Studied by 116 peopleWhat is an integer?
An integer is any number that can be expressed without a fraction, decimal, percentage sign, or symbol.
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.
What is a number line?
A number line is a simple diagram that arranges numbers from least to greatest.
What is a prime number?
A prime number is a number that has exactly 2 factors: 1 and itself.
All prime numbers are ____?
All prime numbers are positive
What is the only even prime number?
The only even prime number is 2.
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
What are composite numbers?
Composite numbers can be divide by more than 2 numbers
What do ratios, proportions, and percentages do?
Ratios, proportions, and percentages all express a relationship between two numbers.
How is a ratio often written?
A ratio is often written as a pair of numbers with a colon between them.
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.
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.
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.
How do we make a fraction into a decimal?
To make a fraction into a decimal, divide the numerator by the denominator.
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.
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.
What is the distance formula(not the one for distance of two points)?
The distance formula is Distance= Rate x Time(d=rt).
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.
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
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.
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.
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.
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}
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.
What is an equation?
On the SAT, an equation is a statement that involves an algebraic expressions and an equal sign.
What is a system of equations?
A system of equations contains two or more equations with the same variables.
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.
What are inequalities?
On the SAT, inequalities are statements that show a particular amount is greater than or less than a second amount.
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.
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.
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.
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.
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.
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.
Formula for exponential growth or decay?
INITIAL AMOUNT OF SUBSTANCE(rate of growth or decay)^amount of time. Or A(b)^x
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.
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%.
What is a constant?
A constant is a number that has a set, defined value that can’t change.
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.
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.
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.
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.
What are complementary angles, and what is special about them?
Complementary angles describe angles whose measures add up to 90 degrees.
What is a transversal?
A transversal is the result when a line crosses two parallel lines.
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
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.
In any triangle, the longest side is always opposite to the {…}?
Biggest angle.
In any triangle, the shortest side is always opposite to the {…}
Smallest angle.
In an equilateral triangle, all the sides are the same length, and all the angles measure add up to {…} each?
60 degrees.
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.
A right triangle is a triangle that includes {…}?
A ninety degree angle as one of its 3 angles.
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.
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.
What are simliar triangles?
Two triangles are similar triangles if they have all the same angle measurements.
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.
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.
What are colinear points?
A set of points that fall on the same line.
How can we find the Distance between two points?
We can use the pythagorean theorem or the distance formula.
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
In a parallelogram, opposite angles are {…}, and the measurements of all the angles added up together equals 360.
Equal to each other.
In a parallelogram, opposite angles are equal to each other, and the measurements of all the angles added up together equals {…}
360
Rectangles are special parallelograms where all the angles measure {…}
90 degrees.
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
What is the the perimeter for a circle?
The perimeter for a circle is the distance around the circle.
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.
How do you find the perimeter of a circle?
The perimeter of a circle is the circumference which is 2πr
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.
What is a radius?
A radius is a line segment drawn from the center point of a circle to the edge of the circle.
All the radii of a circle have the {…} since all points on the circle are the {…} from the center point.
Length. Same distance.
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.
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.
Formula for area of a circle?
Formula for area of a circle is A= πr^2
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.
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.
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.
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.
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.
What is an inscribed angle?
An inscribed angle is an angle created by two cords that meet on one end to form a vertex.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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