Incorrect from past papers calc

Question 1

When given a difficult fraction like 2x^2 - 6x - 56 whats one thing you can do to help

Answer 1

Half it into 2(x^2 - 3x - 28) BUT MAKE SURE TO ADD THE 2 AT THE FRONT OTHERWISE YOU LOSE VARIABLES

then you can factorise the bit inside the fraction and just add 2 infront ie:

2(x-7)(x+4)

Question 2

when given a ratio question, if one ratio of 3 people having a sum of money is (for example) 3:4:2 and we know what one person has in £… then how do we find out everyones sum of money if one person gives some money to others, thus changing the ratio (ie: to 2:5:3)

Answer 2

We know what one person has so we know what everyone has
we add up the total sum of money for everyone
THE TOTAL SUM OF MONEY DOESNT CHANGE ONLY THE AMOUNT PER PERSON DOES
So we can add up all the parts in the 2nd ratio and do the total sum of money / total sum of parts to find out how much money each part is
Then we just multiply per person

Question 3

How do we solve an eq like this

y is proportional to x2
y = 3 when x = 0.5

x is inversely proportional to w
x = 2 when w = 0.2

Find the value of y when w = 2

Answer 3

We find out k for both eqs

since x is in both these eqs, we find out x when w is 2
Then we find out y with this value of x

Question 4

Where do i make the most silly mistakes

Answer 4

Histograms/bar charts

Question 5

How to find the median from a histogram

Answer 5

We find the median position with n+1//2
(n = total freq)
We find the class interval the median is in

Then we do the position of the median - the cumulative freq of the previous class interval (ie: if the median is in the 3rd class interval and the cf for the 2nd interval was 210 but median position is 285.5 we do 285.5 - 210)

Then we take that value and divide it by the individual frequency of that interval/bar and multiply that by class width

We take that value and add it to wherever the class interval starts at (ie: if the x axis for that bar starts at 50 then we add it to 50)

Question 6

WHAT DO YOU REMEMBER WHEN DOING HANDWRITING

Answer 6

MAKE 4s LOOK like 4s NOT 9s and
MAKE 7s LOOK LIKE 7 NOT 1 or 2

Question 7

when finding the gradient of a straight line graph, what does the slope tell you about the gradient

Answer 7

pos = slope upward
neg = slope downward

Question 8

When youve rearranged something to make something else the subject what must you check

Answer 8

If anything can be factorised

(you can just factorise the numerator or just the denominator or factorise both individually btw)

Question 9

If a question asks (cumulative freq question)

one item is picked at random, whats the prob that this will have a (height for example) of higher than 9cm (out of 80 plants)

Answer 9

Go to 9cm on x axis, draw line up to cf graph and plot it on the y axis

Lets say that y axis num = 74

we need to find anything higher than that so we do 80 - 74 // 80 * 100 to get 7.5%

Question 10

If a question asks for proving similar shapes but there isnt an obvious scale factor between the big and small triangles (in this case the small triangle is in the big one) then wyd

Answer 10

Try making 2 triangles seperate

then rotate the smaller/bigger one (if they share an angle then flip the sides connecting the angle so that if one side was on the floor previously the shape would be rotated so the otherside would be facing down, keeping the angle the same)

now with the sides being swapped with the angle kept the same try and see if there is any scale factor now

(we seperated the big one so because we had to add the sides together when the sides werent flipped to get the big triangle, well have new combinations for checking SF)

Question 11

When a question asks to solve a quadratic (CALCULATOR PAPER) What must you FIRST do

Answer 11

USE
THE
QUADRATIC
FORMULA

Question 12

What is an invariant point in translation

Answer 12

In translation, an invariant refers to a property or characteristic that remains unchanged when a shape or object is moved from one location to another

ie: if a point on the y axis is translated by f(-x) then that point will be invariant as it doesnt change position

Question 13

if a question asks to find one possible column vector of a translation what does this usually mean

Answer 13

Usually this is for rotation/flipping/enlargement since they dont have the same vector for each point

This means take one point and find the column vector of that change

So you wanna do the change first (ie: rotate the shape) and then get one point and find the vector for that change from orig to new