The SAT
®
Mathematics
Review
, Mathematics Review Number and Operations
● Integers: . . . , −4, −3, −2, −1, 0, 1, 2, 3, 4, . . .
Number and Operations (20–25%) (Note: zero is neither positive nor negative.)
● Arithmetic word problems (including percent, ● Consecutive Integers: Integers that follow in
ratio, and proportion) sequence; for example, 22, 23, 24, 25. Consecutive
● Properties of integers (even, odd, prime numbers, integers can be more generally represented by
divisibility, etc.) n, n + 1, n + 2, n + 3, . . .
● Rational numbers
● Odd Integers: . . . , −7, −5, −3, −1, 1, 3, 5, 7, . . . ,
● Sets (union, intersection, elements) 2k + 1, . . . where k is an integer
● Counting techniques ● Even Integers: . . . , −6, −4, −2, 0, 2, 4, 6, . . . , 2k ,
● Sequences and series (including exponential . . . , where k is an integer (Note: zero is an even
growth) integer.)
● Elementary number theory ● Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19, . . .
(Note: 1 is not a prime and 2 is the only even prime.)
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Algebra and Functions (35–40%) ●
(Note: the units digit and the ones digit refer to the
● Substitution and simplifying algebraic expressions same digit in a number. For example, in the number
● Properties of exponents 125, the 5 is called the units digit or the ones digit.)
● Algebraic word problems
● Solutions of linear equations and inequalities Percent
● Systems of equations and inequalities
● Quadratic equations Percent means hundredths, or number out of 100. For
● Rational and radical equations 40 2
example, 40 percent means or 0.40 or .
● Equations of lines 100 5
● Absolute value
● Direct and inverse variation Problem 1: If the sales tax on a $30.00 item is $1.80, what
● Concepts of algebraic functions is the sales tax rate?
Newly defined symbols based on commonly used n
● Solution: $1.80 = × $30.00
operations 100
n = 6, so 6% is the sales tax rate.
Geometry and Measurement (25–30%)
Percent Increase / Decrease
● Area and perimeter of a polygon
● Area and circumference of a circle Problem 2: If the price of a computer was decreased from
● Volume of a box, cube, and cylinder $1,000 to $750, by what percent was the price decreased?
● Pythagorean Theorem and special properties of
isosceles, equilateral, and right triangles Solution: The price decrease is $250. The percent decrease
● Properties of parallel and perpendicular lines 250 n
Coordinate geometry is the value of n in the equation = . The value of
● 1, 000 100
● Geometric visualization n is 25, so the price was decreased by 25%.
● Slope
● Similarity increase n
Note: n% increase means = ;
● Transformations original 100
decrease n
n% decrease means = .
Data Analysis, Statistics, and original 100
Probability (10–15%)
● Data interpretation (tables and graphs)
● Descriptive statistics (mean, median, and mode)
● Probability
14 SAT Preparation Booklet
2 SAT Mathematics Review
®
Mathematics
Review
, Mathematics Review Number and Operations
● Integers: . . . , −4, −3, −2, −1, 0, 1, 2, 3, 4, . . .
Number and Operations (20–25%) (Note: zero is neither positive nor negative.)
● Arithmetic word problems (including percent, ● Consecutive Integers: Integers that follow in
ratio, and proportion) sequence; for example, 22, 23, 24, 25. Consecutive
● Properties of integers (even, odd, prime numbers, integers can be more generally represented by
divisibility, etc.) n, n + 1, n + 2, n + 3, . . .
● Rational numbers
● Odd Integers: . . . , −7, −5, −3, −1, 1, 3, 5, 7, . . . ,
● Sets (union, intersection, elements) 2k + 1, . . . where k is an integer
● Counting techniques ● Even Integers: . . . , −6, −4, −2, 0, 2, 4, 6, . . . , 2k ,
● Sequences and series (including exponential . . . , where k is an integer (Note: zero is an even
growth) integer.)
● Elementary number theory ● Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19, . . .
(Note: 1 is not a prime and 2 is the only even prime.)
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Algebra and Functions (35–40%) ●
(Note: the units digit and the ones digit refer to the
● Substitution and simplifying algebraic expressions same digit in a number. For example, in the number
● Properties of exponents 125, the 5 is called the units digit or the ones digit.)
● Algebraic word problems
● Solutions of linear equations and inequalities Percent
● Systems of equations and inequalities
● Quadratic equations Percent means hundredths, or number out of 100. For
● Rational and radical equations 40 2
example, 40 percent means or 0.40 or .
● Equations of lines 100 5
● Absolute value
● Direct and inverse variation Problem 1: If the sales tax on a $30.00 item is $1.80, what
● Concepts of algebraic functions is the sales tax rate?
Newly defined symbols based on commonly used n
● Solution: $1.80 = × $30.00
operations 100
n = 6, so 6% is the sales tax rate.
Geometry and Measurement (25–30%)
Percent Increase / Decrease
● Area and perimeter of a polygon
● Area and circumference of a circle Problem 2: If the price of a computer was decreased from
● Volume of a box, cube, and cylinder $1,000 to $750, by what percent was the price decreased?
● Pythagorean Theorem and special properties of
isosceles, equilateral, and right triangles Solution: The price decrease is $250. The percent decrease
● Properties of parallel and perpendicular lines 250 n
Coordinate geometry is the value of n in the equation = . The value of
● 1, 000 100
● Geometric visualization n is 25, so the price was decreased by 25%.
● Slope
● Similarity increase n
Note: n% increase means = ;
● Transformations original 100
decrease n
n% decrease means = .
Data Analysis, Statistics, and original 100
Probability (10–15%)
● Data interpretation (tables and graphs)
● Descriptive statistics (mean, median, and mode)
● Probability
14 SAT Preparation Booklet
2 SAT Mathematics Review
