The Student Room Group

Further Maths GCSE AQA Paper 1 (Unofficial mark scheme)

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 :smile:.
(edited 7 years ago)

Scroll to see replies

I got 39 degrees for the circle theorems question
Reply 2
Original post by mattedwards8972
I got 39 degrees for the circle theorems question


Oh yeah thanks buddy :smile:.
180 - 3x

2x + 58 = 2(180 - 3x)
2x + 48 = 360 - 6x
8x = 312
x = 39? :smile:
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
Root 10? - radius

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
So the answer is -80
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
:smile:
Posted from TSR Mobile
Reply 4
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
So the answer is -80
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
:smile:
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.
(edited 7 years ago)
Reply 5
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
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 :frown:
Reply 7
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.
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 :/
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?
Reply 10
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.
Reply 11
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.
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
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 :frown:


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.
I've dropped from 61-62 to around 56 OMG.
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
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
Root 10 - radius

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 ?
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 :biggrin:
Oh, also I didn't get +75x for the cubic, I got +25x. I'm probably wrong though haha
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

Quick Reply