Praxis 5003: Mathematics
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
