Math Praxis 7003
Percent of a number
1. Change percent to a decimal 2. Multiply decimal times number
Area of a rectangle 1
A = l*w
Line
A collection of points that extends forever in both directions. Use any two points on a line to name it. Line AB <---->
origin
A fixed point from which coordinates are measured. (0,0)
algebraic expression
A mathematical phrase involving at least one variable and sometimes numbers and operation symbols.
Prime numbers
A positive integer that only has 1 and itself as factors.
unit rate
A rate with a denominator of 1.
Rotation
A rotation spins or rotates a figure about a point or line. A rotated figure will be in a different place and will have a different orientation.
acute triangle
A triangle that contains only angles that are less than 90 degrees.
right triangle
A triangle with one angle equal to 90 degrees.
obtuse triangle
A triangle with one angle that is greater than 90 degrees.
area of a rectangle with sides doubled
A= 2l *2w =2^2(l*w)
Area of a triangle
A=1/2bh The base and height are always perpendicular to one another, so a dotted line is added to show the height for different types of triangles.
Area of a trapezoid
A=1/2h(b1+b2) Because a trapezoid can have either base at the bottom, the base lengths are averaged, then multiplied by the height (h).
Area of a rectangle
A=bh The base (b) and height (h) are always perpendicular to one another for all figures.
Area of a parallelogram
A=bh The base (b) and height (h) are always perpendicular to one another, so a dotted line is added to show the height.
Area of a circle
A=πr² The area of a circle uses the radius, which is the length from the center of the circle to a point on the circle.
Cube
All sides of a cube are squares all sides have the same length all angles equal
Reflection
Another term for a reflection is flip or mirror image. Reflections "flip" an image over a line or axis. Each vertex point of the new figure will be the exact same distance from the line as the original image, in the direction of the reflection. You may have to be able to identify the axis over which the reflection occurred. The axis that the figures are on either side of will be the axis over which the figure was reflected.
Translation
Another term for translation is slide. A translation changes the position of an image by moving it left, right, up. or down. The figure will look exactly the same but in a different place.
expanded form
Another way to teach place value is by writing numbers in expanded form. A number in expanded form is written in such a way that the place value of each number is represented as part of a sum.
Rational Numbers
Any number that can be expressed as a fraction. include all terminating and repeating decimals.
Circumference of a circle
C= 2πr = πd The circumference measures the distance around the outside of a circle.
Circle
Diameter goes through the center of the circle to the edge of the circle. Radius starts at the center of the circle and ends on the edge of the circle. The radius is half the length of the diameter.
Test tip p.195
Exam items may ask you to describe or manipulate a number or the place value of a number in terms of multiplication or division by 10 or a power of 10.
Pythagorean Theorem
If two sides of a right triangle are given, the Pythagorean theorem is a way to find the third side. a^2 + b^2 =c^2 where a and b represents the lengths of the legs (two sides that make the right angle) of the triangle and c represents the length of the hypotenuse.
multistep linear equations
Isolate the variable using inverse operations, remembering what is done to one side has to be done to the other to keep the expressions equal. The steps that follow outline one way to approach multistep equation. 1. Distribute any numbers outside of parentheses on both sides of the equation, if necessary. 2.Combine like terms on the same side of the equal sign. 3. Move variables to one side of the equation using inverse operations (add or subtract). 4.Isolate the variable term using inverse operations (add or subtract). 5. Divide both sides by the coefficient with the variable. 6. Look out for no solution or infinitely many solutions. When an equation has no solutions or infinitely many solutions, the variable, the variable terms are eliminated when moved to one side. This leaves only numbers on both sides of the equations. No solution: Equation in the form a=b Example: 2=3 ; because 2 does not equal 3, there are no solutions Infinitely Many Solutions: Equation in the form a=a Example: 2=2; because 2 equals 2 , any solution will work for the equation, so there are inf. many solutions.
Manipulatives (physical models)
It is important to understand how manipulatives are used to represent counting, patterns, operations, physical attributes of geometric figures, and formulas, and formulas. Its not enough to know that snap cubes exist; you also need to be aware of how they are used.
Test tip 3 p. 212
Know what the "set up" of problems look like. You may be required to identify expressions or problems that could be used to find the percent of a number, the unit rate, the total cost, etc. Remember, there is more than one way to write expressions, so your answer may not match exactly to answer choices listed in a question.
Opposites and reciprocals
Make sure you understand that the opposite of a number is the same number with a different sign, so the opposite of 5 is -5 and the opposite of -2 is 2. Important facts about opposites include: - The sum of a number and its opposite equals 0. for example 5 +(-5)= 0 - Zero does NOT have an opposite. In addition to opposites, know that the multiplicative inverse, or reciprocal, of a number is what the number is multiplied by to get 1. To find a reciprocal, write the number as a fraction, if it is not already a fraction, then flip the fraction. For ex. to find the multiplicative inverse of 3, write it as a fraction, 3/1, then flip the fraction to 1/3. Thus, the multiplicative inverse of 3 is 1/3 because 3(1/3) = 1. Important facts about multiplicative inverses includes: - The product of a number and its reciprocal is 1. - Zero does NOT have a reciprocal.
Test Tip 2
Memorize the decimal values of common fractions. You have access to a scientific calculator, but your time is limited. Knowing the decimal conversions for thirds, fourths, fifths, eighths, and ninths will save you valuable time. You will encounter several of these fractions that need converting on the praxis exam.
number theory
Numbers are classified into various groups based on their properties. Notice that for each of the types of numbers defined in the table that follows, the numbers continue forever, hence the, ".." at the end. The arrows at the end of the number line represent the concept of the numbers continuing forever. Numbers in the Real Number System that are addressed at various stages in grades K-6 are classified further into the groups shown in the table.
Triangles
One of the most important facts to remember about a triangle is that the sum of the measures of the angles inside a triangle is 180 degrees. Often Praxis exam items give only one or two angles, and the third is needed in order to solve the problem. Additional triangle facts that you should know include classifying triangles by sides and angles.
PEMDAS "Order of Operations"
Please Excuse My Dear Aunt Sally (Parenthesis, Exponents, Multiply, Divide, Add, Subtract); order in which an equation is worked out - multiplication and division as well as adding and subtracting can be interchanged, depending on which comes first (from left to right) in the equation. - On the praxis exam, you will be expected to recognize order of operations in various problems. When solving all problems, pay close attention to the order in which you are solving.
Percent of change (increase/decrease)
Questions that require finding the percent of increase or decrease will either ask for the percent of increase/ decrease or the percent of change. To find the percent of change, begin by finding the following fraction new number - original number / original number Next convert the fraction to a decimal, and then convert the decimal to a percent. If the percent is positive, the percent of change was an increase. If the percent is negative, the percent of change was a decrease. The negative sign is not included in the answer of a percent decrease. It is instead denoted with the word decrease.
Perimeter of a rectangle or square
Rectangle: P= b+h+b+h= 2b+2h Square: P=4s Add all of the sides of the figure for both the rectangle and the square.
Test tip 2
Test questions may have numeric expressions with numbers written in a form which typically would not be used to test your knowledge of equivalent forms.
Vocabulary Lookout 1
Test questions may use terms that are part of a basic operation problem. Know what each of these terms mean. Vocabulary terms used most often include: - added -sum -difference -product -quotient
greatest common factor (GCF)
The greatest number that is a factor of two or more given numbers.
Quick tip p.247
The hypotenuse of a right triangle is always the longest side of the triangle.
Number representation
The same number can be written several ways. Be prepared to know how to write a number in different forms and to recognize equivalent forms of the same number. Also, be prepared to compare numbers written in different forms.
least common multiple (LCM)
The smallest multiple (other than zero) that two or more numbers have in common.
place value
The value of each digit in a number based on the location of the digit.
Writing an equation (function rule) from a table
To write an equation of a line, or a function rule, from a table, it is easiest to use slope-intercept form, y=mx+b, where m represents the slope and b represents the y-intercept. When writing an equation given a table, two different scenarios may occur, one where the y-intercept is part of the table, & one where it is not. In both cases, find the slope of the line, then determine the y-intercept based on the information given.
Quadrant I
Top right quadrant (+,+)
Transformations
Transformations change the location or size of a figure. Types of transformations you will see on the exam include translations, rotations, rotations, and reflections. Translations, rotations, and reflections create a new image that is congruent to, or the same size as, the original image. Transformations are typically performed on a coordinate plane so that the exact changes are reflected in the coordinates of the vertices of the image.
Parallel Lines
Two lines in the same plane that are exactly the same distance apart. Parallel lines will never intersect at given point. Lines may also be named using a lower case letter.
perpendicular lines
Two lines in the same plane that intersect at a 90 degree angle. perpendicular lines AB and CD.
Quick tip p.235
Use an open circle for less than or greater than (< or>). Use a closed circle for less than or equal to or greater than or equal to.
Snap cubes
Used to teach number sense, counting, place value, and addition and subtraction. - are also useful for demonstrating concrete representations of the base 10 system.
Volume of a rectangular solid with sides doubled
V= 2l * 2w * 2h = 2^3(l*w*h)
Area of a Rectangular Solid with sides doubled
V= 2l * 2w *2h = 2^3 (l*w*h)
Area of a Rectangular Solid
V= l*w*h
Volume of a sphere
V=4/3πr³ Multiply r ^3 times 4 and pi, if not in terms of pi, then divide this answer by 3.
Volume of a rectangular solid
V=l*w*h
Percent of total
When a question asks what percent a situation represents, this requires writing numbers as a fraction, converting the numbers to decimals, and then converting the decimal to a percent.
Quick tip p.258
When converting feet to inches in geometry word problems, always convert before finding the area.
Operations and properties of rational numbers
When learning to add and subtract in kindergarten through second grade, students learn to approach a problem from different points of view. Various points of view help students understand operations and number facts and prepare them for solving for an unknown value in later grades.
Test tip p.240
When looking for a pattern, it is helpful to create a table to organize your information, especially if the problem asks for an answer that requires finding three or more items in the sequence.
scientific notation
When numbers are very large or very small, they are often written in scientific notation. is a number greater than or equal to 1 and less than 10 multiplied by the power of 10. When a number is written in scientific notation, the number multiplied by the power of 10 must have 1 number in front of the decimal point.
Test tip p.226
When the phrases less than or fewer than are in a math sentence, the numbers in the sentence will be "flipped." Example: 5 less than 10 is written 10-5.
Remember p. 261
When the sides of a figure change by a factor it means you are multiplying each side by the same number. Thus, the following rules apply: The area is multiplied twice by that number. The volume is multiplied three times by that number.
Remember p.261
When the sides of a figure change by a factor it means you are multiplying each side by the same number. Thus, the following rules apply: The area is multiplied twice by that number. The volume is multiplied three times by that number.
Test tip p. 241
You can also substitute points from the table into the equations that are listed as answer choices. When doing this, make sure at least two different points from the table satisfy the equation.
Unit Fractions
a fraction where the numerator is 1.
Geometric Sequences
a list of values where the difference between one term and the next term is always a multiple of the same value. This value is called the common ration. For example. given the sequence 1,2,3,4,8... the common ratio is 2 because we are multiplying each previous term by 2 to get the next number in the list. You do NOT need to know the technical terms or vocabulary associated with sequences. You only need to identify the common difference or ratio and apply it to find additional numbers in the sequence.
Arithmetic Sequences
a list of values where the difference between one term and the next term is always the same value. This value is called the common difference. Example: given the sequence 2,5,8,11,... the common difference is 3 because 3 is the difference between each value. To continue the pattern, 3 is added to each of the previous terms to get the next term.
Base 10 Number System
a number system in which all numbers are expressed using the digits 0-9
odd
a number that is not divisble by 2
Line Segment
a part of a line that has two endpoints. Use each endpoint to name the line segment. a ------ b
composite
a positive integer that has factors other than 1 and itself.
Equilateral
a triangle with all sides congruent. Angles in an equilateral triangle are all congruent , equal to 60 degrees.
isosceles triangle
a triangle with at least two congruent sides. Angles opposite the congruent sides are also congruent.
Scalene
a triangle with no congruent sides
independent variable
a variable (often denoted by x ) whose variation does not depend on that of another.
dependent variable
a variable (often denoted by y ) whose value depends on that of another.
Commutative Property of Addition
a+b=b+a Changing the order of two numbers being added does not change their sum.
Commutative Property of Multiplication
ab=ba Changing the order of the factors does not change the product.
rectangle
all angles are right angles. opposite sides have the same length A special type of parallelogram Opposite sides parallel 4 sides
Square
all sides equal All sides have the same length A special type of parallelogram A special type of rectangle opposite sides are parallel 4 sides
polynomials
an expression that does not have a variable in the denominator of a fraction.
Pythagorean triples
are whole numbers that satisfy the Pythagorean theorem. Memorizing Pythagorean triples is an effective test-taking strategy because they are often embedded in exam items or are the answer to an exam question. Although other Pythagorean triples exist, the following list appears most often on exams. 3-4-5 6-8-10 5-12-13 The longest side will always be the hypotenuse.
decomposing fractions
breaking a fraction into parts.
even
divisible by 2
Ray
has one endpoint and extends indefinitely in one direction. Use the endpoint first and then any other point on the ray to name it. ----> Ray AB
Rounding
in addition to being able to compose and decompose numbers, you will be expected to round a given place value. Questions involving rounding will require you to know place values. To round, look at the number to the right of the place value to which you are rounding. If the number to the roght is between 0 and 4, the number does not change. If the number to the right is between 5 and 9 , the place value to which you are rounding is rounded up 1.
ratio
is a comparison of two numbers using a fraction, a colon, or the word to. They have the same units. When rations have different units, they are referred to as a rate.
Cardinal number
is a number that says how many of something they are. they are used for counting.
Ordinal number
is a number that tells the position of something in a list. These numbers are used specifically when referring to the order of an object.
sphere
perfectly symmetrical Radius starts at the center and ends at any point on the sphere The distance around a sphere is the circumstance of a circle.
prime factorization
refers to finding all the prime numbers, when multiplied together, result in a composite number. For example, the prime factorization of 24 is 2*2*2*3 or 2^3*3. A common method for finding the prime factorization of a number is using factor trees.
x-axis
the horizontal axis on a coordinate plane
Quadrant II
the top left quadrant in the coordinate plane with ordered pairs (-,+)
y-axis
the vertical axis on a coordinate plane
supplementary angles
two angles that add up to 180 degrees
complementary angles
two angles that add up to 90 degrees.
compound linear inequalities
two simple inequalities joined together by the word "and" or "or". The solution set of inequalities joined by the word "and" is the intersection of the two inequalities, making solutions between the two solution values. Typically, "and" inequalities are written as a single math sentence with less than/ greater than or equal to symbols as shown in the table that follows.
Nets
two- dimensional shape when a three-dimensional figure is opened and laid flat; think of a net as the pattern for the three-dimensional figure. Nets are useful when teaching surface area and characteristics of three-dimensional figures. To determine the name of a three-dimensional figure, use the following tips: A prism will have two bases. All other shapes are the sides of the prism. A pyramid will have one base. All other shapes are the sides of the pyramid. The Shape of the base is used to name the prism or pyramid.
y-intercept
where the line crosses the y axis. Rise /Run
slope formula
y2-y1/x2-x1
