# maths

• MATHS
• expand/factorise linear: factorise
• for an expression of the from a(b+c), expanded version is ab+ac
• i.e mutiply the term outside the bracket by evereyting inside the bracket
• for an expression of the form (a+b) (c+d) the expanded version is ac+ad+bc+bd
• everything in the first bracket should be mulitplied by everything in the 2nd
• factorising
• reverse of expanding brackets
• e,g, 2x2 +x-3 into the form (2x+3) (x-1)
• first step is to 'take out' any common factors which the terms have
• diffrence of two squares
• if you are asked to factorize an expression  which is one square minus another yuo can factorise it immdiately becuase a2+b2= (a+b) (a-b)
• factors and prime: product of prime factors
• to find a product of a prime number do a prime factor tree and find the circled prime numbers and x them together
• e.g 2x2x2x2x5
• pythagoras therom
• you are given the measurments for the hypotenus,c, and one leg,b , the hypotenus is always opposite the right angle and it is always the longest side of the triangle. to find the lenght of A substitute the known values into phythagoas therom
• phythagoras therom: a2 +b2 =c2
• venn diagrams: find intersection, union and not probability
• A n B means the overlap in the middle
• A U B means lookking at both circles
• data graphs: frequency polygons
• simultaneous equations: diffrent coefficients
• some pairs of simulaneous equaions may not have any common coefficents
• both equations may not have any common coefficients
• getting the/some of the same numbers/letters in equations
• e.g. 3a+2b=17 4a+b=30
• mutiply by 2 as bx2=2b which is then a coefficient
• polygons: exterior angle between identical polygons
• if the side of a polygon is extended the angle fromed outisde the polygon is the exterior angle
• the sum of exterior angle is 360
• calculating the interior angles by working out how many traingles in shape
• example: a pentagon contains 3 trainagles so the interior angle sum is 180 x 3= 540
• bearings: use trigonometry to find bearing
• use the cosine rule when: you need to find a side and you know 2 sides and he included angle
• you need to find a angle and konw three sides
• use the sine rule when: you need to find a side and know one side and hree angles
• a bearing is the agle in degrees measured clockwise from north
• 3 figures always
• repeated percentages
• percentage change = difference/original
• rearranging fromula
• in order to change the subject of a formula items in fomula need to be rearranged so diffrent variable is subject
• the formula A=BH needs to be rearranged to make B subject of formula
• to make B subject of formula it needs to be isolated, the letter B is multiplied by H so divide H (both sides) to isolate B
• example: A=BH  A/H BH/H A/H=B