Algebra Flashcards
What is the quadratic formula?
x = (-b ± √ b² - 4(a × c)) ÷ 2a
What is the equation for the quadratic formula?
x = ax² + bx + c = 0
What is Pythagoras’ theorm?
a² + b² = c²
What is the equation for the area of a triangle?
1/2 base × height
What is the cosine rule?
a² = b² + c² - 2bcCosA
What is the sine rule?
SineA/a = SinB/b =SinC/c
How do you use sine to work out the area of a triangle?
1/2 abSinC
What is SOHCAHTOA?
SinX = Opposite/Hypotenuse CosX = Adjacent /Hypotenuse TanX = Opposite/Adjacent
What are the 3 rules for surds?
- √a × √a = a
- √a × √b = √a × b
- √a ÷ √b = √a ÷ b
In the equation y = mx + c
What does the m stand for?
m stands for the gradient.
In the equation y = mx + c
What does the c stand for?
c stands for the y intercept. (where the line crosses the y-axis)
How do you work out the gradient of a line?
Rise/run
How do you calculate volume?
Volume = cross sectional area × length
In a cumulative frequency graph, The cumulative frequency is what?
The previous frequency + current frequency
When plotting a cumulative frequency graph do you use the end or midpoints?
You use the end points.
How do you calculate the mean from a frequency table?
Frequency × midpoint for all ranges + together ÷ by total frequency
How do you calculate the upper bound
You either × or ÷ the upper bound by the other lower bound value.
How do you calculate the lower bound?
You either × or ÷ the lower bound by the other upper bound value.
How do you calculate the bound?
You calculate the middle of the upper bound either × or ÷ by the other lower bound value and the lower bound either × or ÷ by the other upper bound value
What is the frequency in a histogram?
The frequency in a histogram is the area of the bars (Class width × frequency density)
How do you calculate a mean from a histogram table?
((Frequency × midpoint) + together) ÷ total frequency
What is the difference between an equation and an identity?
An equation has a solution for a specific value of x to make the equation true for example 5n - 7 = 8
and an identity does not need a specific value for x to be true for example 2(n + 3) = 2n + 6 which simplifies to 2n + 6 = 2n + 6
How do you calculate frequency density?
Frequency × class width
How wide are the bars on a frequency density graph?
The bars are as wide as the classes
What is the equation for density?
Density = mass ÷ volume
