Math ACT PREP

Chord

A Chord joins any two points on a Circle. It cuts across the circle. Note that the diameter is the longest Chord.

Trapezoid

A Quadrilateral with exactly two parallel sides, called bases.

Parabola

A U-shaped graph that has an equation with an x^2. For example y=x^2-4x+7.

Binomial

A binomial is a Polynomial with 2 terms.

Coefficient

A coefficient is the number in front of an x term, such as the 3 and 6 in "3x^2-6x". Coefficients can be negative.

Vertex

A corner of a shape.

Pentagon

A five sided polygon.

Quadrilateral

A four sided polygon.

Function

A function looks like f(x)=2x^2-1. The "f(x)" part is read, "f of x" and means "a function of x", not f times x. On the ACT, you should replace "f(x)" with y to change the function into a regular equation: y=2x^2-1

Transversal

A line that intersects two or more other lines. The other lines are often (but not always) parallel.

Prime

A number is Prime if it has exactly 2 factors: 1 and the number itself. For example, 7 is Prime because its factors are 1 and 7, but 9 is not Prime because its factors are 1,3,and 9. Not 0 and 1 are not Prime.

Complex Numbers

A number such as 3-4i that is made of a Real Number, in this case 3, and an Imaginary Number, in this case 4i.

Imaginary Numbers

A number that includes i. Imaginary Numbers are square roots of negative numbers. They also make up part of a complex number.

Polynomial

A polynomial has terms with x,x^2,x^3.

Rhombus

A quadrilateral with equal sides.

Polygon

A shape, like a rectangle or pentagon. They are named according to the number of sides they have. A triangle has 3, a quadrilateral has 4, a pentagon has 5, a hexagon has 6...

Hexagon

A six sided polygon.

Scalene

A triangle with all different sides and angles.

Isosceles

A triangle with at least two sides and two angles congruent. Note that isosceles triangles can be acute, right or obtuse.

Range

All of the possible Y values of a graph.

Domain

All of the possible x values of a graph.

Equilateral

All sides are equal. Equilateral usually refers to a triangle in which all three sides are equal and all three angles are 60 degrees.

Radians

Angles can be measured in either Degrees or Radians. Make sure you know which one applies and that you have your calculator in the right mode. You should remember this conversion: 180=pieRadians.

Inequalities

Any expression that includes: "<",">"

Integers

Any real number that doesn't have fractions or decimals including 0 and all negative "whole numbers". For example: ...-2,-1,0,1,2...

Bisect

Bisect means cut into two equal segments or angles.

Congruent

Congruent means equal when referring to physical objects. It means they have the same size and shape.

Constant

Constant just means "number". If you see the word "constant" on the ACT, cross it out and write "number"

Digit

Digits are only the numbers 0 to 9, so 4 is a Digit, and 7 is a Digit, but 12 is not a Digit. It is made up of the Digits 1 and 2.

Real Numbers

Every number that does not have i in it.

Reflection

Flipped over.

Surface Area

For a 3-dimensional object, such as a cube, the surface area is the sum of the areas of all of the faces.

Geometric Sequence

In a geometric sequence each term comes from multiplying the previous term by a fixed number.

Arithmetic Sequence

In an arithmetic sequence each term comes from adding a fixed number to the previous term by.

Equidistant

Just means the same distance away. On a circle, all points are Equidistant from its center.

Parallel

Lines that don't intersect because they have the same slope.

Perpendicular

Lines that have slopes that are negative reciprocals of each other.

Adjacent

Means next to.

Consecutive

One after the other, like 3,4,5... you can also have consecutive even integers (2,4,6...) or consecutive odd integers (11,13,15...)

Arc

Part of the circumference made by a wedge of a circle.

Probability

Probability is a fraction with the number of successful ways on top and total number of ways on the bottom.

Slope

Remember that the Slope of a Line is "Rise over Run".

Equivalent

The ACT likes to ask what an Expression is Equivalent to. When they ask this, they just want you to simplify or evaluate it.

Expression

The ACT refers to things like "4x^2y^3" as Expressions. They are just. Pieces of an equation when there is no equal sign. You will usually be asked to simplify or evaluate an expression.

Hypotenuse

The Hypotenuse is the longest side of a Right Triangle (and only a Right Triangle). It is opposite the Right Angle and can be found using a^2+b^2=c^2

Remainder

The amount left over when you divide, but the number doesn't go in evenly.

Straight Angle

The angle formed by a straight line. It has a measure of 180. When two angles combine to form a Straight Angle they are Supplementary.

Exterior Angle

The angle formed by extending one of the sides of a polygon.

Interior Angle

The angles on the inside of a polygon.

Period

The distance a wave travels before it repeats its pattern.

Diameter

The distance across a circle through its center. It is also twice the radius.

Circumference

The distance around the circle. Equivalent to the perimeter of a circle. The circumference is given by c= 2pier where r is the radius.

Perimeter

The distance around the outside of a shape. You calculate the perimeter by adding up the length of each side. Don't confuse the perimeter with the area.

Radius

The distance from any point on the circle to the center.

Directly Proportional

The equation for Directly Proportional is Y=kx, where k is a constant.

Altitude

The height of a triangle that makes a 90-degree angle with the base of the triangle.

Maximum

The highest y value of a graph.

Diagonal

The line between non-consecutive corners in a polygon.

Minimum

The lowest y value of a graph.

Median

The middle number when the numbers are in order. For example, 4 is the median of: 2,2,3,4,5,5,6, because it is the middle number.

Mode

The most frequently listed number. For example, 6 is the mode of: 3,3,4,4,5,6,6,6,6 because it is the number that shows up most often. Note that it does not have to be in the middle.

Origin

The point (0,0), which is usually marked with "O"

Midpoint

The point exactly halfway between two other points.

Sum

The result when you add numbers. For example, the sum of 5 and 7 is 12.

Quotient

The result when you divide numbers.

Product

The result when you multiply numbers.

Difference

The result when you subtract numbers. The difference between 7 and 4 is 3. Just remember "difference means subtraction"

Symmetric

The same on one side as it is on the other.

Quadrant

The x-axis and y-axis divide the xy-plane into 4 parts, called Quadrants.

Translate/Translation

To move a line segment or entire graph horizontally or vertically without rotating it.

Acute

When referring to an angle acute means less than 90 degrees. When referring to a truangle, acute means that all angles are less then 90 degrees.

Obtuse

When referring to an angle obtuse means greater than 90 degrees. When referring to a triangle, obtuse means that one angle is greater than 90 degrees.

Right

When referring to an angle right means 90 degrees. When referring to a triangle, right means that one angle is 90 degrees.

Ratio

You probably learned Ratio as two numbers with a colon between them, such as 4:7. However on the ACT it is helpful to think of a Ratio as a fraction, such as 4/7.