HSPT Math Review
Inequality
A mathematical sentence that shows the relationship between quantities that are not equivalent. i.e. 5‹8 5b + 2 ≥ 12
INEQUALITY
A mathematical sentence that uses a symbol (<, >, ≤, ≥, ≠) to indicate that the left and right sides of the sentence hold values that are different Ex. The inequality x > 8 has an infinite number of solutions.
Equation
A mathematical sentence that uses an equals (=) sign to indicate that the side to the left of the equals sign has the same value as the side to the right of the equals sign Ex. Theequationx+4=10hasasolutionofx=6
Probability
A number from 0 to 1 that tells how likely an event is to happen. i.e. What is the probability that I will get "heads" when I flip a coin? 1 out of 2, 50%, 0.5, 1:2, 1⁄2
Factor (noun)
A number or symbol that divides evenly into a larger number. For example, 6 is a factor of 24.
Prime Number
A number that can be divided by only itself and one.
Reciprocal
A number that can be multiplied by another number to make 1 (numerator and denominator are switched) Ex. is the reciprocal of because × = 1
Irrational Number
A number that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal. i.e. 4.45683127406792103694396... ∏ = 3.14159265358979323846...
Scientific Notation
A number that is written as the product of a decimal greater than or equal to 1 and less than ten and a power of 10. i.e. Write 6,224,000,000,000 in scientific notation. 6.224 • 1012
Coefficient
A number that multiples a variable
TERM
A number, a variable, or product of a number and a variable(s) Ex. There are 3 terms in the expression: 4x + y + 2
Ordered Pair
A pair of numbers that gives the location of a point in the coordinate plane. Also referred to as the "coordinates" of a point Ex. The ordered pair (3, 2) describes the location that is found by moving 3 units to the right of zero on the x-axis and then 2 units up from the x-axis.
Coordinate Plane
A plane formed by two number lines (the horizontal x-axis and the vertical y-axis) intersecting at their zero points
POWER
A product of equal factors. 4 × 4 × 4 = 43, reads "four to the third power" or "the third power of four." Power and exponent are some× used interchangeably.
Exponent
A raised number that tells the power of the base. i.e. 43 = 4 • 4 • 4 = 64 62 = 6 • 6 = 36
Unit rate
A rate that has a denominator of 1 Ex. The unit rate describing his speed was 14 meters per second.
Percent
A ratio that compares a number to 100 Ex. 25% is a percent that represents ( ).
arithmetic sequence
A sequence where each term is found by adding or subtracting the exact same number to the previous term Ex. 4, 6, 8, 10, 12...is an arithmetic sequence (add 2)
Geometric sequence -
A sequence where each term is found by multiplying or dividing by the exact same number to the previous term Ex. 2, 6, 18, 54, 162...is a geometric sequence (multiply 3)
Sequence
A set of numbers that follow a pattern Ex. 4, 6, 8, 10, 12...is a sequence of numbers.
PROPORTION
A statement (equation) showing two ratios to be equal Ex. = is a proportion.
Constant
A term with no variable part (i.e. a number)
Central Tendency -
An attempt to find the "average" or "central value" of a given set of data. Ex. In statistics, there are three main measures of central tendency: MEAN, MEDIAN, MODE
Proportion
An equation that states that two ratios are equivalent. i.e. 5 = 25 12 60
Rational Number
Any number that can be expressed as a ratio of two integers. i.e. 6 can be expressed as 6, and 0.5 as 1. 12
Grouping Symbols
Ex. (parenthesis), [brackets], {braces}, long division bar
Range
The difference between the greatest data value and the least data value in a data set. i.e. Find the range of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33, 31 The largest data item is 49. The smallest data item is 12. Subtract the two: 49 - 12 = 37. Therefore the range is 37 for this data set.
Absolute Value
The distance a number is from zero on the number line Ex. |-3| = 3; "The absolute value of -3 is 3."
Circumference
The distance around a circle Ex. The circumference of a circle whose radius is 4 inches is: 2π(4) = 8π inches or approximately 25.12 inches.
Perimeter
The distance around the outside of a figure Ex. The perimeter of a rectangle whose length is 18 feet and width is 5 feet is: 18+5+18+5 = 46 feet.
X-axis
The horizontal number line that, together with the y-axis, establishes the coordinate plane
Origin
The intersection of the x-axis and the y-axis on the coordinate plane Ex. The origin is described by the ordered pair (0,0).
Mode
The item or items that appear the most often in a data set. i.e. Find the mode of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33, 31 The # that appears the most is 31.
Greatest Common Factor (GCF)
The largest factor common to two or more numbers.
Median
The middle item in a data set ordered from least to greatest. i.e. Find the median of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33, 31 1. Arrange data from least to greatest 12, 15, 22, 25, 27, 29, 31, 31, 32, 33, 40, 45, 49 2. Find the center # 31
AREA
The number of square units inside a 2-dimensional figure Ex. The area of a rectangle whose length is 18 feet and width is 5 feet is: 18×5 = 90 square feet.
Y-Coordinate
The number that indicates the position of a point above or below the x-axis Ex. The 3 in (4,3) is the y-coordinate, and tells you to move 3 places above the x-axis
X-COORDINATE
The number that indicates the position of a point to the left or right of the y-axis Ex. The 4 in (4,3) is the x-coordinate, and tells you to move 4 places to the right of the y-axis
Order of Operations
The procedure to follow when simplifying a numerical expression 1 - Grouping symbols 2 - Exponents 3 - Multiplication and Division (from left to right) 4 - Addition and Subtraction (from left to right)
Zero Product Property
The product of any number and zero equals zero. i.e. 3•0=0
Multiplicative Inverse
The reciprocal of a number. Any number multiplied by its multiplicative inverse equals 1.
Quotient
The result of division.
DIFFERENCE
The result of subtraction.
Integers
The set of positive whole numbers, negative whole numbers and zero. i.e. ...-4, -3, -2, -1, 0, 1, 2, 3, 4
Least Common Multiple (LCM)
The smallest multiple that is common to two or more numbers.
Lowest Common Denominator (LCD)
The smallest number that can be divided evenly by all denominators in the problem.
Y-axis
The vertical number line that, together with the x-axis, establishes the coordinate plane
Evaluate
To replace variables with numbers and then simplify an expression Ex. To evaluate 4x + 10 when x = 3, replace "x" with 3 and simplify: 4(3)+10=12+10=22
DIAMETER
A chord that passes through the center of the circle R Ex. RS is a diameter
RATIO
A comparison of two quantities by division Ex. The ratio of students to faculty members at a given university is 16:1 (also 16 to 1...or 16/1).
CHORD
A line segment that runs from somewhere on the circle to another place on the circle OA Ex. AB is a chord
RADIUS
A line segment that runs from the center of the circle to somewhere on the circle Ex. OA is a radius
Radius
A line segment that runs from the center of the circle to somewhere on the circle Ex. OA is a radius
Numerical Expression
A mathematical phrase that contains numbers and operation symbols Ex. 14+8÷4-21
Variable Expression
A mathematical phrase that contains variables, numbers, and operation Ex. 45-(x+3y)
Identity Property
Has 2 parts. The sum of any number and Zero is that number. The product of any number and One is that number. i.e. 8 + 0 = 8 45(1) = 45
Distributive Property
If you multiply a sum by a number, you will get the same result if you multiply each addend by that number and then add the products. i.e. 4(7 + 6) = 4(7) + 4(6)
Mean
In a numerical data set, the sum of all the data divided by the number of data items. i.e. Find the mean of the following data: 12, 45, 32, 15, 40, 25, 29, 49, 22, 27, 31, 33, 31 1. 12+45+32+15+40+25+29+49+22+27+31+33+31 = 391 2. 391 ÷ 13 = 30.076923 3. Round to the hundredths place = 30.08
Compatible numbers
Numbers that can be divided evenly; useful in estimating quotients Ex. 27.2÷4.14 ≈ 28÷4=7...28and4arecompatible#s.
Quadrant
One of four sections on the coordinate plane formed by the intersection of the x-axis and the y-axis
Inverse Operations
Operations that undo each other Ex. Addition and subtraction are inverse operations. Multiplication and division are also inverse operations.
Opposites
Pairs of numbers that have the same absolute value Ex. 4 and -4 are opposites because they are 4 units from 0
Expanded Notation
Pointing out the place value of a digit by writing a number as the digit × its place value. For example, 342 = (3 × 102 ) + (4 × 101) + (2 × 10).
Deductive Reasoning
Reasoning logically from given facts to a conclusion
Commutative Property
States that two or more numbers can be added or multiplied in any order and still arrive at the same sum or product. i.e. 8 + 20 = 20 + 8 7 • 12 = 12 • 7
LIKE TERMS
Terms with the same variable part (including exponent)...like terms can be combined using the distributive property in reverse Ex. 4x+6x=(4+6)x=10x
DISCOUNT
The amount by which a price is decreased Ex. If shoes marked at $56 have a discount of $10, the new price is now $46.
Markup
The amount by which a price is increased Ex. If the jacket was purchased at $25 from the manufacturer, and a $50 markup is applied, the new price is $75.
