Math 2021 Flashcards
What is 5x times 6x^2?
30x^3
What does f(x) mean?
“the function of x” or, more simply, “y” when x is substituted into the expression.
What is f(2) if f(x) = x - 3 ?
f(2) = -1 Why? 2 - 3 = -1
What is a Pythagorean Triple?
Three side lengths that will always form a right triangle.
Name three pythagorean triples
3, 4, 5
6, 8, 10
5, 12, 13
What is 5pi?
5pi is between 15 and 16 because pi is slightly more than 3. 5 x 3 = 15
What change does a dilation of 1 cause?
None! Multiplying by 1 has no effect!
What should you do if faced with:
x + y = 12
x - y = 2
Add the two equations together to get:
2x = 14 (the y’s cancel out because they are opposites)
x = 7 !
How would you graph, y = x - 4?
Begin at (0,-4) then rise up 1 and run right 1
What does > mean?
Greater than
Solve for x: -3x > -6
X < 2. BE SURE TO SWITCH THE SIGN because you divided by a negative. (Also true for multiplying)
How should you draw the “line of best fit” (also called a trend line) on a scatter plot?
Create a straight line that includes as many points as possible.
How do we know if a graph represents a function?
If it passes the VERTICAL LINE TEST!
What is the Median of 1, 3, 5, 2, 4?
3 It is in the middle when the numbers are put in order.
What is the Median of 1,3,5,2,4,6?
3.5 3 and 4 are in the middle so we have to take the middle of those two numbers.
How do we calculate the Mean?
Add up all the numbers and divide by the number of numbers you added
What is the Mode?
The number or numbers that appear most often. Sometimes there is no mode. Sometimes there are more than one.
How do we calculate range?
Subtract the smallest number from the largest.
What are the ends of the whiskers of a box plot called?
The extremes or the max and min.
What are the sides of the box of a box plot called?
The upper and lower quartiles
What is the line inside the box of a box plot called?
The Median
How much of the data does the space between each of the five components of a box plot represent?
25 Percent.
How do we calculate the interquartile range?
Subtract the lower quartile from the upper quartile.
How can we calculate the midpoint of a line?
Add the x’s of the end points together, divide by 2. Repeat for the y’s
How do we calculate probability?
Create a fraction.
Numerator: The part we are asked about
Denominator: The total number of possibilities
How do we turn a decimal into a percent?
Move the decimal point 2 spaces to the left OR multiply by 100
What is a solution?
A value (or values) that make an equation true.
How do we know if a number is a solution?
Substitute it in and see if it creates a true equation!
How do we create a percent?
part over whole
How do we know a point is a y intercept?
The x value is zero. Example (0, 2)
How do we know a point is an x intercept?
The y value is zero. Example ( -1, 0)
What is the difference between calculating perimeter and area?
When calculating perimeter we ADD the sides.
When calculating area we MULTIPLY.
What do we mean by being “similar?”
Same shape but different size.
CORRESPONDING ANGLES ARE CONGRUENT.
CORRESPONDING SIDES ARE PROPORTIONAL (THEY MAKE EQUAL RATIOS SUCH AS 1/2 , 2/4, 3/6)
Rational Number
A number that can be written as a fraction
As a decimal it either ends or repeats in a pattern.
Irrational Number
A number that cannot be written as a fraction.
As a decimal it doesn’t repeat and doesn’t end.
Pi
Is an IRRATIONAL NUMBER
Can you make irrational numbers rational by adding, subtracting, multiplying or dividing?
NO!
In a volume formula, what does B mean?
The AREA of the base. We must calculate the area of the base (a separate formula) and then use that number in the volume formula.
The formula for volume of a rectangular prism is
V=Bh. If the length of the base is 6 and the width of the base is 4 and the height of the prism is 10, what is the volume?
The volume is 240 cubic units.
B = 4 x 6 = 24
V = Bh
V = 24(10) = 240
Parallel
Do not intersect. SLOPES ARE EQUAL
Perpendicular
Intersect at 90 degrees/make right angles
SLOPES ARE OPPOSITE RECIPROCALS!
Slope of a horizontal line
ZERO
Slope of a vertical line
UNDEFINED
Rate of Change
Slope!
Sum of the interior angles of a triangle
180 degrees
Exterior angles
Always add to 360 degrees!
Number of degrees in a circle
360
Sum of the interior angles of a quadrilateral
360
If a diameter is 13, what is the radius?
6.5
What is (x + 5)(x - 2) ?
x^2 + 5x - 2x -10 = x^2 + 3x - 10
