a cube number is any number that is to the power 3 for example 2 to the^ 3 an example is 8 a natural number is any number that is positive and is a whole number for example 243 a square number is any number that is squared for example 2^2 which is four a prime number is a number that can only be divisible by itself and one an example is 7 a common multiple of 4 and 17 would be 68 first common multiple you have to find the factors so in this case it will be 32 here 80 here the factor four will multiply to 8 and here 20 and then further four will multiply by 2 and multiply by 5 hence 4 * 4 * 2 * 5 = 160 so the answer is 160 to calculate the upper bound of something you look at this statement here nearest millimeter is 0.1 divide this by two you get 0.05 hence your upper bound will be 6.5 + 0.05 and since we have to calculate the height of the tower you multiply by this by three giving us a final answer of 19.65-cu multiply this by 105 that will give you the increase to calculate original price you do and this is since it's reduced what you do is you do 100 - 16 giving us 84 and then you do 105 / 84 over 100 and this will give you 125 and that's how you do it simple interest and compound interest here is the formula I is the interest earned p is the money borrowed invested R is the rate of interest and T is the time for compound interest a is the accumulated account this is the invested or bored amount then this is 1 + r which is the interest rate which is R and T is the time Tak to answer any of your questions you use these formulas exchange rates you simply have to do if $1 is equal to 24.3 Japanese Yen how much will $80 equals 2 you cross multiply and you can find the value of x speed distance and time speed equals to distance over time speed here is 18 distance we have to calculate and time is in minutes so you do 55/ 60 to convert into hours you cross multiply and D will be 16.5 km I this equation what you simply have to do is 5 * 3 which is 15 5 * n which is 5 N - n * 3 which is - 3 n and - n + n which is - n^ 2 this gives us n^ 2 + 2 n + 15 as the final answer like this you put both x's on one side and the whole numbers on the other side so 11 x - 3x is equal - 7 -5 giving us 8X is = -22 x = - - 22 8 giving us -2.75 as xous equation like this we use the substitution method since we know Y is = X /2 I will substitute in in the second equation making it 2x minus I substitute y value here so x / 2 = 1 2x - half X = to 1 by opening it up and now I can find the value of x the value of x is 2 over3 to find the value of y you put 2 over3 into the first equation by doing 2 3/ 2 giving us a value of 1 3 subject of the formula what you simply do here is Square both sides to get rid of the root so y^2 = x^2 + 1 take one the other side becomes y^2 - 1 and then you root this + - = x therefore that is your answer variation is like this Y is inversely proportional to x² to get rid of the inverse you do y = k /x^2 by introduce a constant you have these values you substitute them in so K over 4 the value of K will be 32 now to find Y in terms of X you simply just plug in the values so Y is going to to be equals to 32 x^2 laws of indices whenever it's power Z it equals to 1 when it's -1 it becomes the inverse when it's multiplication you add the two Powers when it's division you minus the powers when it's like this you can multiply the two Powers when it's n / M you can write it in this format is the same as equations you put both x's on one side so that will be 13 - 7 is equal to 2x this will become 6 uh equal to 2X therefore 3 is 2X and hence the final answer is X is less than or equal to 3 insation formulas you can pause the screen and remember these formulas that you'll be needing them in your paper polygons you need to know these three formulas the sum of all angles of an n-sided polygon is n minus 2 * 180 each angle of a regular polygon can be used by this formula N - 2 * 180 Over N to find sum of all the exterior angles of a polygon must add up to 360° the circle theorems you can pause PA the video and look at each of the scenarios and remember how to tackle them when you get a question on circles a question of Pythagoras Theorem each side can be labeled by a b and c if you want to find the value of B you need to know this formula a s + b² = C 2 a s here is 8 2 + b s we need to find out c^ s is 18 s to rearrange you get 18 s - 8 s and if you root this you can get the value of B this is Pythagoras Theorem supposed to find the symmetry of a shape in this shape it's a rombus so there's only two lines of symmetry which is like this so there's only two lines of symmetry they can give you other shapes and you have to find the lines of symmetry a line of symmetry is simply when you have two opposite mirrors when you cut the line through this is a question on similar triangles this side is similar to this side hence we can equate them to each other 15 / 5 is equals to and this side is equals to this side or is similar to this side so therefore 16.5 is equals to EF if you want to find EF you have to cross multiply so 15x = 16.5 * 5 x will equal to 5.5 and therefore your value of EF is 5.5 this is a question on trigonometry in these questions you need to remember so where this is s this is cos and this is 10 in this case we need to find BC which is the hypotenuse so we have the opposite and the hypotenuse so if we have opposite and hypotenuse you use S so sin 52 is equal to 8.6 / CB and you can then therefore make the subject CB the formula and that will be 8.6 over sin 52 and you can find your value of BC questions on lines you need to know the format of a equation of a line where Y is equal MX plus C where m is the gradient and C is the Y intercept for lines that are parallel to each other the gradients are always the same so in this case the values of M are always the same for lines that are perpendicular what that means is If I multiply the two gradients of the lines I will get1 one on sets when it's a subset it means it's within a set when it's a proper subset that means uh the elements of A and B are within when it's disjoint sets they are not together when they're intersection that means the middle part will be intersected and the sign is like this so it's an n a union is when both the elements are together so both elements A and B Union or you have to include all elements within the set and a complement is everything except that set is a complement here is a question on vectors so you simply have to just minus it like this 5 - 3 is 2 - 1 + 2 is 1 for this you can write it as a is uh 36 and B is 510 if I want to find a to B so I just simply have to do 5 um sorry uh 510 - 36 giving us 2 4 under Transformations we have to know four types of Transformations which invol reflection where you simply draw a mirror line and the two images there's the rotations which um can be from 90° 180° to 70° we then have translations which um are written in the form like this uh where negative uh where the top means you know going um right or left and down going up or down and then we have enlargement which is simply using a scale factor uh to enlarge the shapes on on probability and how you answer this question is here first of all they've given the total number they've said six are red nine are blue the rest are white so I believe five are white to write down the probability what you simply have to do is there's a chance to pick six red balls out of the 20 so the probability is 6 out of 20 there's five chances five balls of white so hence there's the probability of 5 over 20 and for yellow uh since yellow there's no yellow bolts hence there will be zero probability will be zero on functions if this is the case you simply have to just plug in 3x into the function so that will give us 3 + 4 into 3x giving us 3 + 12x as the answer related to angles of a sector you need to know how to calculate the AR length the area of the sector and the perimeter of the sector something like this what you simply do is multiply these two together so that becomes 6X then you do 3 - 1 so it become squared and this will just be three so this would be the differential uh the differentiation of this