# SAT MATH TOOLKIT

Studied by 104 people
5.0(1)
get a hint
hint

What is an integer?

1 / 88

## Tags and Description

Basic topics you'll need for SAT Math Write in full sentences.

### 89 Terms

1

What is an integer?

An integer is any number that can be expressed without a fraction, decimal, percentage sign, or symbol.

New cards
2

What is the only thing that can be odd or even?

Only integers can be odd or even- A fraction or symbolic number is neither odd or even.

New cards
3

What is a number line?

A number line is a simple diagram that arranges numbers from least to greatest.

New cards
4

What is a prime number?

A prime number is a number that has exactly 2 factors: 1 and itself.

New cards
5

All prime numbers are ____?

All prime numbers are positive

New cards
6

What is the only even prime number?

The only even prime number is 2.

New cards
7

Why is 1 not a prime number?

1 is not a prime number because it has only 1 factor(itself), while prime numbers must have exactly 2 factors

New cards
8

What are composite numbers?

Composite numbers can be divide by more than 2 numbers

New cards
9

What do ratios, proportions, and percentages do?

Ratios, proportions, and percentages all express a relationship between two numbers.

New cards
10

How is a ratio often written?

A ratio is often written as a pair of numbers with a colon between them.

New cards
11

How is a proportion often written?

A proportion is usually written as a fraction with a number in the numerator compared to the number in the denominator.

New cards
12

What do we say If the relationship between two quantities is the kind where increasing one quantity results in a consistent increase in the other quantity?

If the relationship between two quantities is the kind where increasing one quantity results in a consistent increase in the other quantity, then we say those two quantities vary directly or are directly proportional.

New cards
13

What do we say If two quantities are related so that increasing one consistently decreases the other.

If two quantities are related so that increasing one consistently decreases the other, then we say those two vary indirectly or are inversely proportional.

New cards
14

How do we make a fraction into a decimal?

To make a fraction into a decimal, divide the numerator by the denominator.

New cards
15

How do you make a fraction into a percentage?

To make a fraction into a percentage, divide the numerator by the denominator, then multiply by 100.

New cards
16

How do you make a percentage into a fraction?

To make a percentage into a fraction, give the original percentage a denominator of 100, and then simplify if necessary.

New cards
17

What is the distance formula(not the one for distance of two points)?

The distance formula is Distance= Rate x Time(d=rt).

New cards
18

What is a rate?

A rate is a ratio that tells us how often one even happens in relation to another event happening. Rates are usually but not always expressed in terms of time.

New cards
19

How do we find the distance traveled by an object?

To find the distance traveled by an object, we can multiply the rate at which the object travels by the time that the object spends traveling at that rate. d=rt

New cards
20

What are some more things we can use the distance formula for (not the one for distance between to points on coord plane)?

We can use the same formula to find out how long an object takes to cover a certain distance in a given time. We can also use the formula to find out the speed of an object that covers a certain distance in a given time. The same relationship can be used to discuss the rates at which other processes happen, not just the rate of movement of an object.

New cards
21

What is a complex conjugate?

For our purposes, the complex conjugate of a complex number is another complex number whose real component is identical but whose imaginary component has the opposite sign but is otherwise identical. For example, if we’re given the imaginary number 5+2i, then its complex conjugate is 5-2i.

New cards
22

How do we remove the imaginary component of a complex denominator, using the complex conjugate?

To do this, we take the fraction with the complex denominator and multiply it by a fraction whose numerator and denominator are both equal to the complex conjugate of the denominator of the first fraction.

New cards
23

What is a set?

In the context of SAT “MATH”, a set is a group of specific things- usually a group of numbers. In set notation, there are curly braces on either end of the set, and commas between the elements of the set. Example:The set of positive integers less than 4 is as follows: {1,2,3}

New cards
24

What is algebra?

For our purposes, algebra is the process of using variables like x to stand for unknown numbers in mathematical expressions, and then manipulating those expressions to find the values of one or more of those unknown numbers.

New cards
25

What is an equation?

On the SAT, an equation is a statement that involves an algebraic expressions and an equal sign.

New cards
26

What is a system of equations?

A system of equations contains two or more equations with the same variables.

New cards
27

What is the solution to a systems of equations?

A solution to a system of equations is a set of values that creates a valid statement when plugged into each equation in the system. It is also an intersection point between two equations on a graph.

New cards
28

What are inequalities?

On the SAT, inequalities are statements that show a particular amount is greater than or less than a second amount.

New cards
29

What does inclusive mean in an inequality?

Inclusive means included in that range. The phrase “from 0 to 10, inclusive,” means that 0 and 10 are included in the range.

New cards
30

What does exclusive means in an inequality?

Exclusive means not included in that range. The phrase “from 0 to 10, exclusive,” means that 0 and 10 are not included in the range.

New cards
31

What is the one difference between the way you solve an inequality and the way you solve an equation?

You solve an inequality the same way you solve an equation, with one difference: when you divide or multiply by a negative number to solve for a variable, you have to switch the direction of the inequality symbol.

New cards
32

What will the solution of the inequality look like when you graph it?

When we graph an inequality, we end up with a shaded region on the side of the line that contains all the points that are solutions to the inequality.

New cards
33

How do we check our solution for the inequality?

We can check whether a particular point is a solution of an inequality by plugging that point into that inequality. If the result is a valid statement, then the point is a solution of the inequality.

New cards
34

What will the solution to a systems of inequalities look like when you graph it?

When we graph a system of inequalities, the solution region will be the set of points in the coordinate plane that satisfy both inequalities.

New cards
35

Formula for exponential growth or decay?

INITIAL AMOUNT OF SUBSTANCE(rate of growth or decay)^amount of time. Or A(b)^x

New cards
36

What does the Growth or Decay part means when were talking about exponetial Growth or Decay?

Growth and Decay refer to the rate the function is increasing or decreasing. If as x approaches infinity/increase the rate increases that’s exponential Growth. If as x approaches infinity/increases the rate decreases it’s exponential decay. EXPONENTIAL GROWTH OR DECAY DOES NOT MEAN THAT THE VALUE OF THE FUNCTION/ Y ITSELF IS INCREASING OR DECREASING AS X INCREASES, IT ONLY TALKS ABOUT THE RATE.

New cards
37

Why does an exponential function that have a rate less than between 0% and 100% has a growth rate when x is negative A(b)^-x.

Because the negative turn the fraction into its reciprocal which is an increasing rate/greater than 100%. A(0.80)^-x —> A(4/5)^-x —> A(5/4)^x, 5/4= 1.25 =125%.

New cards
38

What is a constant?

A constant is a number that has a set, defined value that can’t change.

New cards
39

What does the degree of a polynomial refer to?

The Degree of a variable in a polynomial refers to the highest exponent to which that variable is raised in the expression.

New cards
40

What are Three types of special angle relationships that appear often on the SAT?

Three types of special angle relationships that appear often on the SAT are vertical, supplementary, and complementary angles.

New cards
41

What are vertical angles, and what is special about them?

Vertical angles are the pairs of angles that lie across from each other when two lines intersect. In a pair of vertical angles, two angles are equal to each other.

New cards
42

What are supplementary angles, and what is special about them?

Supplementary angles are pairs of angles whose measurements add up to 180 degrees. When supplementary angles are next to each other, they form a straight line.

New cards
43

What are complementary angles, and what is special about them?

Complementary angles describe angles whose measures add up to 90 degrees.

New cards
44

What is a transversal?

A transversal is the result when a line crosses two parallel lines.

New cards
45

What is the sum of the measures of the angles in any triangle?

The sum of the measures of the angles in any triangle is 180 degrees

New cards
46

What is the formula for finding out how much the angles of a shape adds up to?

(n-2)x180, where n is the number of sides.

New cards
47

In any triangle, the longest side is always opposite to the {…}?

Biggest angle.

New cards
48

In any triangle, the shortest side is always opposite to the {…}

Smallest angle.

New cards
49

In an equilateral triangle, all the sides are the same length, and all the angles measure add up to {…} each?

60 degrees.

New cards
50

In a Isosceles triangle, {…} are the same length, and {…} are the same size as each other.

Two of the 3 sides. Two of the 3 angles.

New cards
51

A right triangle is a triangle that includes {…}?

A ninety degree angle as one of its 3 angles.

New cards
52

What is a pythogorean triple?

A Pythagorean triple is a set of numbers that can be all the lengths of the sides of the same right triangle.

New cards
53

What do we get when we multiply each number in a pythagorean triple by the same number?

When we multiply each number in a pythagorean triple by the same number, we get another pythagorean triple.

New cards
54

What are simliar triangles?

Two triangles are similar triangles if they have all the same angle measurements.

New cards
55

What is the relationship between the corresponding sides of two similar triangles.

Between two similar triangles, the relationship between any of your corresponding sides is the same as between any other two corresponding sides.

New cards
56

What is a midpoint on a line?

Between any two points on a line, there is a midpoint that is halfway between the two points.

New cards
57

What are colinear points?

A set of points that fall on the same line.

New cards
58

How can we find the Distance between two points?

We can use the pythagorean theorem or the distance formula.

New cards
59

What is the pythagorean theorem and what is the Distance formula?

Pythagorean theorem is A^2+B^2=C^2 Distance formula is -B+- sqrt B^2 -4ac /2a

New cards
60

In a parallelogram, opposite angles are {…}, and the measurements of all the angles added up together equals 360.

Equal to each other.

New cards
61

In a parallelogram, opposite angles are equal to each other, and the measurements of all the angles added up together equals {…}

360

New cards
62

Rectangles are special parallelograms where all the angles measure {…}

90 degrees.

New cards
63

What is the perimeter for a two dimesional object that is not a circle?

The perimeter of a two dimensional object that is not a circle is the sum of the lengths of its sides

New cards
64

What is the the perimeter for a circle?

The perimeter for a circle is the distance around the circle.

New cards
65

How do you find the perimeter of a non-circle 2d shape?

To find the perimeter of a non-circle, just add up the lengths of its sides.

New cards
66

How do you find the perimeter of a circle?

The perimeter of a circle is the circumference which is 2πr

New cards
67

How do you find the area of a polygon besides a triangle, parallelogram, or circle?

To find the area of a polygon besides a triangle, parallelogram, or circle, just divide the polygon into smaller triangles, polygons, and/or circles and find the area of these pieces.

New cards
68

A radius is a line segment drawn from the center point of a circle to the edge of the circle.

New cards
69

All the radii of a circle have the {…} since all points on the circle are the {…} from the center point.

Length. Same distance.

New cards
70

What is a diameter?

A diameter is a line segment drawn from one edge of a circle, through the center of the circle and all the way to the opposite edge.

New cards
71

How do you find the diameter and why can you find it using that method?

A diameter always has a length equal to twice the radius of the circle, because a diameter can be broken into two opposite radii.

New cards
72

Formula for area of a circle?

Formula for area of a circle is A= πr^2

New cards
73

What is a tangent?

A tangent is a line that intersects a circle at only 1 point. A tangent is perpendicular to the radius ending at the shared point.

New cards
74

What is an Arc on a circle and how can we measure it?

An arc is a portion of a circle that is measured in degrees, like an angle. We can measure an arc by drawing radii to the endpoints of the arc, and then measuring the angles formed by the radii at the center of the circle.

New cards
75

What arcs can two points on the circumference form?

Two points on the circumference of a circle can define two different arcs. One arc is the shorter distance between the two points, while the other arc is the longer distance between the two points. When context isn’t sufficient we can use the term minor and major arc.

New cards
76

What is a central angle on a circle?

A central angle is an angle whose vertex is the center of a circle and whose sides are radii of that circle.

New cards
77

What is a chord on a circle?

A chord is a line segment whose endpoints are points on the circumference of a circle. Note that the diameter is a chord that passes through the center of the circle.

New cards
78

What is an inscribed angle?

An inscribed angle is an angle created by two cords that meet on one end to form a vertex.

New cards
79

What is a sector of a circle?

A sector is a portion of a circle defined by the center of the circle and two points on the circle.

New cards
80

How do we find the area of a sector?

We can find the area of a sector by finding the area of the entire circle, and then multiplying by the fraction of the circle represented by the sector.

New cards
81

What is the mean or arithmetic mean?

The mean or arithmetic mean of a set of numbers is the result you get when you add all the numbers together and then divide by the number of things you added.

New cards
82

What is the median and what do you do if they’re are two?

The median of a set of numbers is the number that appears in the middle of the set when all the numbers in the set are arranged from least to greatest . If there are 2 numbers left in the middle combine the 2 then divide it by 2.

New cards
83

What is the mode of a set of numbers?

The mode of a set of numbers is the number that appears most frequently in the set.

New cards
84

What is the range in statistics?

The range of a set of numbers is the difference between the highest number in the set and the lowest number in the set.

New cards
85

What is an outlier?

An outlier is a data point that doesn’t follow the trend established by the other data points in the set.

New cards
86

What is a probability?

The probability of an event is a fraction from 0 to 1 that describes how likely the event is to happen. If the fraction is closer to 1, the event is more likely to happen; if the fraction is closer to 0, the event is less likely to happen.

New cards
87

How do you find the probability of something?

To determine the probability, you first calculate the total number of possible outcomes and place this number in the denominator of the fraction; then, you determine the number of outcomes that satisfy the event’s requirements, and place this number in the numerator of the fraction.

New cards
88

How do you find the probability of two or more events happening?

To find the probability of two or more events happening in a sequence, we just find the probability of each event by itself, and then multiply them by each other.

New cards
89

What should a sample include?

A sample should include as many different parts of the whole as possible, to maximize the chance that it will accurately reflect the whole

New cards

## Explore top notes

Note
Studied by 16 people
Updated ... ago
5.0 Stars(2)
Note
Studied by 8 people
Updated ... ago
5.0 Stars(1)
Note
Studied by 51 people
Updated ... ago
5.0 Stars(4)
Note
Studied by 19 people
Updated ... ago
5.0 Stars(1)
Note
Studied by 5 people
Updated ... ago
5.0 Stars(1)
Note
Studied by 23 people
Updated ... ago
5.0 Stars(2)
Note
Studied by 40 people
Updated ... ago
5.0 Stars(2)
Note
Studied by 79 people
Updated ... ago
5.0 Stars(2)

## Explore top flashcards

Flashcard31 terms
Studied by 133 people
Updated ... ago
5.0 Stars(3)
Flashcard101 terms
Studied by 20 people
Updated ... ago
5.0 Stars(1)
Flashcard100 terms
Studied by 4 people
Updated ... ago
5.0 Stars(1)
Flashcard42 terms
Studied by 24 people
Updated ... ago
5.0 Stars(2)
Flashcard62 terms
Studied by 10 people
Updated ... ago
5.0 Stars(1)
Flashcard48 terms
Studied by 26 people
Updated ... ago
5.0 Stars(1)
Flashcard65 terms
Studied by 19 people
Updated ... ago
5.0 Stars(2)
Flashcard35 terms
Studied by 4 people
Updated ... ago
5.0 Stars(1)