SAT: 100 Essential Math Concepts

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100 terms · This is a list of all 100 of the SAT Math Concepts

Number Categories

Integers are whole numbers; they include negtavie whole numbers and zero, Rational numbers can be expressed as a ratio of two integers, irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.

Addomg/Subtracting Signed Numbers

To add a positive and negative integer first ignore the signs and find the positive difference between the two integers, attatch the sign of the original with higher absolute value, to subtract negative integers simply change it into an addition problem given that two negatives make a positive, to add or subtract a string of positive and negative integers simply change the whole problem into addtion.

Multiplying/Dividing SIgned Numbers

To multiply or divide integers, firstly ignore the sign and compute the problem, given 2 negatives make a positive, 2 positives make a positive, and one negative, and one positive make a negative attach the correct sign

PEMDAS

Parentheses, Exponents,Multiplication and Division(reversible), Addition and Subtraction (reversible)

Counting Consecutive Integers

To count consecutive integers, subtract the smallest from the largest and add 1

Exponential Growth

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Union and Intersection of Sets

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Factor/Multiple

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Prime Factorization

To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime

Relative Primes

Relative primes are integers that have no common factor other than 1, to determine whether two integers are relative primes break them both down to their prime factorizations

(Least) Common Multiple

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Greatest Common Factor

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Even/Odd

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Multiples of 2 and 4

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Multiples of 3 and 9

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Multiples of 5 and 10

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Remainders

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Reducing Fractions

To reduce a fraction to lowest terms, factor out and cancel all factors the numerator and denominator have in common

Adding/Subtracting Fractions

To add or subtract fraction, first find a common denominator, then add or subtract the numerators

Multiplying Fractions

To multiply fractions, multiply the numerators and multiply the denominators

Dividing Fractions

To divide fractions, invert the second one and multiply

Mixed Numbers and Improper Fractions

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, then add the numerator over the same denominator, to convert an improper fraction to a mixed number, divide the denominator into the numerator to get a whole number quotient with a remainder, the quotient is the whole number, the remainder is the numerator, and the denominator remains the same

Reciprocal

To find the reciprocal of a fraction switch the numerator and the denominator

Comparing Fractions

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Converting Fractions and Decimals

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Repeating Decimal

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Identifying the Parts and the Whole

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Percent Formula

Part = Percent x Whole

Percent Increase and Decrease

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Finding the Original Whole

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Combined Percent Increase and Decrease

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Setting up a Ratio

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Part-to-Part Ratios amd Part-to-Whole Ratios

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Solving a Proportion

To solve a proportion, cross multiply

Rate

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Average Rate

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Average Formula

Add up numbers and divide by the number of numbers: Average=Total A/Total B

Average of Evenly Spaced Numbers

Avearge the smallest and largest numbers

Using the Average to Find the Sum

Sum=(Average) x (Number of Terms)

Finding the Missing Number

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Median and Mode

The median is the value that falls in the middle of the set, the mode is the value that appears most often

Counting the Possibilities

If there are m ways one event can happen and n ways a second event can happen, then there are m × n ways for the 2 events to happen

Probability

Probability= Favorable Outcomes/Total Possible Outcomes

Multiplying and Dividing Powers

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Raising Powers to Powers

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Simplifying Square Roots

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Adding and Subtracting Roots

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Multiplying and Dividing Roots

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Negative Exponent and Rational Exponent

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Determining Absolute Value

The absolute value of a number is the distance of the number from zero, since absolute value is distance it is always positive

Evaluating an Expression

To evaluate an algebraic expression, plug in the given values for the unknowns and calculate according to PEMDAS

Adding and Subtracting Monomials

To combine like terms, keep the variable part unchanged while adding or subtractubg tg coefficients

Adding and Subtraction Polynomials

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Multiplying Monomials

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Multiplying Binomials-FOIL

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Multiplying other Polynomials

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Factoring out a Common Divisior

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Factoring the Differnce of Squares

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Factoring the Square of a Binomial

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Factoring other Polynomials-FOIL in reverse

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Simplifying an Algebraic Fraction

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Solving a Linear Equation

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Solving "In Terms Of"

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Translating from English into Algebra

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Solving a Quadratic Equation

ax squared + bx + c = 0

Solving a System of Equations

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Solving an Inequality

To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign

Radical Equations

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Function, Notation, and Evaulation

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Direct and Inverse Variation

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Domain and Range of a Function

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Finding the DIstance Between Two Points

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Using Two Points to Find the Slope

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Using an Equation to Find the Slope

To find the slope of a line from an equation, put the equation into slope-intercept form (m is the slope): y=mx+b

Using an Equation to Find an Intercept

To find the y-intercept put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y; to find the x-intercept plug y=0 and solve for x

Finding the Midpoint

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Intersecting Lines

When two lines intersect, adjacent angles are supplementary and vertical angles are equal

Parallel Lines and Transversals

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Interior and Exterior Angles of a Triangle

The 3 angles of any triangle add up to 180 degrees, an exteriror angles of a triangle is equal to the sum of the remote interior angles, the 3 exterior angles add up to 360 degrees

Similar Triangles

Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional

Area of a Triangle

Area of Triangle = 1/2 (base)(height), the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex

Triangle Inequality Theorem

The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides

Isosceles and Equilateral triangles

An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal, an equaliteral is a triangle where all 3 sides are equal, thus the angles are equal, regardless of side length the angle is always 60 degrees

Pythagorean Theorem

For all right triangles: (leg1)2 + (leg2)2 = (hypotenuse)2

The 3-4-5 Triangle

If a right triangle's leg-to-leg ratio is 3:4, or if the leg-to-hypotenuse ratio is 3:5 or 4:5, it's a 3-4-5 triangle and you don't nee dtp ise the Pythagorean theorem to find the third side

The 5-12-13 Triangle

If a right triangle's leg-to-leg ratio is 5:12, or if the leg-to-hypotenuse ratio is 5:13 or 12:13, it's a 5-12-13 triangle and you don't nee dtp ise the Pythagorean theorem to find the third side

The 30-60-90 Triangle

The sides of a 30-60-90 triangle are in a ratio of x:x square root 3: 2x, you don't need the Pythagorean theorem

The 45-95-90 Triangle

The sides of a 45-45-90 triangle are in a ratio of x:x:square root 2.

Characteristics of a Rectangle

A rectangle is a four-sided figure with four right angles opposite sides are equal, diagonals are equal; Area of Rectangle = length x width

Characteristics of a Parallelogram

A parallelogram has two pairs of parallel sides, opposite sides are equal, opposite angles are equale, consecutive angles add up to 180 degrees; Area of Parallelogram = base x height

Characteristics of a Square

A square is a rectangle with four equal sides; Area of Square = (Side)2

Interior Angles of a Polygon

The sum of the measures of the interior angles of a polygon = (n - 2) × 180, where n is the number of sides

Circumference of a Circle

Circumference = 2πr

Length of an Arc

An arc is a piece of the circumference. If n is the degree measure of the arc's central angle, then the formula is: Length of an Arc = 1 (n/360) (2πr)

Area of a Circle

Area of a Circle = πr2

Area of a Sector

A sector is a pieece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (πr)2

Tangency

When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact

Surface Area of a Rectangular Solid

Surface Area = 2lw + 2wh + 2lh

Volume of a Rectangular Solid

Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)3

Volume of a Cylinder

Volume of a Cylinder = πr2h

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