Topic 2. Passport to advanced mathematics
 2.1 Solving quadratic equations
 2.2 Interpreting nonlinear expressions
 2.3 Manipulating quadratic and exponential expressions
 2.4 Radicals and rational exponents
 2.5 Radical and rational equations
 2.6 Operations with polynomials
 2.7 Polynomial factors and graphs
 2.8 Graphing quadratic functions
 2.9 Graphing exponential functions
 2.10 Linear and quadratic systems
 2.11 Structure in Quadratic expressions
 2.12 Isolating quantities
 2.13 Function notation
Topic 3. Problem solving and data analysis
SAT Math Section Exam Pattern
The Math section of the SAT is used to analyse the mathematical aptitude of the candidates. With the new changes to the SAT exam pattern, candidates will now be able to use calculators for the entire Math section of an SAT.
Number of Questions  58 
Duration  80 minutes 
Types of Questions  Multiple Choice Questions 
Questions 

Syllabus Details : Heart of Algebra
Solving linear equations and linear inequalities
 Solve linear equations
 Type: \(3x0.6=1.8\) What value of \(x\) satisfies the equation above
 Type: If \(2x4=5x\) what is the value of \(x\) ?
 Type: What is the solution to the equation \(\frac{1}{2}x+\frac{1}{5}=\frac{1}{7} \)
 Type: \(2(x7)=2\) what is the value of \(x\)
 Type: \(2x+5y=1\) and \(x=5\) what is the value of \(2y\)
 Type: If \(3x1=5\), what is the value of \(x40\) ?
 Type: solve for \(\left 2x+1 \right =10\)
 Solve linear inequalities
 Type: What values of \(x\) satisfy the inequality \(5x+1>7\)
 Recognize the conditions under which a linear equation has one solution, no solution, and infinitely many solutions
 Type: \(2x−4=a(x−2)\) If \(a=2\), is the equation above, what value of \(x\) satisfies the equation?
Understanding linear relationships
 basics of linear relationships.
 writing linear equations based on word problems
 important features of linear functions
 Type: Tobias rented a kayak from a sports equipment store. For the rental, the store charged \($\)60 per day plus \($25\) for delivery. If Tobias was charged a total of \($\)325, for how many days did he rent the kayak?
 Type: The width of a rectangular vegetable garden is \(W\) feet. The length of the garden is 16 feet longer than its width. Which of the following expresses the perimeter, in feet, of the vegetable garden in terms of \(W\) ?
linear inequalities
 Type : Hammer can harvest at least 48 pounds of honey from her bee colony. If he wants to package the honey harvest in \(1.51\) pound jars, what is the minimum number of jars he can fill?
 Type : Laila wants to buy at least 40 prizes for rewarding her students throughout the semester. The prize pool will be made of small and large prizes, which cost $3 and $5 each respectively. Her budget for the prizes can be no more than $100. She wants to buy at least 15 small prizes and at least 5 large prizes. Which of the following systems of inequalities represents the conditions described if x is the number of small prizes and y is the number of large prizes?
Graphing linear equations
 features of linear graphs from their equations
 Write linear equations based on graphical features
 Determine the equations of parallel and perpendicular lines
 Identify solutions to systems of linear inequalities as regions in the \(xy\) plane
Solving systems of linear equations
 solve systems of linear equations algebraically: substitution and elimination.
 systems of linear equations have one solution, no solutions, or infinitely many solutions: graphically
Syllabus Details : Passport to Advanced Math
Solving quadratic equations
 Solve quadratic equations in several different ways
 Determine the number of solutions to a quadratic equation without solving
Nonlinear expressions
 Area of a rectangle
 Height versus time
 Population growth and decline
 Compounding interest
Exponential expressions
 change time units
 Adding and subtracting exponential expressions
 Multiplying and dividing exponential expressions
 exponent operations to rational exponents
Radicals and rational exponents
 Rational exponents refer to exponents that can be represented as fractions \(\frac{1}{3},5,\frac{2}{5}\) etc..
 Radicals are another way to write rational exponents. For example, \(x^{\frac{1}{2}}\; and\; \sqrt{x}\) are equivalent.
 Exponent operations to rational exponents
 Equivalent rational and radical expressions
Operations with polynomials
 adding and subtracting polynomials
 multiplying two polynomials
Polynomial factors and graphs
 factors of polynomial functions to the \(x\)intercepts of polynomial graphs
 polynomial remainder theorem
 The polynomial remainder theorem states that when a polynomial function \(p(x)\) is divided by \(xa\), the remainder of the division is equal to \(p(a)\), left parenthesis, a, right parenthesis.
 determine the zeros of a polynomial function
 \(x\)intercepts, \(y\)intercept and end behavior
Graphing quadratic functions
 features of a parabola
 function at several different values of \(x\)
 inputoutput pairs as points in the \(xy\)plane.
 Sketch a parabola that passes through the points
Graphing exponential functions
 Graphing exponential growth & decay
 Using points to sketch an exponential graph
 yintercept ,
 slope of the graph positive or negative,
 value of y as the value of x becomes very large
 shift the horizontal asymptote
 shift the yintercept
Linear and quadratic system
 graphs of linear and quadratic systems
 number of solutions for linear and quadratic systems
 solve linear and quadratic systems algebraically
 solutions to linear and quadratic systems from graphs
Structure in quadratic expressions
 Factoring quadratic expressions
 factor by grouping
 Special factoring
 Square of sum
 Square of difference
 Difference of squares
Isolating quantities
 Using equations and formulas with multiple variables
 Manipulating formulas
 Translate the word problem or given context into an equation.
 Like solving equations, but with more variables
Function Notation
 Evaluating functions algebraically and using tables
 Determine inputs and outputs using tables
 Evaluating composite functions algebraically and using tables \(f(g(x))\)
Syllabus Details : Problem Solving and Data Analysis
Ratios, rates, and proportions
 Identify and express ratios
 Parttopart ratio
 Parttowhole ratio
 Word problems using proportions
 Applying a per unit rate
 \(speed=\frac{distance}{time}\)
 \(price=\frac{total price}{units purchased}\)
Percentages
 percentages using part and whole values
 equivalent forms of percentages
 Calculating a percent value
 Finding complementary percentages
 Switching between forms of percentages
 Calculating percent change
Unit conversion
 Applying unit to unit ratios
 Converting units within rates
Table data
 Read twoway frequency table
 calculate proportions and probabilities
 Use proportions and probabilities to find missing values
 find missing values
Scatterplots
 line of best fit to describe scatterplots
 Make predictions using the line of best fit
 Fit functions to scatterplots
Key features of graphs
 Bar graphs, dot plots, and histograms
 Reading bar graphs
 Reading line graphs
 draw line graphs based on verbal descriptions
 line graphs
Linear and exponential growth
 two variables have a linear or exponential relationship based on their values
 Linear
 Changes (i.e., increases or decreases) at a constant rate
 Changes by \(c\) per unit of time.
 Exponential
 Changes by ,\(c%\) percent of the initial value per unit of time
 Changes by a factor of \(c\) (e.g., halves, doubles) per unit of time
 realworld scenario exhibits linear or exponential growth
 Writing equations based on tables
Data inferences
 Estimating using sample proportions
 estimate=sample proportion⋅population
 margin of error
 range=estimate ± margin of error
Center, spread, and shape of distributions
 mean, median, and mode.
 range and standard deviation
 The effect of outliers
 Missing value given the mean
Data collection and conclusion
 good and bad sampling methods
 Sampling methods and their implications
 Correlation and causality
 Identifying study types
 Sample surveys
 correlation and causation.
Probability
 \(Probability=\frac{desired \: outcome}{all \: possible \: outcome}\)
 “odds” of any particular event
 get tails or head if you flip a coin
 Either/Or Probability
 Conditional Probability
Syllabus Details : Problem Solving and Data Analysis
Volume word problems
 volumes and dimensions of threedimensional solids
 dimension changes affect volume
 Volume of a cone
 Impact of increasing the radius
Right triangle problems
 Pythagorean theorem
 Calculating missing side lengths in right triangles
 Using trigonometric ratios to find side lengths
 Recognizing Pythagorean triples
 sine, cosine, and tangent of similar triangles
 sine and cosine of complementary angles
Congruence and similarity
 Finding angles in triangles
 Triangles, vertical angles, and supplementary angles
 Triangles and parallel lines
 proportional relationships using similarity
Length, perimeter, Area, Angles, arc lengths, and trig functions
 Convert between radians and degrees
 Special right triangles in circles
 Trigonometry using radian measures
 unit circle
 \(x=rcos\theta =cos\theta \)
 \(y=rsin\theta =sin\theta\)
\(\frac{y}{x}=tan\theta\)
Circle theorems
 central angle, arc length, and sector area
 \(\frac{central \: angle}{360^o} =\frac{arc \: length}{circumference}=\frac{sector \: area}{circle \: area}\)
 Circumference of a circle \(C=2\pi r\)
 Area of a circle \(A=\pi r^2\)
 Number of degrees of arc in a circle \(360\)
Circle equations
 Standard form equation of a circle
 In the \(xy\)plane, a circle with center \((h, k)\) and radius \(r\) has the equation:
 \((xh)^2 +(yk)^2 = r^2\)
 Rewriting circle equations in standard form
Complex numbers
 square roots of negative numbers
 complex number \(z=a+ib\)
 add and subtract complex numbers
 multiply and divide complex numbers