Year 10 Term 1 Flashcards
How to work out HCF using Venn diagrams?
Factorise 2 numbers using factor tree
Put into Venn diagrams
Product of crossover is HCF
How to work out LCM using Venn diagrams?
Prime factorise using factor tree
Put onto Venn diagrams
Product of all numbers Is LCM
Look in your book for surds it’s too hard to do on flashcards
Stones bones skibidi scones
How to rationalise a denominator in form a± root b
Multiply numerator AND denominator by the conjugate of the denominator (switch the symbol)
Define formula
A rule that shows that shoes the relationship between two or more variables
How to factorise a quadratic equation when c = 0?
Linear factorisation
X² +4x
= x(x+4)
How to factorise a quadratic equation in full form?
Quadratic factorisation
Find 2 numbers that multiply together to make c, and add together to make b
Eg. X²+6x+5 = (x+1) (x+5)
How to factorise a quadratic equation when b = 0 and c is a square?
DOTS
Eg. X²-49 = (x+7) (x-7)
How to factorise a quadratic equation in full form when a>1?
Multiply together a and c to get ac
Find 2 numbers that multiply to ac and sum to b
Write out equation again, but split b term into those two numbers
Then factorise as 2 parts iykwim
How to solve quadratic equations?
Always set to equalling zero
Find numbers that make both sides 0
There can be 2 answers
How to complete the square?
Rearrange to
a[ (x + ½b)² - (½b)² ] +c
The second term in the square brackets must always be negative
What is the quadratic formula?
_______
-b ± √b² - 4ac
x = ——————–
2a
Use formula with both + and - before the root part to get two answers
How to find turning point of a quadratic graph?
Complete the square of the equation
But please look in your book quadratic graphs are so hard to explain
Equation for direct proportion?
y = kx
Equation for indirect proportion?
y = k/x
How to combine ratios?
Use LCMs
Equation for speed and units?
Distance/time
M/s
Equation for density and units?
Mass/volume
Kg/m³
Equation for pressure and units?
Force/area
N/m²
Equation for exponential graphs?
Y = k^x
Equation for reciprocal graphs?
Y = k/x
Equation for circle graphs?
X² + y² = r²
Equation for volume and SA of a sphere?
Volume = 4/3πr³
SA = 4πr²
Equatipn for volume and SA of a cone?
Volume = ⅓πr²h
SA = πr² + πrl
Use pythag to find l, the slanted surface
Equation for arc length?
angle/360 x πd
Equation for sector area?
Angle/360 x πr²
Equation for volume of a prism?
Area of crossection x length
Equation for volume of cylinder?
πr²h
Equation for SA of cylinder?
2πr² + hc
Equation for circumference, c?
C = πd
