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SAT Math Prep Course Packet
Course Outline
Day 1
- Introduction
- Test Format
- General Strategies
- Diagnostic Test Questions
- Math Topics: Linear Equations, Systems, Inequalities
- Practice
- Homework: Practice Test #
Day 2
- Practice Test #1 Questions
- Math Topics: Problem Solving, Ratios, Proportions, Scatterplots, Probability, Statistics
- Practice
- Homework: Practice Test #
Day 3
- Practice Test #2 Questions
- Math Topics: Exponents, Polynomials, Radicals, Advanced Equations, Functions
- Practice
- Homework: Practice Test #
Day 4
- Practice Test #3 Questions
- Math Topics: Quadratics, Imaginary Numbers
- Practice
- Homework: Practice Test #
Day 5
- Practice Test #4 Questions
- Math Topics: Lines, Angles, Triangles, Similarity, Congruence, Proofs, Circles, Solids, Trigonometry
- Practice
- Course Evaluation
All practice tests, course materials, and solutions will be posted on my school website.
Go to VMHS.net, click on Teachers, Click on Alan Tupaj, Click on SAT Math Prep Course.
Day 1
I. Introduction
Student Info – Name, School, Previous Score, Goal, College choices
Personal Background
Course format
II. SAT Math Test Format
Section Questions Time
3 20 Questions – 15 multiple choice, 5 grid in answers
No Calculator Allowed
25 minutes
4 38 Questions – 30 multiple choice, 8 grid in answers
Calculator Allowed
55 minutes
No penalty for guessing
III. General Breakdown of Questions
Categories of questions:
1. Algebra I (19 questions)
2. Problem Solving / Data Analysis (17 questions)
3. Advanced Math (16 questions)
4. Geometry (6 questions)
No logarithms. All other Algebra 2 topics are included along with some trigonometry
IV. General Strategies
1. Read and re-read the problem carefully. Don’t rush the reading.
2. Identify what the problem is asking for. Don’t answer x if the problem asks for 2x.
3. Write in the test booklet. Draw and label diagrams if not to scale.
4. Pace yourself – Approximately 1 minute per problem on section 3 and 1.5 minutes per problem on section 4.
5. Don’t leave any problem blank
6. Know the rules for grid-ins.
7. Look for a known relationship, plug in given values, and solve for missing value
8. Identify a specific algebra skill. Factoring, simplifying, equation solving
9. Work backwards. Plug in the answer choices.
Day 1: Linear Equations, Systems, Inequalities Notes
1.
2.
3.
X y
If graphed, the ordered pairs in the table above would form a line. Where would this line intersect the x-axis?
Johanna picked 3 pounds of strawberries at a " pick-your-own " patch. At this particular patch, the cost is $1.50 for the pail and
$3.99 per pound of strawberries picked. If a linear equation is created to represent the situation and written in the form y = mx+
b, which piece of the equation would the value 13.47 in this scenario most likely represent?
@b
®m ©x
@y
3y - X X y
If y = 12 - x and - + 11 - - , what is the value of - + -?
® 4
© 4
Rasha volunteers at a charity that helps feed the homeless. He
collects donations and then uses the money to buy food for care
packages. This week, he collected $145. Each care package will
include canned vegetables and bags of rice in the ratio 3: 1. The
cans cost $0 .89 each, and the bags of rice cost $3.49 each.
Using the given ratio, what is the maximum number of complete
vegetable / rice care packages Rasha can make?
y
----------x
+----+----• L
Line L shown in the graph could be the graph of which equation?
@ X + y = - @x+y=O ©x+y-2=x
@ x + v + 2 =x i
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5.
A picture framing shop sells ready-made frames and also does custom framing using di fferent kinds and widths of wood or metal. The
shop has a three-day sale. During the sale, for an 11-inch x 14- inch frame , a ready-made frame costs $12 and a custom frame
costs $30. Over the course of the three days, the shop sells ninety-two 11 x 14 frames and collects $ 1, 788. Solving which system
of equat ions would yield the number of 11 x 14 ready-made frames rand the number of 11 x 14 custom frames c that the shop
sold during the three-day sale?
@ r 1 2r.c +^ - 30c•2 - l, : 88
®
{ r + C • l,
12r + 30c - 92 x 3
©
{ r + C • l,7 88
1 2r + 30c - 92
®
{ r + C • 92
12r + 30c - 1, 788
Cost per City Square Foot
Detroit $62.
Atlanta $74.
New York City $288.
San Franci sco $420.
In real estate , locat ion is often the number one determ i nant of home pr ices. The table above shows the average pr ice per square
foot of houses in four c ities. Assuming an average home size of 1,500 to 2,000 square feet , wh i ch inequali ty represents how much
more in dollars a house in New York Ci ty would cost than in Detro it?
@ X ~ 226. 13
@ 62.45 S XS 288.
© 93,675 S XS 432,
@ 339, 195 S X S 452, 260
9.
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Day 1: Linear Equations, Systems, Inequalities Practice
1.
2.
3.
A publishing company ships books to schools, some of which are hardback te xtbooks and some are paperback workbooks. Each shipping box can hold a maximum of 20 te x tbooks or 64 workbooks. Each te x tbook takes up 192 cubic inches of space, and each workbook takes up 60 cubic inches of space. One box can hold a maximum of 3,840 cubic inches. The shipping department is packing a box containing both types of books. Which of the following systems of inequalities can the department use to determine
how many te xtbooks, t, and workbooks, w, can be shipped in one box?
t s 20
® w s 64
60t +192w s 3, 840
t :i: 20
® w^ :i:^64
192t + 60w :. 3, 840
t s 20
© w s^64
1 92t +60w s 3. 840
t :,; 192
@ Ws 60
20t + 64w s 3, 840
Which of the following does not represent a linear relationship?
® I ; I -: I -
31 I : I ~ 1 I -
53 I
© I ; I -
15 I -
25 I ~^5 1 -: I -
55 I
® I ; I -: I -
11 I : I : I : I
Ax - 2y ,-1 8
Bx + 6y .. 26
If the graphs of the lines in the system of equations above intersect at ( 4, -1 ), what is the value of !!..?
A
If 0.2x + 1.8 = 3 - 0.6x, what is the value of x?
Equation 1 Equation 2
X y^ X y
5 -8 -8 3
4 - 5 - 6 4
3 -2 -4 5
2 1 - 2 (^6)
The tables above represent data points for two linear
equations. If the two equations form a system, what is the
x-coordinate of the solution to that system?
y T
R
-----,-+-, ~----x
' \
u • ·--·-· ,./ - \ -·--·- ➔
' \
: \
Which of the following lists correctly orders the lines in the figure above according to their slopes, from least to greatest?
@ R, T, S, U
@ S, U, R, T
© S, R, U, T
@ U, S, R, T
6.
7.
8.
Price per Pencil
Projected Number of Units Sold $0. 20 150, $0. 25 135,
$0.30 120, $0. 35 105, $0.40 90,
$0.45 75 ,
Generally, the price of an item is a good indicator of how many units of that item will be sold. The lower the price, the more units will be sold. A marketing department develops a table showing various price points and the projected number of units sold at that price point. Which of the following represents the linear relationship shown in the table, where x is the price and y is the number of units sold?
® y = 0.03x + 150,
® y = 300,000x + 75,
© V = -300.000X + 90.
@ y = -300,000x + 210,
A mailing supply store sells small shipping boxes in packs of 8 or 20. If the store has 61 packs in stock totaling 800 small shipping boxes, how many packs have 20 boxes in them, assuming all the packs are full?
**9. Calculator
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Provider 1
A company's market share is the percent of consumers who utilize the services or buy the products of that company. The pie chart above shows the different market shares of cable prov iders in a certa in region. If the ratio of the market shares of Provider 1 to Provider 2 is 3 : 2, what is Provider l's market share?
Water is vital to human health. An average person should consume approximately 2.5 ounces of water per hour. However , because of the salt in it, seawater actually dehydrates the human body and should not be consumed. This is why boats must carry a supply of fresh water when embarking on long trips. Suppose a sailboat is traveling at an average speed of 4 nautical miles per hour with 3 people on board and the trip is 232 nautical miles. What is the minimum number of ounces of water the boat should stock before leaving?
Diabetes Prevalence t (^) 20 .$ a:^111
QI 15
QI
"O 10
·v
.$^ "' 5 QI
..c 111
i
Inactivity Rate(%)
Increased physical activity has been linked to a lower incidence rate of diabetes. The scatterplot above shows the relationship between the percent of people in a certain country whose daily activity qualifies them as " inactive " and the incidence rate of diabetes in that country. The line of best fit for the data is also shown. Whi ch of the following best represents the meaning of the y-intercept of the line of best fit in the conte xt of this question?
® IThe predicted incidence rate of diabetes when the entire country is considered active
® The predicted incidence rate of di abetes when the ent ire country is considered i nactive
© The predicted percent of people who will be active when the incidence rate of diabetes is 0%
@ The predicted percent of people who will be inactive when the incidence rate of diabetes is 0%
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Year
The bar graph shows the percent of the United States population that was unemployed as of January 1 on each of the years shown. A governmental agency wants to use the 5-year mean of the da t a to estimate how many people were unemployed in a certain geographic area between 2010 and 2014. If the total adult population of the area was 250,000, appro x imately how many adults were unemployed in that area during the indicated time period?
© 20 , 950
Use the data in the scatterplot and the line of best fit shown to answer the following question
Which of the following values most accurately reflects the average rate of change of the data based on the line of best fit?
3 ®a
3
© 3
® ~ 3
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-· 90 I 80 I^ - (^) • • 70 .-·-..__^ - f--^ •
f-- 60
so (^) - (^) - (^) • I.
40 l I
30 -^ >--- (^20 ) 10 -.l
Di sta nce (in f ee t)
The figure above shows part of the path of a planned roller coaster hill. What is the sum, in feet, of the vertical height and the horizontal distance that the roller coaster will travel while on this particular hill?
Z' a,^6
.S! 5
J:. ~ a, 3 ... 2
I I I
I J_ 1.1 (^1 1) t y
](
v~ I • -l
/
-,-
t V / -t-+ t --I^ I
Tot al Bod y Length (i n feet)
The Florida Department of Wildlife caught and tagged 10 adult female alligators as part of an effort to protect this endangered species. They took various measurements and readings related to body size and health. The total body length is plotted against the tail length in the scatterplot shown above, along with a line of best fit. Which of the following equations best models the data?
@ ~ O.Sx
@ y=ZX
© y = 0.4x + 1
@ y = 0. 6x - 1
The American political system is largely a twoparty system. In fact, only six candidates who were not associated with ei ther the Republican or the Democratic Party have been elected governor in any state since 1990. In one such election, the ratio of votes received for the Independent candidate to the Democratic candidate to the Republican candidate was approximately 19 : 18 : 13. If 510,000 votes were cast in the election, how many more votes were cast for the Independent candidate than for the Republican candidate?
© 61,2QQJ
Day 2: Problem Solving, Statistics, Probability, Proportions, Percents Practice
1.
2.
3. Calculator
Selection Method
Number of States
Election 22
Gubernatorial Appointment 11
Legislative Appointment 2
Missouri Plan 15
There are four ways in which state judges are selected for their positions. One is by election , another is appointment by the governor ( usually with the confirmation by the state legislature) , and a third is appointment by the state legislature. The final way is a hybrid of the last two, called the Missouri Plan, in which a nonpartisan legislative committee recommends a list of candidates and the governor chooses from this list. The table above shows the number of states that engage in each process for the hi ghest court of the state , usually called the state Supreme Court. What percent of states select judges using the Missouri Plan?
A dendrologist (a botanist who studies trees exclusively) is examining the way in which a certain tree sheds i ts leaves. He tracks the number of leaves shed each day over the period of a month , start ing when the first leaf is shed. He organizes the data in a
scatterplot and sees that the data can be modeled using an ex ponent ial function. He determines the exponential model to be f( x ) =
6 ( 1.92 )", where xis the number of days after the tree began to shed i ts leaves. What does the value 1.92 in the function tell the dendrologis t?
@ The number of leaves shed almost doubles each day.
® The number of leaves shed almost doubles every si x days.
© The number of leaves left on the tree is reduced by about 92 % each day.
@ The number of leaves left on the tree is reduced by about 92 % every six days.
Plants are capable of cross-pollinating with related but different plants. This creates a hybrid Sometimes, a hybrid plant is superior to the two different plants from which it was derived. Th is as " hybrid vigor ." Scientists can examine the DNA of a plant to see if it is a hybrid. This can information because if the plant appears superior, it w ould be beneficial to develop more of these An agricultural scient i st examines an orchard that has several types of apple trees and orange which ones are hybrids. Some of the information she collected is shown in the table below.
Apple Orange Total Trees Trees Hybrid 402
Non-hybrid 118
Totals 628
Based on the data , if 45% of the apple trees are not hybrids, how many apple trees are hybrids?
® so
The scientist wants to study the orange trees to check for hybrid vigor. If she chooses one orange tree at random , what is the probabil i ty that it will be a hybr id?
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Day 3: Exponents, Radicals, Polynomials, Advanced Equations, Functions Notes
1. Calculator
2.
3.
4.
If M = 3x2 + 9x - 4 and N = sx2 - 12, what is 2{M - N)?
@ -2x2 + 9x + 8
® -4x2 + 18x - 32
© -4x2 + 18x + 16
@ 8x 2 + 9x - 16
If his a function defined over the set of all real numbers and h (x - 4) = 6x 2 + 2x + 10, then which of the following defines h(x)?
® h(x ) = 6x 2 - 2x + 114
® h(x ) = 6x 2 - 46x + 98
© h(x ) = 6x 2 + 2x + 98
@ h(x) = 6x 2 + SOX+ 114
Which of the following functions has a domain of x ~ 2?
@ f(x) = -x^2 + 2
® g(x ) - -J x - 2
© h(x) • - X + 2
@ k(x) • - I x - 2 I
16 2
Which of the following represents the number shown above as an integer?
@
@ 12
© 48
@ 164
x 2 - 1, if X s 0
x
g(x) = J + 1, if O < X s 3
5x+3, if X > 3
For t he piecewise defined function g(x) shown above,
what is the value of g( 2)?
X 2 1 -- - - = -- x - 1 x x - 1
What is one possible solution to the rational equation shown
above?
Which of the following is equivalent to the expression given above?
36x^4 y 7
@ 2
® 6xy 2,{y
© 6x 2y 3,{y
® (36x4y 7r 2
5.
6.
7.
