2023 H2 Mathematics Paper 1 Answers

Short answers to the A Level H2 Math Paper.

Click on the question number to access full solutions.

{{y = - 10 \mathrm{e} x + 21 \mathrm{e}.}}

2 .

(a)

{{u_n = 4 n^3 + 23 n^2 - 46 n + 29.}}

(b)

{{n \geq 17.}}

3 .

(a)

{{\left| \mathbf{a} \times \mathbf{b} \right| = 1.}}

(b)

{{\theta = 135 \degree.}}

4 .

(a)

{{\frac{\sin (p+q)x}{2(p+q)} + \frac{\sin (p-q)x}{2(p-q)} + C.}}

(b)

{{\frac{x \sin nx}{n} + \frac{\cos nx}{n^2} + c.}}

(c)

{{k = -2}}

{{k = 0.}}

(d)

{{\frac{\pi}{4}.}}

5 .

(a)

{{ \ln \left( \frac{n+1}{n} \right) - \ln 2.}}

(b)

{{ - \ln 2.}}

(c)

{{ \ln \frac{189}{200}.}}

6 .

(a)

Show question.

(b)

{{\frac{81 \pi}{8} \left( \pi - \frac{9}{8} \sqrt{3} \right).}}

7 .

(a)

Asymptotes: ${{y=2}}$ and ${{x=3.}}$

(b)

{{ R_f = \left[ 0, \infty \right).}}

(c)

{{ R_f \not \subseteq D_f.}}

(d)

Greatest value of ${{a = -2.}}$

(e)

{{ f^{-1}(x) = \frac{4+3x}{x-2}.}}

{{ D_{f^{-1}} = \left[ 0, 2 \right).}}

8 .

(a)

{{ z = 2 \mathrm{e}^{\frac{2}{3} \pi \mathrm{i}}.}}

(b)

Smallest positive integer ${{ n = 2.}}$

(c)

{{w = - 4 + 3 \mathrm{i}, v = - 2}}

{{\quad w = - 4 + \frac{21}{5} \mathrm{i}, v = - \frac{12}{5}.}}

9 .

(a)

{{a=2.}}

Coordinates of

{{B = \left( 1, 3, 6 \right).}}

(bi)

{{ \frac{20}{\sqrt{14}}.}}

(bii)

{{ \theta = 63.0 \degree.}}

(c)

{{- 3 x + 4 y + z = 15.}}

10 .

(a)

{{\frac{\operatorname{d}\!M}{\operatorname{d}\!t} = k \left( C - 30M \right).}}

(b)

{{3300.}}

(c)

{{ M = 88 + 22 \operatorname{e}^{-30kt}.}}

(d)

{{51. }}

(ei)

(eii)

{{0 < C < 2400.}}

11 .

(a)

Smallest ${{a= 513.89.}}$

(b)

{{400000(1.001)^n -}}

{{1000x (1.001^n - 1).}}

(ci)

{{\$ 1323.63.}}

(cii)

{{\$ 76508.52.}}

(di)

{{k = 287}}

{{y = 1321.54.}}

(dii)

{{\$15990.}}