5733 - Math Flashcards
What is a prime number?
a number divisible only by itself and 1
2, 3, 5, 7, 11, 13 . . .
In the number 12,408.57, what place is the number 7 in?
hundredths
Multiplying a negative number by a negative number always results in a ______ number.
positive
What is a numerator?
the number on the top of a fraction
How is a decimal converted to a percent?
multiply the decimal by 100
0.37 × 100 = 37%
x^0 =
x^0 = 1
What are irrational numbers?
e, π,√3
Irrational numbers are numbers that cannot be written as fractions.
What is the distributive property?
a(b + c + d) = ab + ac + ad
The distributive property is used to multiply a single term by two or more terms inside a set of parentheses.
How can miles per hour be converted to feet per second?
x miles 5,280ft 1 hour (x)(5,280)
———- x ———– x ———— = ————–
hour 1 mile 60 secs 60 secs
Multiply the original value by the appropriate conversion factors. The original units should cancel, leaving only the new units.
What does PEMDAS stand for?
The order of operations: parentheses, exponents, multiplication/division, and addition/subtraction.
How is percent difference calculated?
new amount - og amount
percent diff = ————————————— x 100
og amount
What is the process for writing a number in scientific notation?
Place a decimal after the first digit and count the number of places the original decimal needs to be moved. The number of places will be the positive exponent for large numbers, and it will be the negative exponent for numbers less than 1.
58,300,000 = 5.83 x 10^7
0.00000124 = 1.24 x 10^-6
ewrite x^-a with a positive exponent.
x^-a
What is the acronym FOIL used for?
(x + 3)(2x - 5) =
2x^2 - 15x + 6x - 15 = 2x^2 - 9x - 15
F O I L
To multiply two binomials
FOIL stands for First, Outer, Inner, Last.
Which terms in the expression 3xy^2 + 6xy - 3y^2 - xy^2 can be added?
3xy^2 and - xy^2
Only terms with the same variables can be added.
What is the formula for finding slope?
Y2 - Y1
m = ————–
X2 - X1
Factor x^2 - y^2
x^2 - y^2 = (x - y)(x + y)
What is the slope of a horizontal line?
0
Which of the following numbers satisfies the inequality 0 < 8 ?
0, 4, 8, 12
4 and 8
When graphing the inequality y > 4x -1, which side of the line will be shaded?
What is the y-intercept form of a linear equation?
y-intercept form: y = mx + b
What is the definition of a function?
a relationship where each input value has only one output value
What determines whether the graph of an inequality is a solid or dashed line?
If the inequality is ≥ or ≤, the line will be solid. If the inequality is either < or >, the line will be dashed.
What are domain and range?
Domain refers to acceptable inputs, or x-values, for a given function. Range refers to the outputs, or y-values, of a given function.
What are the sides of a 45 - 45 - 90 right triangle?
x, x, and x√2
How many points are needed to draw a line?
2
Two lines that intersect to form a 90° angle are _______.
perpendicular
Two lines that lie in the same plane but never intersect are _______.
parallel
What kind of angle is larger than 90°?
obtuse
Complementary angles add to _____ degrees.
90
In a circle, what is the relationship between the diameter and the radius?
The diameter is twice the length of the radius.
How many angles have measurements greater than 90° in an obtuse triangle?
1
What is the Pythagorean theorem?
c^2 = a^2 + b^2
Which quadrilateral has exactly one pair of parallel sides?
trapezoid
What is sum of the exterior angles for any polygon?
360 degrees
What is the formula for the area of a circle?
A = πr^2
How many degrees are there in a quadrilateral?
360 degrees
Will an outlier have the biggest effect on the value of the mean, median, or mode?
Outliers affect mean by shifting it away from the median. Outliers do not affect mode.
What is the fundamental counting principle?
the total number of possible outcomes is the product of the total possible number of outcomes in each trial
What is the sum of all probabilities in any probability distribution?
The sum of all probabilities is always 1.
What is the mean of a data set?
Mean is the average value, or the sum of the values divided by the number of values in the set.
What is the median of a data set?
Median is the number in the middle of the set.
What is the mode of a data set?
Mode is the number that occurs most often in the set.
What is a line graph?
A line graph is typically used to show data that is changing continuously over time. The graph looks like a scatterplot with line segments connecting each point.
What is a histogram?
A histogram plots the frequency of quantitative data with number ranges grouped together.
What is the formula for finding the probability of a single event?
successful outcomes
probability = ——————————-
possible outcomes
What information is shown in a pie chart?
Pie charts show the percentages of each element of a set.
What do the terms “skewed to the left” and “skewed to the right” mean?
The mean of a data set that is skewed to left is less than the median, and the mean of a data set that is skewed to the right is greater than the median.
In a Venn diagram with two circles representing the probability of A and the probability of B, what is represented by the area outside the circles?
The area outside of both circles is the probability of neither A nor B.
Rewrite x^a . x^b as a single term
x^a . x^b = x^a+b
What is the y-intercept form of a linear equation?
y-intercept form: y = mx + b
