Advanced Higher Maths 2019 Unofficial Markscheme

@leavemeblank

Hey hope you don't mind but I moved this to a separate thread to make it easier for people to find

What is the working for Q18. I was really confused by it.
Thanks in advance

Has anyone got working for Q6, 10b and 13 as well?

For Q7b, in the brackets is it not just p in the brackets instead of (p+1)?

Yep, thank you. Just realised I made this mistake in the exam!

That’s my working for 10)b)
And that’s the working for 13) however my answer ain’t the same as what the original posts answer so so idk with 13 tbh

Sort of unofficial marking scheme for AH Maths 2019:

1. Differentiation (a) 6x^5cot5x - 5x^6cosec^2(5x) (b) -27x^2/(x^3-4)^2 (c) - 4
2. Matrix algebra (a) p = -3 (b) Row 1: q+16, 5, Row 2: 8 - 3q, -12, Row 3: 20 - 2q, -7) (c) Not a square matrix
3. Graphs (a) Even as symmetrical about x-axis: f(x) = f(-x) (b) reflection of negative parts across x-axis (w shape)
4. Partial fractions (a) 3 + (4x+19)/(x^2-x+12) (b) 3 + 5/(4-x) - 1/(x+3)
5. Parametric differentiation (a) 2t^2 + 7t (b) 1/2(8t^2 + 42t + 49)
6. Related rates of change: -5/3π cm^3s^-1 (units usually required!)
7. Summation formula: (a) 3n^2 + 16n (b) 1520 - 3p^2 - 16p
8. Homogenous second order differential equation: y = 3e^-4x -3e^-7x
9. Binomial theorem general term: (a) (7Cr)(2)^7-r(-d)^r(x)^14-5r (b) d = 5
10. Implicit differentiation (a) dy/dx = y-2x/2y-x (b) k = +/- 2
11. Proof by counterexample and contrapositive (a) n=4,n=7 or n=0, etc. (b) if n is even, n^2-2n+7 is odd. (ii) Proof
12. Number bases (application of division algorithm): 276 to the base 10 = 543 to the base 7.
13. Variables separable differential equation: V =e^kt + 2 (not V = 12 - 10e^-kt)
14. Proof by induction: prove true for n=1, LHS = RHS = 1, assume true for n = k, consider n = k + 1
Summation of k+1 from n=1 r! r = (k + 1)! - 1 + (k+1)!(k+1) = (k+1)! + (k+1)!(k+1) - 1 = (k+1)![1 + k+1] - 1 = (k+1)!(k+2) - 1 = (k + 2)! - 1 = ((k+1)+1)! -1 therefore true for n = k+1. If true for n=k, also true for n=k+1 but since also true for n=1, by induction true for all positive integers, n.
15. Vectors. (a) Sub parametric equations into the equation of plane to prove. (b) Angle = 90-cos^-1(n.d/|n||d|) = 13.15 degrees
(c) Don't intersect - not sure if this is right but I did the cross product with π3 and L1 for the d vector, got parametric equations, solved for the separate variables and as they didn't satisfy both of the z co-ordinates, no intersection.
16. Applied integration: (a) 1/32(e^4 - 13) (b) π/2(e^4 - 13) units^3
17. (a) 63, -21, 7 hence r = -1/3 (b)(i) -1 < -1/3 < 1. (ii) 189/4 (47.25) (c) (i) ar^2/ar = ar/a gives quadratic when cross multiply, solve for x= -3. (ii) -7, 7, -7 (iii) S2n = 0 as (1-r^n) = 0.
18. (a) (i) a - root3ai (ii) w = 2a (cos (-π/3) + isin (-π/3) (b) (i) k=2, m = -9 (ii) Really not sure on this one, keep changing my mind but 2(cos5π/9 + isin5π/9) and 2(cos-7π/9 + isin(-7π/9).

There we go! Let me know if there's any mistakes and disagreements. This is generally the consensus on what has already been discussed above. Remember there's no chance this is 100% accurate and you will always get partial and follow through marks if you make any mistakes. DLB Maths have started uploading solutions so check them out! -
https://www.youtube.com/user/DLBmaths/videos

For 13, im think the answer is the other way around V = 12 - 10e^-kt Not, V =e^kt + 2

Are these all your answers though? Let's just say I did waaaaaayyyyyyy worse that you :/

For 13, im think the answer is the other way around V = 12 - 10e^-kt Not, V =e^kt + 2

2019 Advanced Higher Mathematics Worked Solutions