Praxis 5003: Mathematics

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partial differences method

first we operate on each column individually, being careful to record a sign of each result. Then we sum the results to yield the final answer

constant

fixed numbers (ex. in 7x + 20y + 3, 3 is a constant as are 20 and 7.)

ray

has exactly one end point. Extends indefinitely in one direction

perpendicular

if two lines intersect at exactly one point and create right angles

variables

in algebraic expression these stand for unknown numbers

addition

indicated by the expressions: sum, greater than, and, more than, increased by, added to, entire, total

point

indicates place or position. Has no length, width or thickness. An infinite number of lines can be drawn through one point.

rational numbers

integers, fractions, mixed numbers,and both terminating and repeating decimals.

angle

intersection of two rays.

multiplication

is shown by: product, times, multiplied by, twice *may include each or per hour

division

is used for: quotient, divided by, ratio *may include each or per hour

rounding

it's important to look at the number in the next smaller place. If this number is 5 or more, the number in the place we're rounding is increased by 1 and all other numbers are changed to 0. If it's less than 5 the number we're looking at stays the same and everything to the right is changed to 0.

line segment

line that has two end points

plane

set of points composing a flat surface. No boundaries.

Place value chart

a way to make sure digits are in the right place

polygon

simple, closed, two-dimensional figures composed of line segments and are named according to the number of sides they have

base ten

standard system. Each place represents ten times the value of the place to its right.

estimation

A way of making sure your answer is reasonable, rounding is a commonly used strategy (aka approximation)

straight angle

measures 180 degrees

rectangle

parallelogram that contains a right angle

rhombus

parallelogram with all sides of equal length

terms

parts of the expression separated by + or -

factors

parts that are multiplied together (ex 7x has the factors of 7 and x)

subtraction

can be expressed by: difference, fewer than, minus, less than, decreased by

triangle

polygon with 3 sides

linear algebraic expressions

1. remove parentheses and identify terms 2. group like terms together 3. add the like terms

steps to solving a word problem

1. restate the problem 2. write an equation 3. solve

find the difference of 152.3 and 36.342

115.958

find the product of 3.52 and 4.1

14.432

find the sum of 152.3 and 36.342

188.642

3(4x + 2)

3(4x) + 3(2)= 12x + 6

find the quotient of 5.3 divided by 1.45

3.7

factor 30 into prime factors

30= 5 x 6= 5 x 3 x 2 or 30= 3 x 10= 3 x 2 x 5

At his job, John gets paid $20 for every hour he works. If John made $940 in a week, how many hours did he work?

940/20=47

(2x + 3) + (3x -2)

=2x + 3 + 3x - 2 =2x + 3x + 3 - 2 =5x + 1

associative property

Changing the grouping of numbers will NOT change the value. For example: (7 + 4) + 8 = 7 + (4 + 8) also works with multiplication

T/F some rectangles are trapezoids.

False. Trapezoids only have one pair of parallel sides.

column addition method

First we add the digits in each column, then we perform the place caries from right to left.

partial sums method

First we sum the columns from left to right, then we add the column values.

common denominator

For two or more fractions, a common denominator is a common multiple of the denominators

congruent

Having the same size and shape

remainder

If a divisor does not divide evenly into a dividend we express the leftover amount as this. Usually indicated a fractional answer.

unit rate

a ratio where the second term is one (ex $4/pound)

linear relationship

a relationship in which a fixed change in one quantity results in a fixed change in another quantity.

cone

a space figure having a circular base and a single vertex.

sphere

a space figure having all it's points the same distance from the center

pyramid

a space figure with a square base and 4 triangle shaped sides

commutative property

The property that says that two or more numbers can be added or multiplied in any order without changing the result.

identity property

The property that states that the product/sum of 1/0 and any number is that number

supplementary angles

Two angles whose sum is 180 degrees

the ski club has 85 members; 80% o the members are able to attend the meeting. How many members attend the meeting

What is 80% of 85? n=0.8 x 85 n=68

inverse property

a number that when added to another number results in 0, or that when multiplied by another number results in 1.

distributive property

a property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses, such as a(b + c) = ab + ac

percent

a ratio where the second term is 100

ratio

comparison of two numbers

proportions

comparison of two ratios

line

considered a set of points. May be straight or curved, but commonly this term refers to straight lines. Extends indefinitely in both directions

coeficients

constant factors that multiply a variable (ex. in 7X + 20y + 3, 20 is the coefficient of y and 7 is the coefficient of x)

converting a percent to a decimal

divide by 100 or merely moving the decimal point two places to the left

powers of 10

each digit to the left of the decimal point increases progressively in powers of ten. Each digit to the right decreases progressively in powers of ten.

expression

encompasses only part of an idea similar to a phrase in the English language. (ex. 7 added to a number or n+7)

recurrence relation

equation that defines a sequence recursively. Each term of the sequence is defined as a function of the preceding terms.

equation

expresses a complete idea and is equivalent to an English sentence. (ex. 7 added to a number is 28 less than the number or n+7=n-28)

T/F all parallelograms are rectangles.

false. Some parallelograms are rectangles.

right angle

measures 90 degrees

acute angle

measures more than 0 degrees but less than 90 degrees

reflexive angle

measures more than 180 degrees and less than 360 degrees

obtuse angle

measures more than 90 degrees but less than 180 degrees.

algorithms

methods or strategies for solving problems

PEMDAS

mnemonic to remember order of operations. Parentheses, exponents, multiply, divide, add, subtract

converting a decimal to a percent

multiply by 100 or merely moving the decimal point two places to the right

prime numbers

numbers whose only factors are 1 and the number itself

place value system

one in which the position of a digit in a number determines its value

quadrilateral

polygon with 4 sides

trapezoid

quadrilateral with exactly one pair of parallel sides

parallelogram

quadrilateral with two pairs of parallel sides

square

rectangle with all sides of equal length

properties

rules that apply for addition, subtraction, multiplication, or division of real numbers.

same change rule

takes advantage of the fact that subtraction is easier if the smaller number ends in zero. Thus, we change each number by the same amount to produce a smaller number ending in zero. (ex 335-78 becomes 337-80)

graphing a linear inequality

the dot will be hollow if the inequality sign is < or >. If the inequality sign is ≥ or ≤ the dot on the graph will be solid. The arrow goes the direction the inequality sign points.

Greatest Common Factor (GCF)

the largest number that is a factor of all the numbers given in a problem.

isosceles trapezoid

the non parallel sides of this trapezoid are congruent

Least Common Multiple (LCM)

the smallest number that all of the given numbers will divide into.

short method

traditional method of multiplication. We decompose only the 2nd term. (ex 84x26 becomes 84x20 and 84x6)

right to left addition

traditional method. We sum the columns from right to left, performing carries mentally or writing them down.

acute triangle

triangle that has exactly 3 acute angles

isosceles triangle

triangle with 2 sides measuring the same length

equilateral triangle

triangle with all 3 sides measuring the same length

scalene triangle

triangle with no sides measuring the same length

obtuse triangle

triangle with one obtuse angle

right triangle

triangle with one right angle

T/F all rectangles are parallelograms

true

T/F all squares are rhombuses.

true

cylinder

two congruent circular bases that are parallel

parallel

two lines in the same plane that do not intersect.

partial products method

we decompose each term into base-ten form, and multiply each pair of terms.

left to right subtraction

we decompose the second number into smaller values and perform the individual subtractions. (ex. to solve 335-78 we break 78 down into 70+8)

partial quotients method

we make note of two simple products and estimate our way toward a final answer.

composite numbers

whole numbers that have more than 2 different factors

evaluate x + 5 for x=3

x + 5 = 3 + 5 = 8


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