Praxis 5003 (Mathematics) Flashcards
Cardinal numbers
whole numbers (1, 2, 3, 4, etc.)
Ordinal numbers
Placement values (1st, 2nd, 3rd, 4th, etc)
Expanded form
written so that the place value of each number is represented as part of a sum (532 = 500 + 30 + 2)
Expanded Notation
each digit is written as the product of its place value
(532 = (5x100)+(3x10)+(2x1))
Order of Operations
Parentheses
Exponent
Multiplication
Division
Addition
Subtraction
What happens when reciprocals are multiplied
they equal 1 (3/1 x 1/3 = 1)
Percent Change Equation
(new number - original number) / Original number
Prime Factorization
finding all the prime numbers (tree style)
Greatest Common Factor
the largest number that divides into all numbers in a given set
Least Common Multiple
find each prime factor in both numbers. Then multiply each prime factor the greatest number of times it occurs in one number between the numbers
Estimating using compatible numbers
estimating by rounding numbers to numbers that are easy to add, subtract, multiply, or divide (31.8 / 5/2 –> 30 / 5)
Estimating using clustering
estimating sums or products when all the numbers are close to a single value (42+38+40+41 –> 40+40+40+40)
Front-end Estimation
estimating by rounding to the greatest place value or the number is front (412+58+1780 –> 400+60+2000)
Algebraic expressions - terms
an expression is segmented by + or - signs (2+4 = 2 terms)
(5a-2+6b = 3 terms)
(a^2 x 5^b x c^3 = 1 term)
Name by term number
1 - Monomial
2 - Binomial
3- Trinomial
Degree of polynomial
the largest sum of exponents in ONE term
(3 x a^2 x b^3 = 5)
(X^2 + 7 = 2)
Rule for dividing a negative number when solving inequalities
You have to flip the sign in the inequality when solving due to
How to solve compound inequalities
Solve each inequality separately
Slope Intercept Equation
y=mx+b
(m = slope)
(b = y-intercept)
How to find slope when using points on a graph
Use any 2 points and stack them vertically then subtract then use the difference
(-1, 3) change in y 2
- (0, 1) change in x -1
———-
(-1, 2) 2/-1 = -2
Complementary Angles
angles that add up to 90°
How to find y-intercept
find the slope then choose a point (x, y) and then plug these into y=mx+b and solve for b
Supplementary Angles
angles that add up to 180°
scalene triangle
triangle with no congruent sides
isosceles triangle
triangle with 2 congruent sides and angles opposite of congruent sides are also congruent
equilateral triange
all sides are congruent and all angles are 60°
Equation to find sum of angles in shapes
(n-2)x180
n = number of sides
Pythagorean Theorm
can only be used with right triangles
a^2 + b^2 = c^2
Transformations - translation
shapes slide around - changes position by moving up/down/left/right)
Transformation - rotation
spins or rotates a figure about a fixed point or line
Transformation - reflection
aka flip or mirror image - “flip” an image over a line or axis
Circle area
A = π r^2
Volume of a sphere
v = 4/3 π r^3
Volume of a box
v = l w h
circumference
2 π r
Frequency table
counts or tallies how many times a value falls within a defined range of values
Bar graph
track and compare change over time
Histogram
display of information gathered in a frequency table
Stem and Leaf plot
organizes numerical data in a way that allows the reader to quickly calculate the mode and range of a data set
Line graph
shows change over time
scatter plot
contains 2 data sets. Tells if there is a correlation
Probability equation
number of ways an event can happen OVER
total number of events that can happen
