MATH: Early Equations and Expressions, Measurements, and Geometry for Praxis 7813

Perimeter of a rectangle

P = b + h + b + h = 2b + 2h

Perimeter of a square

P = 4s

Area of a rectangle

A = bh

Area of a circle

A = πr²

Area of a triangle

A = 1/2 bh

Area of a trapezoid

A = 1/2 h (b₁ + b₂)

Volume of a sphere

V = 4/3 πr³

Volume of a rectangular prism

V = lwh

Pythagorean Theorem

a² + b² = c²

Three-dimensional figures

Solid shapes that have three dimensions: length, width, and height.

Face

A two-dimensional figure that makes up the side of a three-dimensional figure.

Edge

The intersection where two faces of a three-dimensional figure meet.

Vertices

The corners or points where edges of a three-dimensional figure meet.

Prism

A three-dimensional figure with two identical ends; the shape of the end is part of the name.

Pyramid

A three-dimensional figure with triangular faces that meet at a point.

Base of a pyramid

The side opposite the point in a pyramid.

Base of a prism

Either of the two identical ends in a prism.

Nets

The two-dimensional shape when a three-dimensional figure is opened and laid flat.

Radius

The distance from the center of the circle to the edge.

Diameter

The distance across the circle through the center.

Cube

A three-dimensional shape where all sides are squares and have the same length.

Properties of a rectangle

All angles equal 90°; opposite sides have the same length.

Properties of a square

All angles equal 90°; all sides have the same length.

Triangular Prism

A prism with triangular bases and three rectangular sides.

Hexagonal Prism

A prism with hexagonal bases.

Rectangular Prism

A prism with rectangular bases.

Triangular Pyramid

A pyramid with a triangular base.

Polygon

A plane figure with sides that are connected to form a shape.

Regular Polygon

A polygon with all sides and angles congruent.

Parallelogram

A quadrilateral with opposite sides and opposite angles congruent.

Rhombus

A parallelogram with all sides congruent.

Rectangle

A parallelogram with all angles congruent (90°).

Square

A parallelogram with all sides and all angles congruent.

Trapezoid

A quadrilateral with one pair of parallel sides.

Kite

A quadrilateral with two pairs of adjacent sides congruent.

Quadrants of a Coordinate System

The four sections of the coordinate plane created by the intersection of the horizontal and vertical number lines.

Scalene Triangle

A triangle with no congruent sides and no congruent angles.

Isosceles Triangle

A triangle with two congruent sides and angles opposite the congruent sides also congruent.

Equilateral Triangle

A triangle with all sides congruent and all angles equal to 60°.

Acute Triangle

A triangle with all angle measures less than 90°.

Right Triangle

A triangle with one angle equal to 90°.

Obtuse Triangle

A triangle with one angle greater than 90°.

Transformation

Change in location or size of a figure.

Translation

Moves an image left, right, up, or down.

Rotation

Spins a figure around a point or line.

Reflection

Flips an image over a line or axis.

Congruent

Figures that are the same size and shape.

Coordinate Plane

A two-dimensional plane for graphing points.

Vertices

Corner points of a geometric figure.

Prime Mark

Indicates transformed vertices, e.g., A'.

Axis of Reflection

Line over which a figure is flipped.

Orientation

The direction a figure faces after transformation.

Image

The result of a transformation applied to a figure.

Slide

Another term for translation in geometry.

Mirror Image

Another term for reflection in geometry.

Identifying Transformations

Recognizing types of transformations in problems.

Distance from Axis

Equal distance maintained in reflections.

Test Types

Transformations commonly tested: translations, rotations, reflections.

Mean

Find the average; add all the numbers and divide by how many numbers were added.

Median

Place numbers in ascending order; find the middle number. If there are two middle numbers, add them and divide by 2.

Mode

The number or numbers that occur the most.

Range

Subtract the smallest number in the set from the largest number in the set.

Mean Calculation Example

On a quiz in Mrs. Fingal's class, 8 students scored 70%, 12 students scored 80%, and 4 students scored 95%. What is the mean score for the quiz? Correct answer: A. 79

Partial Sums for Mean

To find the mean of a list that groups values in sets, find the sum of each like group of values, then add the sums together and divide by the total number of values.

Mode Calculation Example

Find the mode of the data: (3, 3, 5, 6, 4, 5, 6, 2, 4, 5, 1, 10). Correct answer: B. 5

Range Calculation Example

Find the range of the data set: {6, 3, 1, 10, 12, 4, 9}. Correct answer: C. 11

Measurement

The measurement portion of the test includes conversions within the U.S. customary system, conversions within the metric system, and an understanding of the relative size of basic measurements.

Metric System

The metric system is based on units of 10.

Metric Conversions

There are two different ways to approach metric conversions: moving the decimal and using a proportion.

Kilo-

Prefix in the metric system representing 1,000.

Centi-

Prefix in the metric system representing 0.01.

Milli-

Prefix in the metric system representing 0.001.

Example Metric Conversion

Complete the following. 4L = 4000 mL. Correct answer: B.

Basic Unit of Length

Meter (m).

Basic Unit of Volume

Liter (L).

Basic Unit of Mass

Gram (g).

Cross-Multiplication in Proportions

Cross-multiply and solve for the unknown in a proportion.

Ascending Order

When finding the median and mode, make sure the data is in ascending order first.

1 foot

12 inches

1 yard

3 feet = 36 inches

1 mile

5,280 feet = 1,760 yards

1 hour

60 minutes

1 minute

60 seconds

1 cup

8 fluid ounces

1 pint

2 cups

1 quart

2 pints

1 gallon

4 quarts

1 pound

16 ounces

1 ton

2,000 pounds

Area of a Circle

A = πr²

Circumference of a Circle

C = πd = 2πr

Surface Area of a Prism

SA = Ph + 2B

Volume of a Prism

V = lwh or V = Bh

Pythagorean Theorem

a² + b² = c²

Approximation of pi

π ≈ 3.14 or 22/7

Conversion from smaller to larger unit

Move the decimal point LEFT the number of spaces between the two units.

Conversion from larger to smaller unit

Move the decimal point RIGHT the number of spaces between the two units.

Finding perimeter of a square

P = 4s, where s is the length of one side.

Example conversion: 4.5 L to KL

Correct response: A. 0.0045 KL

Example conversion: 4 km to mm

Correct response: C. 4,000,000 mm