The document outlines a seminar focusing on the SAT structure, specifically the math section, where various strategies for test preparation are provided. It details the types of math topics covered on the SAT, sample questions, and effective pacing strategies for test-taking. Additional tips for successful completion, including practicing without a calculator and familiarizing oneself with the test format, are also highlighted.

1. In association with
Tuesday, 27th December 2016, 5 PM – 6 PM IST

2. Mapping student’s potential to Globally Available
Opportunities !

3. MR.VENKATV R PRASAD
(SAT,SAT Subject AP Calculus Faculty With 9+ Years of teaching experience)

4.  SAT Structure
 SAT Math Topics
 SAT Math Question Distribution
 Strategies to Pace SAT Math Test
 Grid in Rules
 Sample SAT Questions & Solutions
 SAT II Syllabus

6. SAT is the test that takes more than 4 hours with essay and breaks.
Structure of SAT Test is
 Section 1 - Reading Test - 65 minutes
o Break - 10 minutes
 Section 2 - Writing and Language Test - 35 minutes
 Section 3 - Math Test - No Calculator section - 25 minutes
o Break - 5 minutes
 Section 4 - Math Test - Calculator section - 55 minutes
o Break - 5 minutes
 Essay - 50 Minutes

7. Order of the
Section
Section No of Questions Time in Minutes Time per Questions
1 Reading 52 65 75 Seconds
2 Writing 44 35 48 Seconds
3 Math No Calc
20(15 MCQ+5 Grid
Ins)
25 75 Seconds
4 Math With Calc
38 (30 MCQ+ 8 Grid
Ins)
55 86 Seconds
5 Essay (Optional) 1 50
Total 154+1(Essay)
3 Hr (No Essay) 3 Hr
50 Min (With Essay)
4Hr 7 Min(With
Breaks and Essay)
On an average 70
Seconds per
Question

9. • Solving Linear Equation and Word Problems
• Solving Linear Inequation and Word Problems
• Solving System of Linear Equations and Word Problems
• Solving System of Linear Inequalities and Word Problems
• Graphing Linear Equations
• Interpreting linear functions and Word Problems
Heart of Algebra
• Solving Quadratic Equations
• Quadratic and Exponential Word Problems
• Manipulating Quadratic and Exponential Expressions
• Interpreting Non linear Expressions
• Linear and Quadratic Systems
• Radicals and Rational Exponents
• Operations With Polynomials and Rational Expressions
• Polynomial Factors and Graphs
• Nonlinear Functions Graphs
• Equivalent Expressions
• Isolating Quantities
• Function Notation
Passport to Advanced Mathematics

10. • Units, Ratios, Rates and Proportions
• Percents
• Table Data
• Scatter Plots
• Key Features of Graphs
• Data inferences, Collection and Conclusion
• Center, Spread and Shape of Distributions
Problem Solving and Data Analysis
• Angles, Congruence and Similarity
• Circle Theorems and Equations
• Volume Word Problems
• Right triangle Trigonometry and Word Problems
• Complex Numbers
Additional topics in Maths

12.  One or max 2 MCQ Questions and one of the grid-ins will be an extended thinking question, which
features a word problem or graphic and asks two or more questions about it.
SAT Math Section 1
(No Calculator)
Heart of Algebra
(8 Qs)
Passport to Advanced Math
(9 Qs)
Additional topics in Math
(3 Qs)
SAT Math Section 2
(Calculator)
Heart of Algebra
(11 Qs)
Passport to Advanced Math
(7 Qs)
Additional topics in Math
(3 Qs)
Problem Solving and Data Analysis
(17 Qs)

14. Familiarize yourself with the test ahead of time
 The instructions are the same at the beginning of every section on every SAT. Read them ahead of time so you
don’t waste time on test day.
 Familiarize yourself with the structure of the test until it feels more comfortable and less foreign.
Practice, practice, practice
 Sit down with a test at home and take it timed.
 Get used to both types of questions on the test and on pacing you’ll need to finish on time.
Plugging In and PITA
 If you're stuck in any of the math question, and if there are variables in question and answer choices try substituting
numbers for variables.
Plugging In tips
• Watch out for one and zero, generally these numbers leads to more than one answer correct.
• Do not use same number for more than one variables.
• Remember to check all answers before you move on
• Pick Good Numbers: Choose the number that makes problems easier, For example if it’s a percentage question
try to plug in 100 and if there are fractions involved try to pick a number that is multiple of the fractions.
PITA( Plugging in the answer)
• When there are numbers in the answer choices. Start with the middle number.

15.  Take care when filling in the answer grid for the student-produced response
questions.(Learn the section directions now; go through them from ANY Original SAT
SAMPLE PAPER )
 Read the words in the question carefully. Be sure to answer the question asked and not
what we get after solving!(99% students make this mistake and call it as silly mistake!!!)
 Calculator Dependence or usage
You have a section that you are not allowed to use calculator, so make sure to practice
questions without using calculator..Use calculator only for complex Calculations
 Do not spend more than 30 seconds on a question, if you do not have any idea about
question go ahead and solve as many questions as possible and come back later on. Circle
the question you left, so that you can quickly come back to it later on.
 Relax the night before the test(Last minute reading will not help)( Make sure that you get
enough sleep the night before. Your brain will be better on test day.

17.  Although not required, it is suggested that you write your answer in the boxes at the top of
the columns to help you fill in the circles accurately. You will receive credit only if the circles
are filled in correctly.
 Mark no more than one circle in any column.
 No question has a negative answer.
 Some problems may have more than one correct answer. In such cases, grid only one answer.
 Mixed numbers such as 3½ must be gridded as 3.5 or 7/2. (if mixed fraction entered into the
grid, it will be interpreted as 31/2, not 3 ½)
 Decimal answers: If you obtain a decimal answer with more digits than the grid can
accommodate, it may be either rounded or truncated, but it must fill the entire grid.
 You may start your answers in any column, space permitting. Columns you don’t need to use
should be left blank.

18. Answer:201- either position is
correct!

20. If the system of inequalities y ≥ 3x + 4 and y > (6/11)x - 2 is graphed in the xy-plane above,
which quadrant contains no solutions to the system?
A. Quadrant II
B. Quadrant III
C. Quadrant IV
D. There are solutions in all four quadrants.
II I
III IV

21. If the system of inequalities y ≥ 3x + 4 and y > (6/11)x - 2 is graphed in the xy-plane above,
which quadrant contains no solutions to the system?
Draw the Graph of y = 3x + 4, x-intercept is (-4/3, 0) y-intercept is (0, 4)
Ans. C (Quadrant IV)

22. Which of the following is an equivalent form of the equation of the graph shown in the xy-plane
above, from which the coordinates of vertex A can be identified as constants in the equation?
A. y = (x - 2) (x – 6)
B. y = x (x + 4) - 12
C. y = (x + 2) (x – 6)
D. y = (x + 2)2 - 16

23. Which of the following is an equivalent form of the equation of the graph shown in the xy-plane
above, from which the coordinates of vertex A can be identified as constants in the equation?
y = x2 + 4x – 12
= (x +2)2 – 16
Vertex from of parabola is y = a (x – h)2+ k
Ans. D

24. The following function models the amount A , of titanium-44 in milli Becquerel's, in a particular
sample after t years A(t)= 81(.73)t . Which of the following equivalent expressions shows, as a
constant or coefficient, the amount of titanium-44 in the sample 2 years prior to initially
measuring the sample?
A. 152 (0.73)(t+2)
B. 43.2 (0.73)(t-2)
C. 81(0.73)2t
D. 81 (0.73) (t/2)

25. The following function models the amount A , of titanium-44 in milli Becquerel's, in a particular
sample after t years A(t)= 81(.73)t . Which of the following equivalent expressions shows, as a
constant or coefficient, the amount of titanium-44 in the sample 2 years prior to initially
measuring the sample?
A (t) = 81 (0.73)t
Samples 2 years prior is
= 81 (0.73)-2
= 152
Ans. A

26. A project manager estimates that a project will take x hours to complete, where x > 200. The
goal is for the estimate to be within 20 hours of the time it will actually take to complete the
project. If the manager meets the goal and it takes y hours to complete the project, which of
the following inequalities represents the relationship between the estimated time and the
actual completion time?
A. x + y < 220
B. y > x + 20
C. y < - 20
D. - 20 < y – x < 20

27. A project manager estimates that a project will take x hours to complete, where x > 200. The
goal is for the estimate to be within 20 hours of the time it will actually take to complete the
project. If the manager meets the goal and it takes y hours to complete the project, which of
the following inequalities represents the relationship between the estimated time and the
actual completion time?
Let x = 250
y = 230 or 270
x – y = 20 or - 20
Ans. D

28. For what value of x is the function g below undefined?
g (x) = 1/((x – 7)2 + 6 (x – 7) + 9)

29. For what value of x is the function g below undefined?
g (x) = 1/((x – 7)2 + 6 (x – 7) + 9)
Let x – 7 = t
g (x) = 1/(t2 + 6t + 9)
= 1/(t+3)2
= 1/(x – 4)2

30. Arun bought a phone at a store that gave a 15 percent discount off its original price. The total
amount he paid to the cashier was q dollars, including an 9 percent sales tax on the discounted
price. Which of the following represents the original price of the phone in terms of q?
A. 0.94q
B. q/0.94
C. (0.85) (1.09) q
D. q/((0.85) (1.09))

31. Arun bought a phone at a store that gave a 15 percent discount off its original price. The total
amount he paid to the cashier was q dollars, including an 9 percent sales tax on the discounted
price. Which of the following represents the original price of the phone in terms of q?
Let initial price be x
0.85x + 9/100 (0.85x) = q
0.85x (1.09) = q
x= q/(0.85)(1.09)
Ans. D

32. f(x) = 3x3 + 6x2 + 9x
g(x) = x2 + 2x + 3
The polynomials f(x) and g(x) are defined above. Which of the following polynomials is divisible
by 3x +5?
A. p(x) = 3 f(x) + g(x)
B. q(x) = f(x) + 5g(x)
C. r(x) = 3f(x) + 5g(x)
D. s(x) = 5f(x) + 3g(x)

33. f(x) = 3x3 + 6x2 + 9x
g(x) = x2 + 2x + 3
The polynomials f(x) and g(x) are defined above. Which of the following polynomials is divisible
by 3x +5?
f(x) = 3x (x2 + 2x +3), g(x) = x2 + 2x +3
f(x) + 5 g(x) = 3x(x2 + 2x +3) + 5(x2 + 2x +3) = (x2 + 2x + 3) (3x + 5)
Ans. B

34. Two function are such that f(x)= 3 + 4x and g (f(x)) = 2x + 1. What is the value of g(7) ?

35. Two function are such that f(x)= 3 + 4x and g (f(x)) = 2x + 1. What is the value of g(7) ?
f(x) = 7 = 3 + 4x => x =1
g(f(x)) = 2(1) + 1 = 3

36. The graph of function g is the graph of function f stretched horizontally by a factor of 5. Which
of the following correctly defines function?
A. g(x) = 5 f(x)
B. g(x) = 1/5 f(x)
C. g(x) = f(5x)
D. g(x) = f(x/5)

37. The graph of function g is the graph of function f stretched horizontally by a factor of 5. Which
of the following correctly defines function?
g(x) = f(x/5)
Ans. D

38. The administrators of a factory modelled the cumulative average construction time in hours per
engine component as a function of the total number of components their employees had
constructed, n, using the following function T(n)= 8.1+ 7(0.6)n .What was the cumulative
average time(in hours) for an employee to construct one engine component when they first
began?

39. The administrators of a factory modelled the cumulative average construction time in hours per
engine component as a function of the total number of components their employees had
constructed, n, using the following function T(n)= 8.1+ 7(0.6)n .What was the cumulative
average time(in hours) for an employee to construct one engine component when they first
began?
n = 0
T(0) = 8.1 + 7 (0.6)0
= 8.1 + 7 = 15.1 hours

40. What is the sum of the solutions to the equation √(p + 5) = p + 3?

41. What is the sum of the solutions to the equation √(p + 5) = p + 3?
√(P +5) = P + 3
P + 5 = (P + 3)2 => P + 5 = P2 + 6P + 9
=> P2 + 5P + 4 = 0
=> (P + 1) (P + 4) = 0
=> P = - 1 or P = -4
but P = - 4 does not satisfy equation
 P = - 1

42. Which of the following is an equation of the line in the -plane that passes through the point (4,5)
and is parallel to the line with equation x = (2/5) y + 2?
A. y = (5/2)x + 2
B. y = (5/2)x - 5
C. y = -5/2 x + 33/2
D. y = 2/5 x + 8

43. Which of the following is an equation of the line in the -plane that passes through the point (4,5)
and is parallel to the line with equation x = (2/5) y + 2?
Slope of x = 2/5 y + 2 is
y = 5/2 (x – 2)
y = 5x/2 - 5
Thus, slope = (5/2)
y = 5x/2 + b
5 = 10 + b => b = - 5
y = 5x/2 – 5
Ans. B

44. An architect is creating a scale model of a building with a rectangular base. The ratio of the
building’s base length to the scale model’s base length is 150 in : 4 in. If the length of the base
of the scale model is 12 inches (in), what is the length of the base of the building to the nearest
foot?

45. An architect is creating a scale model of a building with a rectangular base. The ratio of the
building’s base length to the scale model’s base length is 150 in : 4 in. If the length of the base
of the scale model is 12 inches (in), what is the length of the base of the building to the nearest
foot?
450 inches but question is asking for foot so divide with 12,
we get 450/12 = 37.5 = 38 foot

46. Jennifer is renting a car. The rental charge is $14.50 per day plus $0.32, per mile. Jennifer can
spend at most $55 for the cost of the car rental. If Jennifer rents the car for one day, which of
the following is one possible number of miles Jennifer can drive the rental car?
A. 83
B. 127
C. 150
D. 190

47. Jennifer is renting a car. The rental charge is $14.50 per day plus $0.32, per mile. Jennifer can
spend at most $55 for the cost of the car rental. If Jennifer rents the car for one day, which of
the following is one possible number of miles Jennifer can drive the rental car?
5+0.32x<= 55
Solving for x we get x is less than or equal to 126.5625
Option A is correct!

49. • Domain and Range, Piece Wise Defined Functions, Odd and Even
Functions, Combination of Functions, Periodic Functions, Inverse
Functions and their existence, Transformations and Reflections,
Asymptotes.
Functions
• Linear Functions, Quadratic Functions, Exponential Functions,
Logarithmic Functions, Rational Functions, Inverse Functions,
Special Functions (GIF, Sig, Mod...).
• Trigonometric Functions: Basic Trigonometric Identities, Signs of
Trigonometric Functions, Period and Amplitude/Graphs of
Trigonometric Functions, Sum and Difference of Angles, Double
Angle Formulas, Functions of Half Angle, Trigonometric Equations,
Inverse Trigonometric Functions, Law of Sines and Cosines.
• Function Notation
Different Types of Functions

50. • Mean, Median, Mode, Range, Interquartile Range and Standard
Deviation, Regression Analysis (Linear, Quadratic and Exponential)
Statistics
• Permutation, Combinations, Probability (Including Binomial
Probability)
• Sequences (Arithmetic, Geometric), Limits, Vectors, Matrices, Polar
Coordinates, Parametric Equations, Polynomial and Rational
Inequalities, Rational Zero Test, Descartes Rule of Signs,
Intermediate Value Theorem, Leading Coefficient Test.
Other topics

51. THANK YOU!