You are Here: Home >< Maths

# Further Maths GCSE AQA Paper 1 (Unofficial mark scheme)

Announcements Posted on
Would YOU be put off a uni with a high crime rate? First 50 to have their say get a £5 Amazon voucher! 27-10-2016
1. Unofficial Markscheme:

Correct me if I'm wrong. The gaps are for answers I don't remember or questions.

1. 3x^2 - 20x [3]
2. a = 3, b = -20 [3]
3. (a) 12th term [2]
(b) 3/5 limiting factor [1]
4. (a)-5, 8 - basically it was opposite the numbers in the brackets [1]
(b) root 10 - radius [1]
5. Prove the two line segments were perpendicular. AB gradient = -10/4 and BC gradients = 4/10, multiply the two gradients to get -1 so they are perpendicular.[3]
6. m = 8, p = -1 [4]
7. 9, 10, 11 [3]
8. x = 121 [3]
9. x^3 - 15x^2 + 75x - 125 [3]
10. -80, x = 16 and y = -1/5 [4]
Should be 11. Circle theorem:
180 - 3x
2x + 58 = 2(180 - 3x)
2x + 48 = 360 - 6x
8x = 312
x = 39 [3]
12. (a) h = 3, k = -7 [2]
(b) -3, -7 [1]
(c) -3 +/- root 7 [1]
13. sqrt(125) + sqrt(20) = sqrt(80) + sqrt(x). Answer: x = 45 [3]
14. (a) When 3 is put into equation and a is 1, the equation is equal to 0. [2]
(x-3)(x-7)(x+2) - use long division first to get quadratic then factorise it [3]
15. 2root7 - 4 [3]
16. -5/6 for the cos and sine question [4]
17. k = 9 [5]
18. What Q? x^4 - 81 (I think it was this) = (x^2 + 9)(x+3)(x-3) [I think 2 marks]
19. (a) Use pythagoras theorem, 9 + 9 = 18, side = root 18 = 3 root 2 [2]
(b) Trapezium - Idk, but I got the answer somehow: the bottom side of the triangle was root 3 and the hypotenuse was 2root3.
Add it all together: 3 + 3 + 3 + 2 root 3 + root 3 = 9 + 3 root 3, thats what u get when u expanded what they gave so it's correct. [4]
20. Cosine rule.
Cos P = 1/3.
Use the rule, you find u have to do 4/12 to get 1/3.
So, you do 13n^2 - 4n^2 = 9n^2
That's w^2 so w = 3n.
w = 3n same as the other side, so the triangle is isoceles. [4]

Well, I thought I had got really low, but after checking it again, it seems way better!

Harsh marking: 53/70
Lenient marking: 59/70

Well, I'm happy .
2. I got 39 degrees for the circle theorems question
3. (Original post by mattedwards8972)
I got 39 degrees for the circle theorems question
Oh yeah thanks buddy .
180 - 3x

2x + 58 = 2(180 - 3x)
2x + 48 = 360 - 6x
8x = 312
x = 39?
4. (Original post by Chittesh14)
Unofficial Markscheme:

Correct me if I'm wrong. The gaps are for answers I don't remember or questions.

3x^2 - 20x

12th term
3/5 limiting factor

-5, 8 - basically it was opposite the numbers in the brackets

m = 8, p = -1
8 < x < 12

x = -55
x^3 - 15x^2 + 75x - 125
80, x = 16 and y = 1/5

h = 3, k = -7
-3, -7
-3 +/- root 7

x = 45
When 3 is put into equation and a is 1, the equation is equal to 0.
(x-3)(x-7)(x+2) - use long division first to get quadratic then factorise it

2root7 - 4
5/6 or -5/6 ?

k = 9 apparently ( i missed it out)

Use pythagoras theorem, 9 + 9 = 18, side = root 18 = 3 root 2
Trapezium - Idk, but I got the answer somehow: the bottom side of the triangle was root 3 and the hypotenuse was 2root3.
Add it all together: 3 + 3 + 3 + 2 root 3 + root 3 = 9 + 3 root 3, thats what u get when u expanded what they gave so it's correct.
x^4 - 81 (I think it was this) = (x^2 + 9)(x+3)(x-3)
Cosine rule.
Cos P = 1/3.
Use the rule, you find u have to do 4/12 to get 1/3.
So, you do 13n^2 - 4n^2 = 9n^2
That's w^2 so w = 3n.
w = 3n same as the other side, so the triangle is isoceles.
1.) Is right
2.) Was the matrices question a=3 b= -20 ( if i remember correctly)
3.) Nth term is correct
cirlce question is correct
39 degrees is the answer to the circle theorem question
8<x < 12 is correct
For the x/y question y= -1/5 as it has to be less than 0
Completing square is correct
Surds is correct
Factor theorem is correct
-5/6 is the correct for the cos theta question
K = 9 is correct
Trapezium question is solved using the 30,60 triangle and the 45,45 triangle . The diagnol side is 2 root 3 and the bottom is root 3
Factorising is correct
Isosceles proof is correct but i did it a different way

Posted from TSR Mobile
5. (Original post by ErinMei)
1.) Is right
2.) Was the matrices question a=3 b= -20 ( if i remember correctly)
3.) Nth term is correct
cirlce question is correct
39 degrees is the answer to the circle theorem question
8<x < 12 is correct
For the x/y question y= -1/5 as it has to be less than 0
Completing square is correct
Surds is correct
Factor theorem is correct
-5/6 is the correct for the cos theta question
K = 9 is correct
Trapezium question is solved using the 30,60 triangle and the 45,45 triangle . The diagnol side is 2 root 3 and the bottom is root 3
Factorising is correct
Isosceles proof is correct but i did it a different way

Posted from TSR Mobile
This is what happens when I rush and don't read questions and skip the information ffs.
x = -55 is right isn't it - the one with the bracket and to the power of 1/3 or something.
6. which question gives x=-55? That isn't right..you can't find square root of -55

(3-root x)^1/3 = -2

3-root x = (-2)^3
3-root x = -8
root x = 11
x = 121
7. There was a question related to completing the square in a quadratic equation and you were meant to answer in the form (a+-sqrt.b).
What if you solved it by using the quadratic formula
8. Its fine. Remember it's just 1 mark (implying 1 minute) and a waste of your time using quad form. Moreso, you've done in in part a.
9. With the question 8<x<12 apparently it asked for the integer values that x could be, i.e. 9,10,11
I put 8<x<12 but others said it asked for integers :/
10. (Original post by Mr sss)
Its fine. Remember it's just 1 mark (implying 1 minute) and a waste of your time using quad form. Moreso, you've done in in part a.
I dont think that question was 1 mark. And is it correct if you use the quad formula instead of completing the square?
11. (Original post by #1Mathlete)
With the question 8<x<12 apparently it asked for the integer values that x could be, i.e. 9,10,11
I put 8<x<12 but others said it asked for integers :/
That's okay. It's the same. 8<x<12 is actually cool. Not used by anyone on the street.
12. (Original post by Darshan98)
I dont think that question was 1 mark. And is it correct if you use the quad formula instead of completing the square?
Its question 12c..1 mark

12a...work out h and k........2 marks ....h=3....k= -7

12b....write down the coordinates of min point......1 mark ....(-3,-7)

And yes..its okay to use quad. form.
13. (Original post by Mr sss)
That's okay. It's the same. 8<x<12 is actually cool. Not used by anyone on the street.
It's not the same 8<x<12 is wrong as it's not the possible integer values, the actual answer is 9, 10 and 11
14. (Original post by Darshan98)
There was a question related to completing the square in a quadratic equation and you were meant to answer in the form (a+-sqrt.b).
What if you solved it by using the quadratic formula
Don't worry :P.

(Original post by #1Mathlete)
It's not the same 8<x<12 is wrong as it's not the possible integer values, the actual answer is 9, 10 and 11
Oh wait, one more question wrong. ffs. I never read questions.
Lol I actually wrote 9, 10 and 11 on my rough paper ffs.
15. I've dropped from 61-62 to around 56 OMG.
16. (Original post by Chittesh14)
I've dropped from 61-62 to around 56 OMG.
That is just an A* distinction i think depending on grade boundaries. I think i got 55 marks at the least

Posted from TSR Mobile
17. (Original post by Chittesh14)
Unofficial Markscheme:

Correct me if I'm wrong. The gaps are for answers I don't remember or questions.

3x^2 - 20x
a = 3, b = -20
12th term
3/5 limiting factor

-5, 8 - basically it was opposite the numbers in the brackets

m = 8, p = -1
8 < x < 12

x = -55
x^3 - 15x^2 + 75x - 125
-80, x = 16 and y = -1/5

h = 3, k = -7
-3, -7
-3 +/- root 7
Circle theorem:
180 - 3x
2x + 58 = 2(180 - 3x)
2x + 48 = 360 - 6x
8x = 312
x = 39
Another question: x = 45
When 3 is put into equation and a is 1, the equation is equal to 0.
(x-3)(x-7)(x+2) - use long division first to get quadratic then factorise it

2root7 - 4
5/6 for the cos and sine question?

k = 9

Use pythagoras theorem, 9 + 9 = 18, side = root 18 = 3 root 2
Trapezium - Idk, but I got the answer somehow: the bottom side of the triangle was root 3 and the hypotenuse was 2root3.
Add it all together: 3 + 3 + 3 + 2 root 3 + root 3 = 9 + 3 root 3, thats what u get when u expanded what they gave so it's correct.
x^4 - 81 (I think it was this) = (x^2 + 9)(x+3)(x-3)
Cosine rule.
Cos P = 1/3.
Use the rule, you find u have to do 4/12 to get 1/3.
So, you do 13n^2 - 4n^2 = 9n^2
That's w^2 so w = 3n.
w = 3n same as the other side, so the triangle is isoceles.
Which question was the x = -55 ?
18. For the inequality, t asked for integer solutions. Wouldn't you therefore have had to put 9, 10 and 11?
Other than that and question 6 (which I knew I'd completely messed up) I think I've done very well
19. Oh, also I didn't get +75x for the cubic, I got +25x. I'm probably wrong though haha
20. Can someone explain the limiting factor one and how it was 3/5? I though it was 2.4 cos then the denominator would equal 0 and the fraction would be undefined

Posted from TSR Mobile

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: June 28, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

Poll
Useful resources