GRE Math Section

Which of the following is an example of the associative property?

(34 + 7) + 11 = 34 + (7 + 11).

How would you factor this polynomial: 4x^2 - 35x + 24?

(4x - 3)(x - 8).

Surface Area of a Sphere

4π times the radius squared.

83.33

5/6

Quantity A: length of the hypotenuse of a right triangle Quantity B: length of one of the legs of the same right triangle (A) Quantity A is greater than Quantity B. (B) Quantity B is greater than Quantity A. (C) Quantity A and Quantity B are equal. (D) There is not enough information to make a determination.

A

Variable

A letter that represents an unknown number. What you solve for in a linear equation.

Sector

A portion of the area of a circle. The degree measure of a sector is the same as its central angle and twice its inscribed angle.

Arc

A portion of the circumference of a circle.

prime numbers

A positive integer that has exactly two positive factors, 1 and itself.//The list of prime numbers in the set of numbers from 1-60 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59.

composite numbers?

A positive integer that has more than two factors.//The list of composite numbers in the set of numbers from 2-60 are all numbers except the prime numbers listed above.

Function

A rule that turns each member of one set into a member of another set (usually numbers, but can be variables).

X -Coordinate

A value that specifies how far left or right a point is from the origin, listed first in the designation of the point's location.

Y -Coordinate

A value that specifies how far up or down a point is from the origin, listed second in the designation of the point's location.

irrational numbers

All numbers that can be expressed as decimals that never repeat and never terminate.//Pi (3.14159265...) is the most well-known irrational number.

integers

All whole numbers plus zero and negative numbers.//...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...

Slope

Also known as rise over run, designates how much a line rises (the change in the y -coordinates) divided by how much it runs (the change in the x -coordinates). A line with a positive slope slants upward from left to right; one with a negative slope slants downward from left to right; horizontal lines have a slope of 0; and vertical lines have an undefined slope.

Inscribed Angle

An angle with endpoints and its center on the circumference of the circle. The degree measure of an inscribed angle is half the degree measure of its intercepted arc.

Central Angle

An angle with endpoints on the circumference of the circle and its center at the center of the circle. The degree measure of a central angle is the same as the degree measure of its intercepted arc.

inequality

An expression where one value is greater or less than, rather than exclusively equal to, another.

Right Angles

Angles measuring 90 degrees that are formed by the intersection of perpendicular lines.

Supplementary Angles

Angles next to each other when two lines intersect that together add up to 180 degrees.

Same-Side Interior Angles

Angles on the same side of a transversal on the interior of two parallel lines that together add up to 180 degrees.

Vertical Angles

Angles opposite each other when two lines intersect that have congruent (equal) values.

Complementary Angles

Angles that together form a 90-degree (right) angle.

Corresponding Angles

Angles with equal measurements because they hold the same relative positions along parallel lines and a transversal.

Circumference of a Circle

Either twice the length of the radius (r) times π or the length of the diameter times π.

Area of a Trapezoid

Half of the height times the sum of the top base (b1) and the bottom base (b2).

Area of a Triangle

Half of the product of the base and height.

linear equations

Has an unknown variable that contains no exponent greater than 1. The variable is what you solve for.

In the equation of a line (y = mx + b), what variable represents the y-intercept value?

b

What is the domain and range of a straight line with a negative slope that contains the point (1,1)?

domain and range are all real numbers

What does a line with positive slope look like on the coordinate plane?

slants upward from left to right

What do variables represent?

unknown values

Y -Intercept

Point where a line crosses the y -axis.

whole numbers? ex?

Positive numbers that aren't fractions.//1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on

what are the three rules to division?

1. If the numbers in a division problem have the same sign, the answer (or quotient) is always positive. If the signs are different, the answer is negative. 2. If you're ever asked to divide a number by zero (or find how many zeros are contained in a number), your answer will always be undefined . If you try this calculation on the calculator, it comes up with an ERROR message. 3. 0 divided by any number equals 0.

what are the 5 multiplication rules?

1. The product of any number and zero is always zero. 2. If the numbers being multiplied have the same sign, the answer is always positive. 3. If the numbers have different signs, then the answer is always negative. 4. When you're multiplying an odd number of negative numbers, the answer will be negative. 5. When you're multiplying an even number of negative numbers, the product is positive because all of the negative numbers are paired up.

50

1/2

33.33

1/3

25

1/4

20

1/5

16.66

1/6

12.5

1/8

What is the equation you would set up for the following: Twenty-five less than ten times a number is equal to forty-five?

10x - 25 = 45.

What is the surface area of a rectangular prism with a length of 8, a width of 4, and a height of 2?

112

Which of the following must be an isosceles triangle?

2 sides with equal length

66.66

2/3

40

2/5

What is the value of x when x is a prime number that is half the product of two consecutive prime numbers?

3

75

3/4

60

3/5

Perimeter of a Square

4 times the length of one of the sides (s).

80

4/5

rational numbers

Integers plus fractions and decimals that end or repeat.// -1, -0.5, 0, 0.5, 1, 1.25, 1.333333..., 1.5, 2, 2 1/2

the absolute value of a number?

Is its distance from 0 on a number line. Since distance is always positive, the absolute value will always be positive. You show absolute value by enclosing a number between two straight lines, like this: |4|.

45-45-90 Triangle

Isosceles right triangle with angles measuring 45, 45, and 90 degrees with a side length ratio of s : s : s √2 where s is the leg length.

If one of the values in a quantitative comparison question was x0, you'd know what about that value?

It is equal to 1.

Jack and Jill cleaned up the yard of Mother Hubbard, and Miss Muffet helped. Hubbard paid Jill $2 more than Muffet and paid Jack twice the $2 that Hubbard paid Muffet. Who of the three was paid the most for cleaning up the yard? Select all such persons. [A] Jack [B] Muffet [C] Jill Muffet = M Jack = 2M Jill = M + 2

Jack and Jill

Central Tendency

Measurement of where the center of a set of values tends to fall.

Finding the circumference of a circle is similar to finding what measurement of a rectangle?

Perimeter.

X -Intercept

Point where a line crosses the x -axis.

in which quadrant on the coordinate plane would a point with the coordinates (-2,3) lie?

Quadrant II

3-4-5 Right Triangle

Right triangle with leg lengths and a hypotenuse in proportionate lengths of 3, 4, and 5.

5-12-13 Right Triangle

Right triangle with leg lengths and a hypotenuse in proportionate lengths of 5, 12, and 13.

Area of a Parallelogram

The base (b) times the height (h).

If a quantitative comparison question gives you only the radius measurement of a circle, which of the following values can you calculate?

The circumference, diameter, and area of the circle.

What does perimeter measure?

The distance around the outside of a two-dimensional object.

Area of a Rectangle

The length (l) times the width (w).

What do you find by using the formula of the Pythagorean theorem?

The length of a hypotenuse of a right triangle when given the lengths of the other two sides.

What is a special characteristic of a 45-45-90 degree triangle?

The length of its sides are in the ratio of 1:1:√2.

You can use the Pythagorean theorem to find which of the following measurements?

The longer leg of a right triangle.

Volume of a Cube

The measure of one of the sides cubed.

Area of a Square

The measure of one of the sides squared.

median?

The middle number in a list of values that are ordered from lowest to highest.

cube root

The number that, when multiplied by itself three times, gives you the original number

Square Roots

The number that, when multiplied by itself, gives you the original number.

Independent Variable (Input)

The number you want to find the function of— x in ƒ( x ).

Origin

The point at which the x -axis and y -axis intersect, known as point (0,0).

Volume of a Cylinder

The product of pi, the square of the radius, and the height

Volume of a Rectangular Prism

The product of the length, width, and height.

Volume of a Sphere

The product of π and the cube of the radius times 4/3.

Area of a Circle

The product of π and the square of the radius.

Dependent Variable (Output)

The result of substituting the independent value into the function (or input)—ƒ( x ).

Quadrant II

The section on the coordinate plane that is left of the y -axis and above the x -axis for which all y -coordinates are positive and all x -coordinates are negative.

Quadrant III

The section on the coordinate plane that is left of the y -axis and below the x -axis for which all coordinates are negative.

Quadrant I

The section on the coordinate plane that is right of the y -axis and above the x -axis for which all coordinates are positive.

Quadrant IV

The section on the coordinate plane that is right of the y -axis and below the x -axis for which all y -coordinates are negative and all x -coordinates are positive

real numbers

The set of all numbers, including rational and irrational numbers.// all of them

Range

The set of all possible values of the dependent variable.

Domain

The set of all possible values of the independent variable.

Surface Area of a Cylinder

The sum of the area of both bases (2pi*r2) and the side (2pi*r*h)

Surface Area of Cubes and Rectangular Prisms

The sum of the areas of each of the six faces.

mean?

The sum of the numbers in a set divided by the number of numbers in that set. Also known as average.

Perimeter of a Rectangle

The sum of twice the width (w) and twice the length (l).

Which two of the following integers have a sum of 125? [A] 32 [B] 47 [C] 78 [D] 83

The two numbers that add up to 125 are 47 and 78. No other combination of numbers results in a sum of 125. So you'd click on the boxes next to choices B and C.

Mode?

The value that occurs most often in a set.

30-60-90 Triangle

Triangle with angles measuring 30, 60, and 90 degrees with a side length ratio of s : s √3 : 2 s where s is the shortest side.

What do the terms in a polynomial consist of?

Variables and coefficients.

Substitution

When you replace a variable with a known value or expression to solve an equation.

Which of the following lines or curves on the coordinate plane would pass the vertical line test?

a line with a slope of 0