D) White
E) Black
The students will be asked to write out the repeating pattern:
GLORCWB
Next, they will be asked to count how many colors there are in the sequence. (7)
After, they will be asked to find out how many times 7 will evenly divide into 86. (12
with a remainder)
Lastly, I will ask the students to tell me what 7 x 12 is and what color this answer
represents. (84 and B)
The students will finally count two more colors until they land on the 86th bead’s color.
(Lime)
The class will also complete p. 246 #6 in their workbooks.
Independent Practice:
Students will answer question numbers 11, 16 and 20 on pages 134 – 136 in their
workbooks.
Closure:
Students will complete question 15 on p.247 in the workbook.
Homework: Complete p.136 in the workbook (omit number 24)
Chapter (14); Sub – Topic (Lines and Angles) (Day 1 of 1)
Aim: How are the properties of lines and angles used?
Objectives:
1. Apply the properties of complementary, supplementary, alternate interior, and
vertical angles.
2. Investigate the relationships between parallel and perpendicular lines.
3. Solve problems involving line segments, midpoints, and ratios of segments.
Active Learning Strategies: Partner activity, matching activity
Anticipatory Set / Do Now: Have students in even rows write everything they know
about parallel lines. Have students in odd rows write anything they know about
perpendicular lines. Next, students will slide next to their partner and share what they
wrote. Partners may add to each others’ lists. Finally, the class will share their
information together.
Procedures:
1. Students will complete p.145 #1 & 2 individually. When reviewing these
problems, go over the definition of vertical angles, straight angles, right angles,
and supplementary angles.
2. Complete p.145 #3 as a class. First, draw a picture and label it. Use POE to
determine that correct answer.
3. Review the properties of two parallel lines cut by a transversal. What is true
about all small angles? All large angles? Any small plus any large angle? Let
students work in pairs on #11 and then review as a class.
Guided Practice: Work in pairs on #13 and 14. Then share/review as a class.
Assessment / Evaluation: Students will complete a matching activity reviewing the
vocabulary of lines and angles and their definitions and pictures.
Closure: Review the matching solutions.
Homework: Complete p.145-147.
Name___________________________
Date________
Do Now: Write down ANYTHING you can think of related to PARALLEL LINES.
Name___________________________
Date________
Do Now: Write down ANYTHING you can think of related to PERPENDICULAR
LINES.
Name__________________________
Match each term to its picture and description.
Date________
1. Vertical angle
Two lines that meet at 90 degree
angles.
2. Right angle
Two equal angles that are formed
by two intersecting lines and are
opposite each other.
3. Supplementary angles
An angle that has 180 degrees and
makes a straight line.
4. Parallel lines
The point on that divides a line
segment into two congruent parts.
5. Straight angle
Congruent angles formed when
two parallel lines are cut by a
transversal.
6. Perpendicular lines
Angles that add to 180 degrees
and form a straight line.
7. Alternate interior angles
Lines that will never intersect.
8. Acute angle
An angle with more than 180
degrees.
9. Obtuse angle
An angle that has 90 degrees.
10. Midpoint
An angle with less than 90
degrees.
Chapter (15); Sub – Topic (Triangles) (Day 1 of 3)
Aim: How can we solve basic triangle problems?
Objectives:
1. Find the interior and exterior angles in a triangle.
2. Find the area of a triangle
3. Use the Pythagorean Theorem to find the side of a triangle.
Active Learning Strategies: Partner work, exit ticket
Anticipatory Set / Do Now: Let students solve p.153 #1 independently. Go over the
question together and review the property that every triangle has 180 degrees and the
property of supplementary angles.
Procedures:
1. Have students read #2 and identify the best strategy to apply. (PITA) Solve the
question together using PITA.
2. Let students determine the strategy to apply to solve #3 (plug in). Solve the
question together using plugging in.
3. Read #13 together. Ask what formula we need to use (area) and write down the
formula. Ask students how we can find the base and height that the formula uses.
Use the Pythagorean Theorem to determine the base and height. Apply the area
formula to find the correct answer.
Guided Practice: Work in pairs on #6, 14-15. Then share/review as a class.
Assessment / Evaluation: Monitor students as they work in pairs.
Closure: Give students an incorrectly solved area problem. Ask students to determine if
the question is solved correctly and if not, to identify the mistake and correct it. (Exusing a side that is not an altitude as the height.)
Homework: p.153 #4, 6, 16-19.
Chapter (15); Sub – Topic (Triangles) (Day 2 of 3)
Aim: How can we solve problems with special right triangles?
Objectives:
1. Solve problems involving special right triangles.
2. Identify the Pythagorean triples.
Active Learning Strategies: Partner and small group work
Anticipatory Set / Do Now: Ask students to identify all of the special right triangles that
they have heard of. Classify them as special angles or Pythagorean triples. Show
students the special right triangles on the SAT formula page and show examples of
possible ratios of the sides. Ask students where they might find each of the special
triangles (in a square or an equilateral triangle).
Procedures:
1. Work as a class to solve p.154 #9. Identify the special triangle and the ratio of the
sides. Use the ratio to find the indicated side.
2. Let students work on #12 in pairs and then go over as a class.
Guided Practice: Work in small groups on # 22, 23. Then share/review as a class.
Assessment / Evaluation: Monitor students as they work in pairs/groups.
Closure: Challenge students to recall all five special triangles.
Homework: p.154 #5, 10, 20, 21, 25.
Chapter (15); Sub – Topic (Triangles) (Day 3 of 3)
Aim: How can we practice solving difficult triangle problems?
Objectives:
1. Apply the triangle inequality theorem
2. Solve difficult level triangle problems.
Active Learning Strategies:
Anticipatory Set / Do Now: Ask students if it is possible to make any three line segments
into a triangle. Use strips of paper to show a set of three sides that does not form a
triangle.
Procedures:
1. Review the triangle inequality theorem. Given any two sides, add them and
subtract them to determine the possible side lengths in between the two results.
2. Let students apply the triangle inequality theorem to solve p.154 #7.
Guided Practice: Have students work in pairs or small groups on p.157 #26-30
Assessment / Evaluation: Monitor students’ progress as they work in groups. Have
students put their solutions on the board and explain their steps.
Closure: Let students complete an exit ticket applying the triangle inequality theorem.
Homework: Complete p.158 #31-34
Chapter (16); Sub – Topic (Quadrilaterals and other Polygons) (Day 1 of 1)
Aim: What are the properties of quadrilaterals and other polygons?
Objectives:
1. Know the definition of a quadrilateral and apply the property of the sum of the
angles of a quadrilateral.
2. Apply the properties of parallelograms, rectangles, and squares.
3. Solve problems involving the area and perimeter of a quadrilateral or polygon.
4. Determine the sum of the interior angles of a polygon other than a quadrilateral.
Anticipatory Set / Do Now: Draw a quadrilateral on the board. Ask students to name the
shape. Ask students for any special properties of all quadrilaterals (they have 360
degrees). If students name incorrect shapes (parallelogram, trapezoid, etc.), talk about
what is special about each of those.
Procedures:
1. Show students a polygon with more than four sides. Ask students how many
degrees are in the shape. Let the students know that there is a formula, but they
can find the degree measure without memorizing another formula. Have students
divide the polygon into triangles. They know each triangle has 180 degrees, so
multiply the number of triangles they made by 180 to find the total number of
degrees in the polygon.
2. Work together to solve p.169 #2. Review the properties of a rectangle and the
definition of perimeter as you work backwards to find each side of the figure.
Review the area formula for a rectangle to find the answer.
3. Read #14 together. Ask students what strategy they can use since they don’t have
any measurements to work with. Encourage students to write down the area
formula and then plug in numbers that could work as the base and height of the
triangle. Use the dimensions to find the base and height of the bigger triangle and
then find its area.
Guided Practice: Have students work in pairs or small groups on p.170 # 7, 8, 19, 20.
Assessment / Evaluation: Monitor students’ progress as they work in groups. Have
students put their solutions on the board and explain their steps.
Closure: Let students look at #15. Have students write down the first thing they would
do to solve this question (break it into familiar shapes). If there is time, let the students
continue to solve the problem.
Homework: p.169 #1, 3-6, 12-16.
Chapter (17); Sub – Topic (Circles) (Day 1 of 2)
Aim: How can we solve problems involving the area and circumference of a circle?
Objectives:
1. Identify the diameter and radius of a circle and know that all radii of a circle are
congruent.
2. Use the area and circumference formulas.
3.
Anticipatory Set / Do Now: Ask students to recall the three basic steps to solving a
geometry question. (Draw a picture, label your picture, write and substitute into relevant
formulas.)
Procedures:
1. Read p.181 #1 together. Ask students to state the steps we should follow. Draw a
picture. Write the are formula, substitute they area, and solve for the radius.
Finally, write the circumference formula and substitute the radius in to find the
answer.
2. Have students read #6 and give the first step (write the area formula). Have
students use the area formula to find the radius independently. Ask the students
where we should label the radius in the diagram (there are two radii in the
picture). Remind the class to always look for all radii and diameters when they
see a circle diagram and that all radii or diameters are equal. Ask the class what
else we need to know to find AB (OA). Tell the students to look for basic shapes
and apply their properties. In this case, there is a right triangle, so they can use
the Pythagorean theorem. Let students use the formula or identify the 6-8-10
triangle. Finally, find the difference between OB and OA to find AB.
Guided Practice: Have students work in pairs or small groups on p.181 #2, 7, 9
Assessment / Evaluation: Monitor students’ progress as they work in groups. Have
students put their solutions on the board and explain their steps.
Closure: Have students complete an exit ticket independently where they are given an
area and asked to find the circumference.
Homework: p.181 #4, 8, 11, 14.
Chapter (17); Sub – Topic (Circles) (Day 2 of 2)
Aim: How can we find the arcs and angles in a circle?
Objectives:
1. Apply the relationship between central angles and arcs and know the number
of degrees in a circle.
2. Determine the area of a sector of a circle.
3. Apply the properties of a line tangent to a circle.
Anticipatory Set / Do Now: Ask the students to figure out how many degrees the minute
hand on the clock has to move before the period will be over. Let students recall that
there are both 360 degrees and 60 minutes in a circle. When converting one set of units
to another, we can use a proportion.
Procedures:
1. Look at p.183 #13. Ask the students what they will need to do even before
they read the question. Have students draw a picture to match the problem.
Label the arc that is 12 pi, and then determine the total circumference. Ask
the students why the answer is not 4 pi (the arc between the two endpoints).
First, it’s too easy for a medium level question and second, because the
shortest distance is a straight line. Let students volunteer how to use the
circumference to find the radius. Next, use special right triangles to find the
hypotenuse of the isosceles right triangle.
2. Have students read #10 together. Ask students what a tangent line means.
Recall the property that a tangent line always makes a right angle with the
radius of the circle. Let students plug in for x and use the Pythagorean
theorem to find the solution.
Guided Practice: Let students work independently on # 5.
Assessment / Evaluation: Monitor students’ progress as they work. Call on students to
describe the steps to get through the problem.
Closure: Have students complete an exit ticket.
Homework: p.181 # 3, 12, 15.
Chapter (18); Sub – Topic (Multiple Figures) (Day 1 of 1)
Aim: How can we solve problems with multiple figures?
Objectives:
1. Solve problems involving overlapping figures.
2. Identify the basic shapes in complicated figures and apply their properties.
3. Determine the relationships between inscribed circles and squares.
Anticipatory Set / Do Now: Let students look over the difficult level questions on p.190.
Ask the students what makes these questions look intimidating (they have unfamiliar
shapes). Remind the students that they know all of the basic shapes and their properties,
they just need to identify what shapes are being combined or overlapped in these difficult
figures.
Procedures:
1. Have students identify the overlapping shapes in #6. What are the important parts
of a circle to identify? What types of triangles should we look for? Review the
basic steps of geometry. Label the picture with the given information. Use the
radius to find the area of the circle. Ask the students if the radius has any other
significance (it’s also the height of the triangle). Let the class know that often the
key to these questions is identifying a side that is shared between the two shapes.
Use the area of a triangle formula to find the base. Ask the students what other
piece we need to find (the overlapping section). What type of triangle do we
have (isosceles right triangle or 45-45-90). Use a ratio to determine the area of
the sector. Let students determine how to combine these three areas to find the
area of the total figure.
2. Work through question #8 together, again letting the students identify the
common parts of the overlapping figures and the area formula to find each area.
Since the final answer, a ratio, will be a fraction, we can plug in our own numbers
to make the work simpler.
Guided Practice: Let students work in pairs on #4.
Assessment / Evaluation: Monitor students’ progress as they work. Call on students to
describe the steps to get through the problem.
Closure: Have students complete an exit ticket.
Homework: p.189 # 1-3, 5, 7.
Chapter (19); Sub – Topic (Coordinate Geometry) (Day 1 of 1)
Aim: How can we solve problems involving coordinate geometry?
Objectives:
1. Plot points on the coordinate plane.
2. Determine the slope of a line given two points.
3. Solve problems involving the equation of a line.
4. Determine the length and midpoint of a line segment given the coordinates of its
endpoints.
Anticipatory Set / Do Now: Let the students solve p.197 #1 independently. Go over the
correct answer and review where the positive/negative x and y-values lie on the
coordinate plane.
Procedures:
1. Read p. 198 #9. Ask students to share the first thing they would do. Encourage
the students to start by sketching a graph and plotting the points. Assign one
student the job of timing how long it takes to make a sketch with the two points to
show students it is worth the small amount of time it takes. Then, have the
students make the line into the hypotenuse of a right triangle, count the length of
the sides, and use the Pythagorean Theorem to find the length of the line.
2. Ask students to describe the meaning of slope. Have students give several
methods of finding a slope. Ask for three volunteers to find slope each using a
different method. Give each student two ordered pairs and have one use the slope
formula, one use a graph and count rise over run, and the third use linear
regression. Ask the class to vote for which method they think will be easiest and
fastest. Give the class another set of ordered pairs and let them choose their own
method to find the slope.
Guided Practice: Students can work in small groups on p.197 #3, 7, 14, 15.
Closure: Have students write on an index card how they would describe to a friend how
to find the slope and distance between two ordered pairs.
Homework: p.197 #1, 2, 4-6, 8, 10-13.
Chapter (20); Sub – Topic (Solids) (Day 1 of 1)
Aim: How can we find the surface area and volume of a solid?
Objectives:
1. Determine the surface area of a rectangular solid.
2. Solve problems involving the volume of a solid.
Anticipatory Set / Do Now: Ask the students to name some common solids. Have the
students attempt to draw a cube and another rectangular solid. Point out the volume
formulas on the reference information. Ask the students to describe surface area and how
it is found.
Procedures:
1. Draw a rectangular solid on the board and assign it a length, width, and height.
Ask the students to find its surface area. Ask how many sides we need to find the
area of. Find each area and help students recognize that there are three pairs of
sides. Ask the students what we need to do with the six areas.
2. Let students read and begin p.207 # 4 independently. Ask them to point out the
trick in the question. (There are two different sets of units.) Let them describe
how to deal with this trick. Encourage the students to change the 1 foot into
inches. Ask them if it matters if we change the units before or after finding the
volume. Let them try it both ways to see if they get the same result.
Guided Practice: Students can work in pairs on p.207 #5, 7, 9.
Closure: Have students write on an index card how they would describe to a friend how
to find the slope and distance between two ordered pairs.
Homework: p.207 #1-3, 6, 8, 10.
Assessments
Name __________________
SAT Math
Chapters 1 – 3
Date __________________
Directions: Answer 6 out of the 8 questions below. Write your final answers in the
answer box on the right of this page. (5 points each)
𝑥
1. If 𝑥−2 =
A)
B)
C)
D)
E)
1.______
39
, then x =
37
2.______
37
39
41
74
78
3.______
4.______
5.______
6.______
1
1
1
1. If 𝑥 = 2, what is the value of 𝑥 + 𝑥−1?
A) –4
B) 0
C) 1
D) 2
E) 3
2. If 𝑎(𝑥 + 𝑦) = 45 and 𝑎𝑥 = 15, what is the value of 𝑎𝑦?
A) 3
B) 5
C) 15
D) 25
E) 30
7.______
8.______
3. If 3𝑥 + 𝑛 = 𝑥 + 1, what is n in terms of x?
A) 4x + 1
B) 2x + 1
C) 2 – x
D) 1 – 2x
E) 1 – 4x
4. How many different positive three – digit integers can be formed if
the three digits 4, 5, and 6 must be used in each of the integers?
A) Three
B) Four
C) Six
D) Eight
E) Nine
5. If k is a positive integer, which of the following must represent an
even integer that is twice the value of an odd integer?
A) 2k
B) 2k + 3
C) 2k + 4
D) 4k + 1
E) 4k + 2
6. If 2(𝑥 − 3) = 7, what is the value of x?
7. If
10
𝑎
𝑏
= 12, what is the value of ab?
Name __________________
Date __________________
SAT Math
Chapters 4 – 6
Directions: Answer 6 out of the 8 questions below. Write your final answers in the
answer box on the right of this page. (5 points each)
1. The total cost of 3 equally priced mechanical pencils is $4.50. If
1.______
the cost per pencil is increased by $0.50, how much will 5 of these
2.______
pencils cost at the new rate?
3.______
A) $7.50
4.______
B) $8.00
5.______
C) $9.00
6.______
D) $9.50
7.______
E) $10.00
8.______
2. Which of the following could be the remainders when 4
consecutive positive integers are each divided by 3?
A) 1, 2, 3, 1
B) 1, 2, 3, 4
C) 0, 1, 2, 3
D) 0, 1, 2, 0
E) 0, 2, 3, 0
3. If the average (arithmetic mean) of x and 3x is 12, what is
the value of x?
A) 2
B) 4
C) 6
D) 12
E) 24
4. How many seconds are there in m minutes and s seconds?
A) 60m + s
B) m + 60s
C) 60(m + s)
D)
E)
𝑚+𝑠
60
𝑚
60
+𝑠
5. If the sum of consecutive integers from –22 to x, inclusive,
is 72, what is the value of x?
A) 23
B) 25
C) 50
D) 75
E) 94
6. In a mixture of peanuts and cashews, the ratio by weight of
peanuts to cashews is 5 to 2. How many pounds of cashews
will there be in 4 pounds of this mixture?
7. What is the greatest of 5 consecutive integers
if the sum of these integers equals 185?
8. For all positive integers j and k, let j R k be defined as the
whole number remainder when j is divided by k. If 13 R k =
2, what is the value of k?
Name __________________
Date __________________
SAT Math
Chapters 7 – 10
Directions: Answer 7 out of the 9 questions below. Write your final answers in the
answer box on the right of this page. (5 points each)
1. If 20 percent of x is 10, what is x percent of 10?
1.______
2.______
A)
B)
C)
D)
E)
50
30
20
10
5
3.______
4.______
5.______
6.______
7.______
2
3
2. If x  6  10 , what is the value of x?
8.______
9.______
A)
B)
C)
D)
E)
4
6
8
27
64
NUMBER OF ITEMS SOLD
TEAM
T-SHIRT
CAP
50
25
A
B
45
18
C
40
30
COST PER ITEM
PRICE
ITEM
T-shirt
$12
Cap
$7
3. The first table above shows the number of T-shirts and caps sold by three teams of
students at Jacoby High School’s annual fundraiser. The second table shows the price of
each item sold. Based on this information, how much more money did team A raise than
team C?
4. Carlos paid $154.00 for 2 tickets to a concert. This price included a 25 percent
handling fee each ticket and a $2 transaction fee for the total sale. What was the price for
a single ticket before the additional fees?
A)
B)
C)
D)
E)
$95.00
$60.80
$57.50
$57.00
$38.00
5. If 3x – 8 < 12 + 5x, then
A)
B)
C)
D)
E)
x > 10
x < 10
x > -10
x < -10
x>0
6. What is the value of a, if 5a  b  c  36 and b  c 
A)
B)
C)
D)
E)
12
9
6
4
3
1
a?
2
7. If x and y are positive integers and 4  2 x   2 y , what is x in terms of y?
A)
B)
C)
D)
E)
y–2
y–1
y
y+1
y+2
8. 5( x 4 y 5 z 6 )3 =
5x 7 z 9
A)
y2
B)
5x12 z18
y15
C)
25x12 z18
y15
125x 7 z 9
D)
y2
E)
125x12 z18
y15
9. If (a + 2)(b - 2) = 0, which of the following could be true?
I.
II.
III.
A)
B)
C)
D)
E)
I only
I and II
I and III
III only
I, II, and III
a = -2
b=2
a = -b
Name __________________
SAT Math
Date __________________
Chapters 11 – 13
Directions: Answer 6 out of the 8 questions below. Write your final answers in the
answer box on the right of this page. (5 points each)
1. If x 2  y 2  20 and x – y = 2, what is the value of x 2  2 xy  y 2 ?
1.______
2.______
3.______
4.______
2. If
3 x 12  x

, what is the value of x?
3
2
A)
B)
C)
D)
E)
2
3
4
16
36
3. If d, e, and f are positive integers and d < e < f, which of the following must be true?
A) d + e > f
B) def > 0
C) d + 2 = e + 1 = f
f
D)
e
d
E) f – e > d
4. For any integer x, define  x by the equation  x  2 x  x( x  3) . Find 10  3 .
A)
B)
C)
D)
E)
3
 4
 7
9
11
5.______
6.______
7.______
8.______
5. If y varies inversely with the cube root of x, and y = 9 when x =
value of y when x =
1
, then what is the
27
1
?
64
6. If half of a number is equal to 4 more than the twice the number, what is the number?
A) -3
8
B) 
3
C) 0
7
D)
2
E) 4
7. A pirate captain sails his ship for two days. The distance he sailed on the first day was
150 miles less than twice the distance he sailed on the second day. If he sailed a total of
600 miles, what was the distance in miles, that he sailed on the second day?
A)
B)
C)
D)
E)
250
275
350
375
450
8. Karen is ordering a hamburger. The restaurant offers 2 different kinds of bread, 3
different condiments, and 2 different kinds of cheese. If Karen selects one type of
bread, one condiment, and one type of cheese, how many ways can she order her
burger?
A)
B)
C)
D)
E)
6
7
9
12
24
Name __________________
SAT Math
Date __________________
Chapters 14 – 16
Directions: Answer 6 out of the 8 questions below. Write your final answers in the
answer box on the right of this page. (5 points each)
1. What is the area of the following square, if the length of BD is
(A)
(B)
(C)
(D)
(E)
1
2
3
4
5
?
1.______
2.______
3.______
4.______
5.______
6.______
7.______
2. In the figure below, what is the value of y?
(A)
(B)
(C)
(D)
(E)
40
50
60
100
120
8.______
Note: Figures not drawn to scale
3. In the figures above, x = 60. How much more is the perimeter of triangle ABC
compared with the triangle DEF.
(A)
(B)
(C)
(D)
(E)
0
2
4
6
8
Note: Figures not drawn to scale
4. In the figure above, if x < 90° then which of the following must be true?
(A)
(B)
(C)
(D)
(E)
y < 90°
y = 90°
y > 90°
5. If the triangle above has an area of 27, then h =
(A)
(B)
(C)
(D)
(E)
3
5
6
8
10
6. If a triangle has sides of lengths 3 and 7, which of the following could not be the
third side of the triangle?
(A) 4.5
(B) 8
(C) 9
(D) 9.5
(E) 11
7. If ∠𝐴𝐵𝐶 + ∠𝐵𝐶𝐷 + ∠𝐶𝐷𝐸 = 330°, then r + s =
(A) 150°
(B) 165°
(C) 180°
(D) 195°
(E) 210°
8. If ABCD is a rectangle, what is x + y + z?
(A) 75
(B) 160
(C) 175
(D) 180
(E) 210
Name __________________
SAT Math
Date __________________
Chapters 17 – 20
Directions: Answer 6 out of the 8 questions below. Write your final answers in the
answer box on the right of this page. (5 points each)
1.
Two circles both of radii 6 have exactly one point in common. If A
is a point on one circle and B is a point on the other circle, what is
the maximum possible length for the line segment AB?
(A)
(B)
(C)
(D)
(E)
12
15
18
20
24
1.______
2.______
3.______
4.______
5.______
6.______
7.______
8.______
2. A right circular cylinder has a radius of 3 and a height of 5. Which of the
following dimensions of a rectangular solid will have a volume closest to the
cylinder?
(A)
(B)
(C)
(D)
(E)
4, 5, 5
4, 5, 6
5, 5, 5
5, 5, 6
5, 6, 6
3. The square ABCD is inscribed in the circle above. The length of the side of the
square is 2 cm. Find the area of the shaded region.
(A)
(B)
(C)
(D)
(E)
π–4
2π – 4
3π – 4
4π – 4
5π – 4
4. In the figure above, if ∠AOB = 40° and the length of arc AB is 4π, what is the area
of the sector AOB?
(A)
(B)
(C)
(D)
(E)
4π
16π
36π
128π
324π
5. If O is the center of the circle above and
angle
(A) 120
(B) 115
(C) 90
(D) 60
(E) 45
?
, what is the degree measure of
6. The circle above has its center at point (4, 3) and passes through point (0, 0). Which
of the following points also lies on the circle?
(A)
(B)
(C)
(D)
(E)
(-1, 1)
(5, -2)
(-2, 4)
(7, 7)
(8, 6)
7. The points labeled in the above figure are the vertices of a triangle with an area of 45.
What is n?
(A)
(B)
(C)
(D)
(E)
5
6
7
9
10
8. The volume of the right circular cylinder pictured above is 81π . If the height of
the cylinder is three times the radius, what is the diameter of circle P?
Works Cited
Cocke, Cornelia. Math Workout for the SAT. First Edition. New York: Random House,
2004.
College Board, The Official SAT Study Guide. New York: College Board SAT, 2005.
Kaplan Test Prep and Admissions, SAT Math Workbook. Third Edition. New York:
Kaplan, 2008.