OCR A Level Maths November 2020 Paper 2: question paper and mark scheme (H240/02)

3 A Level questions like these, with worked solutions

Written and checked by us, not taken from the OCR paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. Trigonometry · 5 marks

   Solve ${\text{cosec}}^{2}x+{\cot }^{2}x=3$ for $0^{\circ }\le x\le {360}^{\circ }$.

   Worked solution

   1. M1 for using the identity ${\text{cosec}}^{2}x=1+{\cot }^{2}x$ to obtain $1+2{\cot }^{2}x=3$.
   2. M1 for rearranging to ${\cot }^{2}x=1$.
   3. M1 for taking the square root to find $\tan x=\pm 1$.
   4. A1 for finding the principal values ${45}^{\circ }$ and ${135}^{\circ }$.
   5. A1 for stating all four correct solutions: ${45}^{\circ },{135}^{\circ },{225}^{\circ },{315}^{\circ }$.

2. Numerical methods · 7 marks

   $f(x)=x^3-3x-4$.
   (a) Show that $f(x)=0$ has a root in $(2,3)$. (2)
   (b) Rewrite the equation in the form $x=\sqrt[3]{3x+4}$ and use this iteration with $x_0=2$ to find $x_1,x_2,x_3,x_4$ each to 4 d.p. State the value of the root to 3 d.p. (5)

   Worked solution

   (a) $f(2)=8-6-4=-2<0$; $f(3)=27-9-4=14>0$   M1 A1.
   (b) $x_1=\sqrt[3]{10}=2.1544$; $x_2=\sqrt[3]{10.4633}=2.1872$; $x_3=\sqrt[3]{10.5616}=2.1940$; $x_4=\sqrt[3]{10.5821}=2.1955$   M1 A1 A1 A1. Root $\approx 2.196$   A1.

3. Sampling and data · 5 marks

   The data in a histogram is grouped into classes. A bar representing the class $100\le x<150$ has a width of $2.5\text{ cm}$ and a height of $4\text{ cm}$. The total area of all bars in the histogram is $90{\text{ cm}}^2$. If the bar for $100\le x<150$ represents a frequency of $20$, calculate the total frequency of the entire data set.

   Worked solution

   1. M1 for calculating the area of the specified bar: $2.5\times 4=10{\text{ cm}}^2$.
   2. M1 for establishing the relationship between area and frequency: $10{\text{ cm}}^2$ represents a frequency of $20$.
   3. A1 for calculating the scale factor: $1{\text{ cm}}^2$ represents $2$ items (since $20/10=2$).
   4. M1 for using the total area to find total frequency: $90{\text{ cm}}^2\times 2$.
   5. A1 for the final answer: $180$ items.

More on these topics: Trigonometry · Numerical methods · Sampling and data

What this paper covers

What this paper is like

• Shape: 15 questions, 100 marks in 2 h (about 1.2 minutes a mark); questions from 3 to 10 marks.
• Biggest question: Q15, 10 marks: discrete distribution and expectation.
• Marks by main topic: Sampling and data 19, Hypothesis testing 13, Statistical distributions 10, Differentiation 9, Integration 9, Trigonometry 8, Vectors 8, Probability 8, Sequences and series 7, Proof 5, Algebra and functions 4.
• More Statistical distributions in other sittings: November 2021 Q14 (11 marks), June 2019 Q12 (12 marks), June 2022 Q11 (7 marks).
• Against the other 7 sittings we mapped: more marks on Hypothesis testing (13 marks here, 5 on average) and Integration (9 marks here, 4 on average); fewer on Statistical distributions (10 marks here, 19 on average) and Coordinate geometry (0 marks here, 5 on average).
• Not on this paper: Coordinate geometry, Exponentials and logarithms, Numerical methods.
• Calculator: allowed.

H240/02: question by question

Labels and topics are ours, read from the H240/02 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Chain and product rules, and an integral (9 marks) · Differentiation, Integration
2. Q2Simplifying an algebraic fraction (4 marks) · Algebra and functions
3. Q3Binomial expansion and an approximation (7 marks) · Sequences and series
4. Q4Trig equation in radians (5 marks) · Trigonometry
5. Q5Pythagorean triples (5 marks) · Proof
6. Q6Proving a compound-angle identity (3 marks) · Trigonometry
7. Q7Position vectors and a ratio of lengths (8 marks) · Vectors
8. Q8Population model solved as a differential equation (9 marks) · Integration
9. Q9Histogram of car prices (4 marks) · Sampling and data
10. Q10Testing a chef's satisfaction claim (7 marks) · Hypothesis testing
11. Q11Grouped data: pebble masses (9 marks) · Sampling and data
12. Q12Testing a change in journey times (6 marks) · Hypothesis testing
13. Q13A three-point game: probability (8 marks) · Probability
14. Q14Large data set: young residents (6 marks) · Sampling and data
15. Q15Discrete distribution and expectation (10 marks) · Statistical distributions

Some Paper 2 statistics questions use OCR's pre-release large data set. We don't write large data set questions, so use your class materials for those.