Maths Formulaes

Question 1

Sector area

Answer 1

Angle over 360 times pi r squared

Question 2

Arc Length

Answer 2

Angle over 360 times pi times diameter.

Question 3

Volumes

Answer 3

Always look for SF and units. Formulae all on test.

Question 4

Prisms

Answer 4

Height times Area.

Question 5

Indicies Multiplying

Answer 5

When multiplying powers add powers together.

X on its own is X to the power of 1. X to the power of 0 equals 1.

Question 6

Indicies Dividing

Answer 6

Take powers away from one another.

Question 7

(X to the power of 7)To the power of 2

Answer 7

Multiply powers in this case would equal X to the power of 14

Question 8

Express with a positive power. When power is negative.

Answer 8

Put it into fraction one over X to the power of y

Question 9

X to the power of a fraction

Answer 9

Bottom X is rooted by, top X is to the power of. I.e 9 to the power of 3 halves would equal 27

Question 10

Surds - Multiplying.

Answer 10

Multiply both of roots together. So Root 7 times root 8 would equal root 56.

Question 11

Simplifying surds

Answer 11

Find highest square factor of root.I.e 4,9,16,25 etc.
Put square factor times No it is factorised by. Root 27 would equal root 9 times three.
Put root of square factor outside root and remove it I side root. I.e Root 9 times 3 would equal 3 Root 3

Question 12

Rationalising denominator

Answer 12

Multiply top and bottom by denominator by root. I.e root 2 would go to root 4 then simplify to 2.
Top add the root to it. 3 on top times by 2 to would be 3 root 2.
Often you can simplify in the questions.

Question 13

Fractions

Answer 13

Add and minus make denominators equal. By multiplying top and bottom by a number that makes both even. Always simplify
Multiplying- multiple top by top and bottom by bottom always simplify.
Divide flip one side and sign then do same for multiply.

Question 14

Algebraic fractions

Answer 14

Similar to numerical. When using brackets remove before adding, subtracting or multiplying makes it easier.
Simplifying can be done by removing top from bottom when all aspects are being multiplied.

Question 15

Calculating gradient

Answer 15

M equals Y2 - Y1 over X2 -X1 where X1 and Y1 are first coordinates and X2 and Y2 are second coordinates.

Question 16

Gradient equation

Answer 16

Y equals Gradient times X take away Y intercept (C)

Common.y have to rearrange.

Question 17

Formula when gradient and a point on the graph are known

Answer 17

Y-b= m(x-a) where m is gradient, a is x co-ord and b is y co-ord.

Question 18

Changing subject

Answer 18

Opposite on both sides

Question 19

Equations and inequations.

Answer 19

Try to remove fractions ASAP. When dividing by a negative flip sign unless it is =.

Question 20

Simultaneous equations

Answer 20

Make one equation have X or Y opposite to other X or Y by multiply them and answer. Then chimney to get I.e. 4y = 16, y = 4.
Then put your value for y into either of the equations and simplify to find X.
State both values at end of equation.

Question 21

Factorising and multiplying out brackets.

Answer 21

First check common factor, if there is a common factor also check for difference of two squares or trinomials to be done.
Then check difference of two square if not then trinomials.

Question 22

Completing square

Answer 22

DRAW ANSWER ALONE WITH NO ARROWS OR ANYTHING.
Put x alone, in bracket and half no. beside X in equation. Both in bracket together. Square bracket and see what needs done to get no on end, put that after bracket squared.

Question 23

Axis of symmetry

Answer 23

Value of X at turning point.

Question 24

Equation for parabola, completing square when turning point is given.

Answer 24

Put X coordinate in point a , express with a plus if graph is left, minus if it is right, put y coordinate in point b.

Question 25

Max Turing point

Answer 25

X equals whatever makes bracket equal to zero. Y equals whatever is outside the bracket.

Question 26

Solving problems by factorising. Asking to show that.

Answer 26

Often use trinomials to solve to the two brackets.

Question 27

Solving problems by factorising. When area is given and you must find X

Answer 27

Make area equal to 0 by taking Area no. away from both sides. Use trinomials to solve to two brackets. Find whatever makes bracket equal 0 in both cases, X must be the positive bracket.

Question 28

Parabolas - Y intersect

Answer 28

X is equal to 0 so y intersect is most commonly 0 + whatever is outside bracket however solve equation to show working. Always state coordinates when done.

Question 29

Parabolas - roots

Answer 29

Y equals 0 so most commonly a trinomials question where you solve to two brackets, brackets may already there, other factorising may be needed. Roots X coord is what makes brackets equal 0. State coordinates when finished.

Question 30

Turning point

Answer 30

X equals halfway between roots. Use equation to solve for Y. State coordinates when finished.

Question 31

Finding real roots. (Discriminant)

Answer 31

b squared - 4ac>0 two real root which are differ/ distinct. b squared - 4ac = 0 there is one real root. b squared - 4ac < 0 there are no real roots.

Question 32

Using quadrat formula- “round your answer”

Answer 32

ax squared + bx + c = 0 | Put these into quad formula - be careful when finding no. under root.

Question 33

Pythagoras Theorem

Answer 33

C squared equals a squared plus b squared. Where in a right angled triangle c is the hypotenuse and a and b are the other sides. Always draw a diagram labelling sides.

Question 34

Converse of Pythagoras, is triangle right angled?

Answer 34

Draw diagram of triangle removing value of hypotenuse. Find length hypotenuse would be if triangle was right angled by using Pythagoras. If length you found is equal to one in question state: The triangle is right angled by the converse of Pythagoras as my number for what the hypotenuse should be in a right angled triangle - Xmas equal to the hypotenuse of the triangle - y. If not say the triangle is not right angled by the converse of Pythagoras as my number calculated for what the hypotenuse should be in the right angled triangle - x was not equal to value in the question - y.

Question 35

Pythagoras in a circle

Answer 35

Draw diagram of circle, give all info that you know, some values may need to be worked out. Draw another diagram of right angled triangle to find side missing. Figure out length of side through Pythagoras. Question may want to use side length to calculate depth or similar so often add or take away value found from radius.

Question 36

Order of operations

Answer 36

When solving - brackets, indicies, divide + multiply, add + subtract. Opposite wat around for undoing.

Question 37

Percentages going forward. | I.e clock used to cost 80 pounds it is on a 20% sale what is new price of clock.

Answer 37

Multiply old cost by percent over 100.

Question 38

Percentages going back. What was the original cost of the meal

Answer 38

Divide new cost by percent over 100.

Question 39

Properties of shapes

Answer 39

Draw diagram showing all known parts. Remember triangle in circle is right angled when across diameter touching circumference.

Question 40

Properties of shapes - regular large shale like dodecagon made up of triangles

Answer 40

Value of top of triangles can be found by dividing 360 by number of triangles. Triangles are always isoceles so bottom values are same.

Question 41

Scientific notation asking for no. of known mass thing in an amount of mass.

Answer 41

Do amount mass divide by mass of known thing. Take into consideration prefixes. Use rationale.

Question 42

When done

Answer 42

Redo, Check units, Check rounding, Check answer is clear and unambiguous.