Maths Flashcards
(48 cards)
Name the 5 most common Pythagorean Triples
(3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17) (20, 21, 29)
What type of angle is the largest angle in a triangle where this is true: h² > a² + b²
Obtuse (x > 90°)
What type of angle is the largest angle in a triangle where this is true: h² = a² + b²
Right-Angle (x = 90°)
What type of angle is the largest angle in a triangle where this is true: h² < a² + b²
Acute (x < 90°)
Factorise ax² + bx + c (Magic Multiplying Method)
a*c = ac Write pairs of factors of ac (y, z) (k, l) Find pair of factors that sum to = b Say y + z = b and k +l ≠ b Then divide these factors by 'a' Simplify Denominator of first fraction (y/a) so 'a' is first number while y is second number (a + y) Now for second bracket do same So it would be (a + z) So final equation is (a + y)(a + z)
3 Rules of Bearings
- Always measured from North
- Always measured clockwise
- Always 3 digits (40° wrong) (040° right)
Simple Interest
Let Original value = x Frequency of payment = y and Interest Rate = z x + y(z*x)
Compound Interest
Let Original value = x Frequency of payment = y and Interest Multiplier (e.g. if interest rate is 10% then interest multiplier is 1.1) = z x * z^y
Recurring Decimals Magic Method 1
0.63 recurring (dots are above 6 and 3) then take that number and put it over an equal set of 9s ( e.g. 63/99 or 547/999 etc.)
Recurring Decimals Magic Method 2
0.16 recurring (dot is only on 6 not 1) First split number into 0.1 and 0.06 (6 is recurring)
Imagine recurring number as 0.6 (6 is recurring)
Use Magic Method one to convert this into a fraction
Add how many ever zeros you originally took away from recurring number and add it to the the denominator of the fraction.
Convert 0.1 into fraction.
Add both fractions together
What should you always do when multiplying and dividing algebraic fractions
F.F.F. Factorise Fully First
Sine Formula
opp = hyp * sinθ
Cosine Formula
adj = hyp * cosθ
Tangent Formula
adj * tanθ = opp
Index Laws
x^a * x^b = x^(a+b) x^a / x^b = x^(a-b) (x^a)^b = x^(a*b) (ab)^n = a^n * b^n (a + b)^n ≠ a^n + b^n
Negative Powers
Divide 1 by the original value by however many times it says in the power (e.g. 4^(-2) is 1/4/4 or 1/16 because it says ‘-2’ so you divide 1 by 4 two times.
Fractional Powers
Take denominator of the fractional power and root the starting number by that denominator (e.g. if fractional power was 1/3 then cube root starting number) We will call this number x
Now do 1 * x^ numerator of fractional power
Standard Form Rules
A * 10^n (1≤A<10) and (n has to be an integer)
Adding and Subtracting in Standard Form
You must first get n to be the same in both parts that you are adding (e.g. (2.5 * 10^5) + (4.3 * 10^4) you must either get both parts to be 10^4 or 10^5 then you can add as normal)
Parallel Lines
Have the same gradient
Perpendicular Lines
Have a negative reciprocal gradient. (flip fraction and multiply by -1) Product of 2 gradients of perpendicular lines = -1
3 Methods of Simultaneous Equations
Elimination, Substitution, Graph
Centimetres (cm) to Millimetres (mm)
x10
How to convert a powered value
Say you have m^2 to cm^2. Then take original conversion (x100) and square or cube or power or whatever (in this case we are doing ^2 so the conversion is 100^2 or x10,000)
