# A-level Maths Pure Mathematics 2 9MA0_02 Unofficial markschemeWatch

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11 months ago
#21
What was the explanation for the decreasing function? dy/dx<0, which I proved by the denominator being positive since its always squared and numerators are negative. I got the part before it wrong though because of incorrect division.
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11 months ago
#22
(Original post by thekidwhogames)
How did you find it; 95+? It was quite challenging and nice
Yeah there were some nice questions. I think it was harder than paper 1, but I think I did good. 95+ is a good estimate, I don't think I really slipped up anywhere.

It's confusing because there were 2 tan questions. For one of the tan questions, yeah there were three solutions (the one that asks for solns between 7pi and 10pi)
There was a another tan question where you had to turn sec^2 into 1+tan^2, and then you get a 3TQ in terms of tan. It's coming back to me as I'm writing.
I remember it factorising into (tan theta + 1)(tan theta -4) = 0
And it asked for solns for theta between -pi/2 and pi/2.
It's -pi/4 and 1.326,
2 solutions.
Unless I'm misremembering / misread the question
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11 months ago
#23
(Original post by thekidwhogames)
Challenging exam, I think I got 96. Bloody he'll compared to old spec
You think it was difficult...but that you got only 4 marks wrong! :O that's amazing
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11 months ago
#24
(Original post by UrBusted)
What was the explanation for the decreasing function? dy/dx<0, which I proved by the denominator being positive since its always squared and numerators are negative. I got the part before it wrong though because of incorrect division.
yeah that's what I did.
Denominators for both terms were something squared, so it's positive,
Numerators for both were -4,
two negative numbers added together makes a negative number.
Negative dy/dx for all x => decreasing function
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11 months ago
#25
(Original post by RedGiant)
Thanks for the input, I'll add these in.

Although I got 3 solutions for the tanx equation. I tested them as well.
These were some of my answers, not saying they are all necessarily correct.
1. g(x) = 2x+5/x-3
a) gg(5) = 40/9
b) 2<g(x)<=7.5
c) g^-1(x) = 3x+5/x-2
Domain = part b

2. a) 6i-7j+10k
b) mod (a)= 2-2root2

3. Prove if m and n are irrational, then mn is not necessarily irrational (disprove with counter-example). Easiest method is m=root 2 and n=root 8

4. Prove 16E1 (3+5r+2^r) = 131798 (split up sigma function)
ii) 325/3

5. Newton Raphson
a) Prove equation for N-R
b) approximation 1 = 3/4
approximation 2 = 2/3
c) Newton Raphson fails at x=0 because f'(x) = 0, so it results in division by zero which is invalid.

6. a) f(2) = 0
b) f(x) = (x-2)(-3x^2+2x-5)
c) 2 solutions (y=+2 or -2)
d) 1 solution (tan equation)

7. a) Show that - in m.s. already
b) pi/12, 5pi/12
c) 61.4 degrees and 208.6 degrees (1 d.p)

8. a) Modelling question: H=-0.03x^2+1.2x
b) Equal H to 3 I think? Quadratic gives 2 solutions, pick greater one
c) Unreliable model as air resistance is not taken into account, which may have an impact on the trajectory.

9. Diff from 1st principles

10. a) R=(-24.5t+125)^1/3 (same as cube root)
b) 5 minutes 6 seconds

11. a) Partial fractions: A=3, B=4, C=-2
b) Show that function is always decreasing - For f'(x), the denominators are always positive (xyz)^2 and numerators are negative. Negative + Negative = negative, so f'(x) is always negative.

12. a) Show that
b) pi/4 and 1.326 (unsure about this one)

13. Integration area under graph. A=5/4, B=1/4
split into triangle and area under xlnx curve, and add together at end.

14. a) Initial mice pop = 90
b) -4ln(3/7)
c) Show that dN/dt = ...
d) Max no. of mice = 300
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11 months ago
#26
(Original post by sivthasan)
These were some of my answers, not saying they are all necessarily correct.
1. g(x) = 2x+5/x-3
a) gg(5) = 40/9
b) 2<g(x)<=7.5
c) g^-1(x) = 3x+5/x-2
Domain = part b

2. a) 6i-7j+10k
b) mod (a)= 2-2root2

3. Prove if m and n are irrational, then mn is not necessarily irrational (disprove with counter-example). Easiest method is m=root 2 and n=root 8

4. Prove 16E1 (3+5r+2^r) = 131798 (split up sigma function)
ii) 325/3

5. Newton Raphson
a) Prove equation for N-R
b) approximation 1 = 3/4
approximation 2 = 2/3
c) Newton Raphson fails at x=0 because f'(x) = 0, so it results in division by zero which is invalid.

6. a) f(2) = 0
b) f(x) = (x-2)(-3x^2+2x-5)
c) 2 solutions (y=+2 or -2)
d) 1 solution (tan equation)

7. a) Show that - in m.s. already
b) pi/12, 5pi/12
c) 61.4 degrees and 208.6 degrees (1 d.p)

8. a) Modelling question: H=-0.03x^2+1.2x
b) Equal H to 3 I think? Quadratic gives 2 solutions, pick greater one

9. Diff from 1st principles

10. a) R=(-24.5t+125)^1/3 (same as cube root)
b) 5 minutes 6 seconds

11. a) Partial fractions: A=3, B=4, C=-2
b) Show that function is always decreasing - For f'(x), the denominators are always positive (xyz)^2 and numerators are negative. Negative + Negative = negative, so f'(x) is always negative.

12. a) Show that
b) pi/4 and 1.326 (unsure about this one)

13. Integration area under graph. A=5/4, B=1/4
split into triangle and area under xlnx curve, and add together at end.

14. a) Initial mice pop = 90
b) -4ln(3/7)
c) Show that dN/dt = ...
d) Max no. of mice = 300
This is looking very nice, I'd agree with all of it. Only thing I would say is 6d) is three solutions since it asked for solution between 7pi and 10pi
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Thread starter 11 months ago
#27
(Original post by sivthasan)
These were some of my answers, not saying they are all necessarily correct.
1. g(x) = 2x+5/x-3
a) gg(5) = 40/9
b) 2<g(x)<=7.5
c) g^-1(x) = 3x+5/x-2
Domain = part b

2. a) 6i-7j+10k
b) mod (a)= 2-2root2

3. Prove if m and n are irrational, then mn is not necessarily irrational (disprove with counter-example). Easiest method is m=root 2 and n=root 8

4. Prove 16E1 (3+5r+2^r) = 131798 (split up sigma function)
ii) 325/3

5. Newton Raphson
a) Prove equation for N-R
b) approximation 1 = 3/4
approximation 2 = 2/3
c) Newton Raphson fails at x=0 because f'(x) = 0, so it results in division by zero which is invalid.

6. a) f(2) = 0
b) f(x) = (x-2)(-3x^2+2x-5)
c) 2 solutions (y=+2 or -2)
d) 1 solution (tan equation)

7. a) Show that - in m.s. already
b) pi/12, 5pi/12
c) 61.4 degrees and 208.6 degrees (1 d.p)

8. a) Modelling question: H=-0.03x^2+1.2x
b) Equal H to 3 I think? Quadratic gives 2 solutions, pick greater one
c) Unreliable model as air resistance is not taken into account, which may have an impact on the trajectory.

9. Diff from 1st principles

10. a) R=(-24.5t+125)^1/3 (same as cube root)
b) 5 minutes 6 seconds

11. a) Partial fractions: A=3, B=4, C=-2
b) Show that function is always decreasing - For f'(x), the denominators are always positive (xyz)^2 and numerators are negative. Negative + Negative = negative, so f'(x) is always negative.

12. a) Show that
b) pi/4 and 1.326 (unsure about this one)

13. Integration area under graph. A=5/4, B=1/4
split into triangle and area under xlnx curve, and add together at end.

14. a) Initial mice pop = 90
b) -4ln(3/7)
c) Show that dN/dt = ...
d) Max no. of mice = 300
Thanks for your answers, have added them in.
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11 months ago
#28
I got -4ln(3/7) also was x=0 A solution for the tanxsin2x one?
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11 months ago
#29
(Original post by have)
This is looking very nice, I'd agree with all of it. Only thing I would say is 6d) is three solutions since it asked for solution between 7pi and 10pi
The tan equation looked complex so it put me off a bit. I only got 1 solution in that range so I probably messed up part d).
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11 months ago
#30
(Original post by DefiniteIntegral)
I got -4ln(3/7) also was x=0 A solution for the tanxsin2x one?
iirc, you had to discard x=0, because it led to having to divide by 0 somewhere in the expression. But I'm having doubts in my mind now about that.
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11 months ago
#31
(Original post by have)
4c) A better comment imo would be to say that the model implies the ball has negative height after 40m.
I disagree, it could have negative height (e.g. if it stuck in the ground). Check your textbook on parabolic motion, it clearly states that air resistance is what makes most models unrealistic.
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11 months ago
#32
(Original post by have)
iirc, you had to discard x=0, because it led to having to divide by 0 somewhere in the expression. But I'm having doubts in my mind now about that.
Okay, makes sense I was unsure myself but put it down because I thought you ought to if you cancelled the sin2x on each side for your quadratic in tan. Didn’t have time to check.
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11 months ago
#33
I'm at GCSE and considering Maths A-Level, would you recommend it?
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11 months ago
#34
(Original post by Year10Studentt)
I'm at GCSE and considering Maths A-Level, would you recommend it?
If you're good at maths, and like maths, definitely.
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Thread starter 11 months ago
#35
(Original post by Year10Studentt)
I'm at GCSE and considering Maths A-Level, would you recommend it?
Yeah go for it, maths skills are desirable in just about any career.
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11 months ago
#36
(Original post by DefiniteIntegral)
I got -4ln(3/7) also was x=0 A solution for the tanxsin2x one?
Yeh think i got 0 as well, i think i put it back in to check and it worked but can't remember, can only hope.
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11 months ago
#37
(Original post by have)
If you're good at maths, and like maths, definitely.
I feel really confident about GCSE maths and love the subject. However, I looked at AS papers and I couldn't answer any questions in them. Did you already know how to answer AS questions from GCSEs, because you were naturally good at maths or were you taught it all?
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11 months ago
#38
(Original post by Year10Studentt)
I feel really confident about GCSE maths and love the subject. However, I looked at AS papers and I couldn't answer any questions in them. Did you already know how to answer AS questions from GCSEs, because you were naturally good at maths or were you taught it all?
You're not gonna be able to do AS papers if you haven't been taught the content lmao. Same with any subject. Being good at maths is part of it, but you need to be taught the content in the first place. Don't let the papers scare you, you progress quickly in terms of content, especially if you take Further Maths
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11 months ago
#39
(Original post by have)
You're not gonna be able to do AS papers if you haven't been taught the content lmao. Same with any subject. Being good at maths is part of it, but you need to be taught the content in the first place. Don't let the papers scare you, you progress quickly in terms of content, especially if you take Further Maths
that's what I thought but I just thought I'd get into the class and people would start picking up concepts faster than me, which I'd be nervous about falling behind
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Thread starter 11 months ago
#40
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