A5

Question 1

If you have a point on a line and the gradient, then how do you find out the x intercept

(ie: tangent on a circle which passes x axis at point P)

Answer 1

As you have the gradient and a point you can find y intercept by substituting everything in

then once you have the full equation you can find x intercept as the y axis will be 0, so you substitute everything with y being 0, and you solve for x

Question 2

How do you solve simultaneous equations (ie: question gives you 2 eqs of a graph and asks you to find the intersection) and what are you doing if oen of them has a fraction for a gradient

Answer 2

As they both equal y (rearrange if not)

eq a = eq b

If one has a fraction as a gradient of smn then multiply both sides by the denominator to get rid of it

Solve for x

input x into one equation and find out y

Question 3

How do we solve quadratic simultaneous equations if one of them is linear and the other quad

Answer 3

if y = (linear)
and
y = (quadratic)

then because they both equal y then substitute the linear eq into the quad eq (if one of them is x you can still substitute but in this instance both = y)

(linear) = (quadratic)

make one side 0 (preferably the linear side) by moving everything from that side over and factorise (solving for y or x)

Then to solve for x, pick one eq (linear preferably) and substitute the the variable you know to find the unknown variable

Do it for both values of x/y as you will get 2 and say: “when x =… y =…. and when x =…. y =…

Question 4

What is a geometric progression

Answer 4

A sequence where the next term is the pervious term times by something

Question 5

If you get a question saying

“a geometric progression goes

8 x 72

find x” wyd

Answer 5

Because they are all times by the same number, x/8 = 72/x

so bring x onto the other side to get x^2/8 = 72 and then get x^2 = … so you can. find x from there (question will ask If its positive or negative

Question 6

How do we find the nth term of a quadratic sequence

Answer 6

The nth term for a quadratic sequence is always
an^2+bn+c
So we find the 2nd difference of the sequence (difference of first difference) and that is 2a (see maths genie vid on quad sequence if u dk). Then we divide the 2nd diff by 2 for a. With this we can go back to our first difference and the first term of the first difference is 3a+b so we know a and thus find b. Now that we know this we go to our original sequence to find c as the first term of the original sequence = a+b+c and we know a and b so thus find c

Question 7

How do you determine where in the sequence a number is (quad sequence)

Answer 7

(nth term of sequence) = num you are looking for
make the eq = 0 so you can factorise (assume n is x)
If you can, divide the nth term by a certain amount to get 1n^2 so its easier to factorise or just as little as possible so its easy to factorise

You will get a negative answer and a positive answer
You will choose the positive answer then

Question 8

if y is directly prop to x^2 what does that mean

+ inverse prop

Answer 8

y = kx^2
y = k/x^2
k can be used no matter the values of your and x