SAT Math Terms & Formulas Flashcards

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Questions and Answers

What is the quadratic formula?

area = (1/2)bh

[-b ± √(b² - 4ac)] / (2a) (correct)

(y₂- y₁) / (x₂- x₁)

average speed = total distance / total time

What is the slope formula?

(y₂- y₁) / (x₂- x₁)

What are integers?

..., -3, -2, -1, 0, 1, 2, 3,...

What are rational numbers?

Fractions (anything expressible as a ratio of integers) Signup and view all the answers

What are real numbers?

Integers, rationals, plus special numbers (like √2 or pi) Signup and view all the answers

What is the order of operations?

PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract) Signup and view all the answers

What is the formula for an arithmetic sequence?

t₁, t₁ + d, t₁ + 2d,... Signup and view all the answers

What is the formula for a geometric sequence?

t₁, t₁· r, t₁· r²,... Signup and view all the answers

What are factors? Give an example.

Factors of 52 are 2, 4, 13, and 26 Signup and view all the answers

What are multiples? Give an example.

Multiples of 20 are 40, 60, 80, 100,... Signup and view all the answers

What is the formula for percentages?

part = (percent / 100) x whole Signup and view all the answers

What is the formula for calculating average?

average = sum of terms / number of terms Signup and view all the answers

What is the formula for average speed?

average speed = total distance / total time Signup and view all the answers

What is the formula for sum?

sum = average x (number of terms) Signup and view all the answers

What is mode?

Mode = value in the list that appears most often Signup and view all the answers

What is median?

Median = middle value in the list Signup and view all the answers

What is the fundamental counting principle?

If an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N x M ways. Signup and view all the answers

What is probability?

Probability = number of desired outcomes / number of total outcomes Signup and view all the answers

What is the formula for adding exponents?

x^a · x^b = x^(a+b) Signup and view all the answers

What is the formula for subtracting exponents?

x^a / x^b = x^(a-b) Signup and view all the answers

What is the formula for negative exponents?

1 / x^b = x^(-b) Signup and view all the answers

What is the formula for multiplying exponents?

(x^a)^b = x^(a·b) Signup and view all the answers

What is the value of x^0?

1 Signup and view all the answers

What is the formula for roots?

√(xy) = √x · √y Signup and view all the answers

What does FOIL stand for?

(x + a)(x + b) = x^2 + (b + a)x + ab Signup and view all the answers

What is the difference of squares formula?

a^2 - b^2 = (a + b)(a - b) Signup and view all the answers

What does a^2 + 2ab equal?

(a + b)^2 Signup and view all the answers

What does a^2 - 2ab equal?

(a - b)(a - b) Signup and view all the answers

What is the distance formula?

√[(x₂ - x₁)² + (y₂ - y₁)²] Signup and view all the answers

What is the mid-point formula?

[(x₁ + x₂)/2 , (y₁ + y₂)/2] Signup and view all the answers

What do intersecting lines indicate?

Opposite angles are equal, and each pair of angles along the same line add to 180 degrees. Signup and view all the answers

What is the formula for the area of a triangle?

Area = (1/2)bh Signup and view all the answers

What do the angles of a triangle add up to?

180 degrees Signup and view all the answers

What is a property of the lengths of triangle sides?

The length of one side is always less than the sum of the other two. Signup and view all the answers

What does equilateral mean in terms of triangles?

Three equal sides, all angles = 60 degrees. Signup and view all the answers

What does isosceles mean in terms of triangles?

Two equal sides, two equal angles. Signup and view all the answers

What does similar mean in geometry?

Same shape, corresponding angles are equal, corresponding sides are in proportion. Signup and view all the answers

What is the formula for the area of a circle?

pi · r^2 Signup and view all the answers

What is the formula for the circumference of a circle?

2 · pi · r Signup and view all the answers

What is a full circle in degrees?

360 degrees Signup and view all the answers

What is the formula for length of arc?

(n degree / 360 degrees) · 2 · pi · r Signup and view all the answers

What is the formula for the area of a sector?

(n degree / 360 degrees) · pi · r^2 Signup and view all the answers

What is the formula for the area of a rectangle?

Area = lw Signup and view all the answers

What is the formula for the area of a parallelogram?

Area = lh Signup and view all the answers

What is the formula for the volume of a rectangular solid?

Volume = lwh Signup and view all the answers

What is the formula for the volume of a right cylinder?

Volume = pi · r^2 · h Signup and view all the answers

What are prime factors? Give examples.

2, 3, 5, 7, 11,... Signup and view all the answers

What is the Greatest Common Factor (GCF)? Give an example.

GCF of 200 and 60 is 20 Signup and view all the answers

What is the Least Common Multiple (LCM)? Give an example.

LCM of 200 and 60 is 600 Signup and view all the answers

What is the equation of a circle?

(x - h)^2 + (y - k)^2 = r^2 Signup and view all the answers

What are logarithms?

y = log(little b)x asks b^y = x Signup and view all the answers

What are complex numbers?

i^0 = 1; i^1 = i; i^2 = -1; i^3 = -i; i^4 = 1; i^5 = i; i^6 = -1; i^7 = -i Signup and view all the answers

What is the sine of an angle?

opp / hyp Signup and view all the answers

What is the cosine of an angle?

adj / hyp Signup and view all the answers

What is the tangent of an angle?

opp / adj Signup and view all the answers

What is the special sin-cos relationship?

sin^2(angle) + cos^2(angle) = 1 Signup and view all the answers

What is the conversion from degrees to radians?

degree# · (pi / 180 degrees) Signup and view all the answers

What is the conversion from radians to degrees?

radian# · (180 degrees / pi) Signup and view all the answers

What is the formula for the area of a trapezoid?

Area = [(base1 + base2) / 2] · h Signup and view all the answers

What is the formula for direct variation?

y = kx Signup and view all the answers

What is the formula for inverse variation?

y = k/x Signup and view all the answers

What is the slope-intercept form?

y = mx + b Signup and view all the answers

What is the point-slope form?

y - y₁ = m(x - x₁) Signup and view all the answers

What is the standard form of a linear equation?

Ax + By = C Signup and view all the answers

What happens when dividing by a negative number in an inequality?

You must flip the sign Signup and view all the answers

What type of line indicates < or > on a coordinate plane?

Dotted line Signup and view all the answers

What type of line indicates ≥ or ≤ on a coordinate plane?

Solid line Signup and view all the answers

How do you shade the graph for ≥ or > on a coordinate plane?

Shade upwards or to the right Signup and view all the answers

How do you shade the graph for ≤ or < on a coordinate plane?

Shade downwards or to the left Signup and view all the answers

What is the formula for circle perimeter?

2 pi r Signup and view all the answers

What is a chord?

The distance from one point on the circle to another point on the circle. Signup and view all the answers

What is a sector?

The part of a circle that looks like a piece of pie, bounded by two radii and an arc. Signup and view all the answers

What is an arc?

Part of a circle connecting two points on the circle. Signup and view all the answers

What is a central angle?

An angle whose vertex is the center of the circle. Signup and view all the answers

Study Notes

Essential Math Terms and Formulas

Quadratic Formula: Used to solve quadratic equations, given by [-b ± √(b² - 4ac)] / (2a].
Slope Formula: Calculates the steepness of a line using [(y₂ - y₁) / (x₂ - x₁)].
Integers: Whole numbers that include negative numbers, zero, and positive numbers ((..., -3, -2, -1, 0, 1, 2, 3, ...)).
Rational Numbers: All numbers expressible as a fraction or ratio of integers.
Real Numbers: Includes integers, rationals, and special numbers like (\sqrt{2}) or (\pi).
Order of Operations: The sequence to solve expressions: Parentheses, Exponents, Multiply, Divide, Add, Subtract (PEMDAS).
Arithmetic Sequences: A sequence of numbers in which the difference between consecutive terms is constant ((t₁, t₁ + d, t₁ + 2d, ...)).
Geometric Sequences: A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number (r) ((t₁, t₁·r, t₁·r², ...)).
Factors: Numbers that divide a given number exactly without leaving a remainder; for example, the factors of 52 are 2, 4, 13, and 26.
Multiples: The product of a number and an integer; for example, multiples of 20 are 20, 40, 60, 80, 100, etc.
Percentages: Calculated as (part = (percent / 100) × whole).
Average: Determined by dividing the sum of terms by the number of terms.
Average Speed: Calculated using the formula (average speed = total distance / total time).
Sum: Can be found by multiplying the average by the number of terms.
Mode: The value that appears most frequently in a data set.
Median: The middle number in a sorted list of numbers.
Fundamental Counting Principle: If one event can occur in (N) ways and another in (M) ways, both can occur in (N × M) ways.
Probability: The likelihood of an event occurring, calculated as (probability = number of desired outcomes / number of total outcomes).
Exponential Rules:
- Adding Exponents: (x^a·x^b = x^{(a+b)})
- Subtracting Exponents: (x^a/x^b = x^{(a-b)})
- Negative Exponents: (1/x^b = x^{-b})
- Multiplying Exponents: ((x^a)^b = x^{(a·b)})
- (x^0 = 1)
Roots: Can be simplified as (\sqrt{xy} = \sqrt{x}·\sqrt{y}).
FOIL Method: Used for multiplying two binomials ((x + a)(x + b) = x^2 + (b + a)x + ab).
Difference of Squares: Formula given by (a^2 - b^2 = (a + b)(a - b)).
Triangle Area: Calculated using the formula (area = (1/2)bh).
Circle Area and Circumference:
- Area: (A = \pi r^2)
- Circumference: (C = 2\pi r)
Volume Formulas:
- Rectangular Solid: (volume = lwh)
- Right Cylinder: (volume = \pi r^2 h)
Inequalities:
- Dividing by a negative flips the inequality sign.
- Graphing (\geq) or (\leq) uses a solid line; (<) or (>) uses a dotted line.
Graphing Techniques:
- Shade upwards for (\geq) or (>) and downwards for (\leq) or (<).
Logarithms: Defined by the relationship (y = \log_b x) such that (b^y = x).
Complex Numbers: Defined by powers of (i) ((i^0 = 1), (i^1 = i), (i^2 = -1), (i^3 = -i), and repeats).
Trigonometric Ratios:
- Sine: (sin) = opposite / hypotenuse
- Cosine: (cos) = adjacent / hypotenuse
- Tangent: (tan) = opposite / adjacent
Special Relationship: (sin^2(angle) + cos^2(angle) = 1).
Area of a Trapezoid: Calculated using the formula (area = [(base1 + base2) / 2] · h).
Direct Variation: Expressed as (y = kx).
Inverse Variation: Given by (y = k/x).
Standard Form of a line: Represented as (Ax + By = C), with specific constraints on coefficients.
Geometry Terms:
- Chord: A line segment between two points on a circle.
- Sector: A pie-slice shaped section of a circle.
- Arc: Part of a circle connecting two points on the circumference.
- Central Angle: An angle with its vertex at the circle's center.
Equations of a Circle: Given in standard form as ((x-h)^2 + (y-k)^2 = r^2), where ((h,k)) is the center.

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Description

This quiz features flashcards covering essential math terms and formulas commonly found on the SAT. You'll review key concepts such as the quadratic formula, slope formula, and types of numbers including integers and rationals. Test your knowledge and prepare effectively for the math section of the SAT.