Questions — OCR MEI AS Paper 2 (99 questions)

Browse by module
All questions AEA AS Paper 1 AS Paper 2 AS Pure C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 S1 S2 S3 S4 Unit 1 Unit 2 Unit 3 Unit 4
Browse by board
AQA AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Paper 1 Further Paper 2 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics M1 M2 M3 Paper 1 Paper 2 Paper 3 S1 S2 S3 CAIE FP1 FP2 Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 4 M1 M2 P1 P2 P3 S1 S2 Edexcel AEA AS Paper 1 AS Paper 2 C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 OCR AS Pure C1 C2 C3 C4 D1 D2 FD1 AS FM1 AS FP1 FP1 AS FP2 FP3 FS1 AS Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Mechanics Further Mechanics AS Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Statistics Further Statistics AS H240/01 H240/02 H240/03 M1 M2 M3 M4 PURE S1 S2 S3 S4 OCR MEI AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further Extra Pure Further Mechanics A AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Pure Core Further Pure Core AS Further Pure with Technology Further Statistics A AS Further Statistics B AS Further Statistics Major Further Statistics Minor M1 M2 M3 M4 Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 Pre-U Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 WJEC Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 Unit 1 Unit 2 Unit 3 Unit 4
Sort by: Default | Easiest first | Hardest first
OCR MEI AS Paper 2 2023 June Q6
6 marks Easy -1.8
6 An app on my new smartphone records the number of times in a day I use the phone. The data for each day since I bought the phone are shown in the stem and leaf diagram.
19
26
389
40122356799
5122234557899
601139
Key: 3|1 means 31
  1. Explain whether these data are a sample or a population.
  2. Describe the shape of the distribution.
  3. Determine the interquartile range.
  4. Use your answer to part (c) to determine whether there are any outliers in the lower tail.
OCR MEI AS Paper 2 2023 June Q7
4 marks Moderate -0.8
7
  1. Use the factor theorem to show that \(( x - 2 )\) is a factor of \(x ^ { 3 } + 6 x ^ { 2 } - x - 30\).
  2. Factorise \(x ^ { 3 } + 6 x ^ { 2 } - x - 30\) completely.
OCR MEI AS Paper 2 2023 June Q8
4 marks Moderate -0.5
8 The pre-release material contains information on Pulse Rate and Body Mass Index (BMI). A student is investigating whether there is a relationship between pulse rate and BMI. A section of the available data is shown in the table.
SexAgeBMIPulse
Male6229.5460
Female2023.68\#N/A
Male1726.9772
Male3524.764
Male1720.0954
Male8523.8654
Female8124.04\#N/A
The student decides to draw a scatter diagram.
  1. With reference to the table, explain which data should be cleaned before any analysis takes place. The student cleans the data for BMI and Pulse Rate in the pre-release material and draws a scatter diagram. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Scatter diagram of Pulse Rate against BMI} \includegraphics[alt={},max width=\textwidth]{82438df0-6550-4ffd-92d8-3c67bec59a6b-06_869_1575_1585_246}
    \end{figure} The student identifies one outlier.
  2. On the copy of the scatter diagram in the Printed Answer Booklet, circle this outlier. The student decides to remove this outlier from the data. They then use the LINEST function in the spreadsheet to obtain the following formula for the line of best fit. \(\mathrm { P } = 0.29 \mathrm { Q } + 64.2\),
    where \(P =\) PulseRate and \(Q = \mathrm { BMI }\). They use this to estimate the Pulse Rate of a person with BMI 23.68.
    They obtain a value of 71 correct to the nearest whole number.
  3. With reference to the scatter diagram, explain whether it is appropriate to use the formula for the line of best fit. It is suggested that all pairs of values where the pulse rate is above 100 should also be cleaned from the data, as they must be incorrect.
  4. Use your knowledge of the pre-release material to explain whether or not all pairs of values with a pulse rate of more than 100 should be cleaned from the data.
OCR MEI AS Paper 2 2023 June Q9
6 marks Easy -1.3
9 The table shows the probability distribution for the discrete random variable \(X\).
\(x\)12345
\(\mathrm { P } ( \mathrm { X } = \mathrm { x } )\)0.10.3\(q\)\(2 q\)\(3 q\)
You are given that \(q\) is a positive constant.
  1. Determine the value of \(q\).
  2. Calculate \(\mathrm { P } ( X \leqslant 4 )\). Two independent values of \(X\) are taken.
  3. Determine the probability that the sum of the two values is 3 . Fifty independent values of \(X\) are taken.
  4. Find the probability that a value of 2 occurs exactly 17 times.
OCR MEI AS Paper 2 2023 June Q10
5 marks Moderate -0.8
10 In this question you must show detailed reasoning.
The diagram shows triangle ABC , where \(\mathrm { AB } = 3.9 \mathrm {~cm} , \mathrm { BC } = 4.5 \mathrm {~cm}\) and \(\mathrm { AC } = 3.5 \mathrm {~cm}\). Determine the area of triangle ABC .
OCR MEI AS Paper 2 2023 June Q11
5 marks Moderate -0.8
11 In this question you must show detailed reasoning.
The equation of a curve is \(y = 2 x ^ { 3 } + 9 x ^ { 2 } + 24 x - 8\).
Show that there are no stationary points on this curve.
OCR MEI AS Paper 2 2023 June Q12
6 marks Easy -1.2
12 Doctors are investigating the weights of adult males registered at their surgery. One week they collect a sample by noting the weight in kilograms of all the adult males who have an appointment at their surgery.
  1. State the sampling method they use.
  2. Explain why this method will not generate a simple random sample of all the adult males registered at their surgery. They represent the data using a histogram. \includegraphics[max width=\textwidth, alt={}, center]{82438df0-6550-4ffd-92d8-3c67bec59a6b-09_1166_1243_726_233} An incomplete frequency table for the data is shown below.
    Weight in kg\(50 -\)\(65 -\)\(75 -\)\(80 -\)\(90 -\)\(100 - 120\)
    Frequency8
  3. Complete the copy of the frequency table in the Printed Answer Booklet. One of these patients is selected at random.
  4. Determine an estimate of the probability that he weighs either less than 60 kg or more than 110 kg .
  5. Explain why your answer to part (d) is an estimate and not exact.
OCR MEI AS Paper 2 2023 June Q13
6 marks Moderate -0.3
13 In a report published in October 2021 it is stated that \(37 \%\) of adults in the United Kingdom never exercise or play sport. A researcher believes that the true percentage is less than this. They decide to carry out a hypothesis test at the \(5 \%\) level to investigate the claim.
  1. State the null and alternative hypotheses for their test.
  2. Define the parameter for their test. In a random sample of 118 adults, they find that 35 of them never exercise or play sport.
  3. Carry out the test.
OCR MEI AS Paper 2 2023 June Q15
7 marks Moderate -0.3
15 A family is planning a holiday in Europe. They need to buy some euros before they go. The exchange rate, \(y\), is the number of euros they can buy per pound. They believe that the exchange rate may be modelled by the formula \(y = a t ^ { 2 } + b t + c\),
where \(t\) is the time in days from when they first check the exchange rate.
Initially, when \(t = 0\), the exchange rate is 1.14 .
  1. Write down the value of \(c\). When \(t = 2 , y = 1.20\) and when \(t = 4 , y = 1.25\).
  2. Calculate the values of \(a\) and \(b\). The family will only buy their euros when their model predicts an exchange rate of at least 1.29 .
  3. Determine the range of values of \(t\) for which, according to their model, they will buy their euros.
  4. Explain why the family's model is not viable in the long run.
OCR MEI AS Paper 2 2024 June Q1
3 marks Easy -1.8
1 Express \(2 x ( x + 3 ) + 5 x ^ { 2 } - 2 ( x - 3 )\) in the form \(a x ^ { 2 } + b x + c\), where \(a , b\) and \(c\) are integers to be determined.
OCR MEI AS Paper 2 2024 June Q2
3 marks Easy -1.2
2
  1. Find the discriminant of the equation \(3 x ^ { 2 } - 2 x + 5 = 0\).
  2. Use your answer to part (a) to find the number of real roots of the equation \(3 x ^ { 2 } - 2 x + 5 = 0\).
OCR MEI AS Paper 2 2024 June Q3
4 marks Easy -1.3
3 A student conducts an investigation into the number of hours spent cooking per week by people who live in village A. The student represents the data in the cumulative frequency diagram below. \section*{Hours spent cooking per week by people who live in village A} \includegraphics[max width=\textwidth, alt={}, center]{ce94c1ea-ffe5-42d0-8f8a-43c47105d6bf-3_796_1494_918_233}
  1. How many people were involved in the investigation?
  2. Use the copy of the diagram in the Printed Answer Booklet to determine an estimate for the interquartile range. The student conducts a similar investigation into the number of hours spent cooking per week by 200 people who live in village B. The interquartile range is found to be 3.9 hours.
  3. Explain whether the evidence suggests that the number of hours spent cooking by people who live in village B is more variable, equally variable or less variable than the number of hours spent cooking by people who live in village A .
OCR MEI AS Paper 2 2024 June Q4
3 marks Easy -1.2
4 In this question you must show detailed reasoning.
Express \(\frac { 1 + 4 \sqrt { 3 } } { 2 + \sqrt { 3 } }\) in the form \(\mathrm { a } + \mathrm { b } \sqrt { 3 }\), where \(a\) and \(b\) are integers to be determined.
OCR MEI AS Paper 2 2024 June Q5
3 marks Easy -1.8
5 The pre-release material contains information for countries in the world concerning real GDP per capita in US\$ and mobile phone subscribers per 100 population. In an investigation into the relationship between these two variables, a student takes a sample of 20 countries in Africa. The student draws a scatter diagram for the data, which is shown in Fig. 5.1. \section*{Fig. 5.1} \section*{Africa 1st sample} \includegraphics[max width=\textwidth, alt={}, center]{ce94c1ea-ffe5-42d0-8f8a-43c47105d6bf-4_433_1043_842_244}
  1. What does Fig. 5.1 suggest about the relationship between real GDP per capita and the number of mobile phone subscribers per 100 population? Another student collects a different sample of 20 countries from Africa, and draws a scatter diagram for the data, which is shown in Fig. 5.2. \section*{Fig. 5.2} \section*{Africa 2nd sample}
    \includegraphics[max width=\textwidth, alt={}]{ce94c1ea-ffe5-42d0-8f8a-43c47105d6bf-4_273_1084_1818_244}
    Mobile phone subscribers per 100 population
  2. What does Fig. 5.2 suggest about the relationship between real GDP per capita and the number of mobile phone subscribers per 100 population?
  3. Explain whether either of the two scatter diagrams is likely to be representative of the true relationship between real GDP per capita and the number of mobile phone subscribers per 100 population, for countries in Africa.
OCR MEI AS Paper 2 2024 June Q6
4 marks Easy -1.2
6 Determine the equation of the line which passes through the point \(( 4 , - 1 )\) and is perpendicular to the line with equation \(2 x + 3 y = 6\). Give your answer in the form \(y = m x + c\), where \(m\) is a fraction in its lowest terms and \(c\) is an integer.
OCR MEI AS Paper 2 2024 June Q7
4 marks Moderate -0.8
7 Determine the coefficient of \(x ^ { 5 }\) in the expansion of \(( 3 - 2 x ) ^ { 7 }\).
OCR MEI AS Paper 2 2024 June Q9
6 marks Easy -1.3
9 A fair six-sided die has its faces numbered 1, 3, 4, 5, 6 and 7. The die is rolled once. \(A\) is the event that the die shows an even number. \(B\) is the event that the die shows a prime number.
  1. Write down the value of \(\mathrm { p } ( A )\).
  2. Write down the value of \(\mathrm { p } ( B )\).
  3. Write down the value of \(\mathrm { p } ( A\) or \(B )\). The die is rolled again.
  4. Calculate the probability that the sum of the scores from the two rolls is even.
OCR MEI AS Paper 2 2024 June Q10
6 marks Easy -1.2
10 The pre-release material contains information about the birth rate per 1000 people in different countries of the world. These countries have been classified into different regions. The table shows some data for three of these regions: the mean and standard deviation (sd) of the birth rate per 1000, and the number of countries for which data was used, n. \section*{Birth rate per 1000 by region}
AfricaEuropeOceania
\(n\)554921
mean29.310.017.8
sd8.431.944.50
  1. Use the information in the table to compare and contrast the birth rate per 1000 in Africa with the birth rate per 1000 in Europe.
  2. The birth rate per 1000 in Mauritius, which is in Africa, is recorded as 9.86. Use the information in the table to show that this value is an outlier.
  3. Use your knowledge of the pre-release material to explain whether the value for Mauritius should be discarded.
  4. The pre-release material identifies 27 countries in Oceania. Suggest a reason why only 21 values were used to calculate the mean and standard deviation.
OCR MEI AS Paper 2 2024 June Q12
6 marks Moderate -0.8
12 Data collected in the twentieth century showed that the probability of a randomly selected person having blue eyes was 0.08 . A medical researcher believes that the probability in 2024 is less than this so they decide to carry out a hypothesis test at the \(5 \%\) significance level.
  1. Write down suitable hypotheses for the test, defining the parameter used.
  2. Assuming that the probability that a person selected at random has blue eyes is still 0.08 , calculate the probability that 3 or fewer people in a random sample of 92 people have blue eyes. The researcher collects a random sample of 92 people and finds that 3 of them have blue eyes.
  3. Use your answer to part (b) to carry out the test, giving your conclusion in context.
OCR MEI AS Paper 2 2024 June Q13
5 marks Moderate -0.8
13 Determine the range of values of \(x\) for which \(y = 4 x ^ { 3 } + 7 x ^ { 2 } - 6 x + 8\) is a decreasing function.
OCR MEI AS Paper 2 2024 June Q14
6 marks Standard +0.3
14 In this question you must show detailed reasoning.
Solve the equation \(5 - \cos \theta - 6 \sin ^ { 2 } \theta = 0\) for \(0 ^ { \circ } < \theta < 360 ^ { \circ }\). Turn over for question 15
OCR MEI AS Paper 2 2024 June Q15
7 marks Moderate -0.8
15 Ali and Sam are playing a game in which Ali tosses a coin 5 times. If there are 4 or 5 heads, Ali wins the game. Otherwise Sam wins the game. They decide to play the game 50 times.
  1. Initially Sam models the situation by assuming the coin is fair. Determine the number of games Ali is expected to win according to this model. Ali thinks the coin may be biased, with probability \(p\) of obtaining heads when the coin is tossed. Before playing the game, Ali and Sam decide to collect some data to estimate the value of \(p\). Sam tosses the coin 15 times and records the number of heads obtained. Ali tosses the coin 25 times and records the number of heads obtained.
  2. Explain why it is better to use the combined data rather than just Sam's data or just Ali's data to estimate the value of \(p\). Ali records 20 heads and Sam records 8 heads.
  3. Use the combined data to estimate the value of \(p\). Ali now models the situation using the value of \(p\) found in part (c) as the probability of obtaining heads when the coin is tossed.
  4. Determine how many games Ali expects to win using this value of \(p\) to model the situation.
  5. Ali wins 25 of the 50 games. Explain whether Sam's model or Ali's model is a better fit for the data. \section*{END OF QUESTION PAPER} }{www.ocr.org.uk}) after the live examination series.
    If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible opportunity.
    For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.
    OCR is part of Cambridge University Press \& Assessment, which is itself a department of the University of Cambridge.
OCR MEI AS Paper 2 2020 November Q1
2 marks Easy -1.8
1 Solve the inequality \(2 x + 5 < 6 x - 3\).
OCR MEI AS Paper 2 2020 November Q2
3 marks Moderate -0.8
2 A student measures the upper arm lengths of a sample of 97 women. The results are summarised in the frequency table in Fig. 2.1. \begin{table}[h]
Arm length in cm\(30 -\)\(31 -\)\(32 -\)\(33 -\)\(34 -\)\(35 -\)\(36 -\)\(37 -\)\(38 -\)\(39 -\)\(40 - 41\)
Frequency145913191717435
\captionsetup{labelformat=empty} \caption{Fig. 2.1}
\end{table} The student constructs two cumulative frequency diagrams to represent the data using different class intervals. These are shown in Fig. 2.2 opposite One of these diagrams is correct and the other is incorrect.
  1. State which diagram is incorrect, justifying your answer.
  2. Use the correct diagram in Fig. 2.2 to find an estimate of the median. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{c08a2212-3104-425e-8aee-7f2d46f23924-05_2256_1230_191_148} \captionsetup{labelformat=empty} \caption{Fig. 2.2}
    \end{figure}
OCR MEI AS Paper 2 2020 November Q3
8 marks Easy -1.8
3 A researcher is conducting an investigation into the number of portions of fruit adults consume each day. The researcher decides to ask 50 men and 50 women to complete a simple questionnaire.
  1. State the type of sampling procedure the researcher is using.
  2. Write down one disadvantage of this sampling procedure. The researcher represents the data in Fig. 3.1. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Number of portions of fruit consumed by adults} \includegraphics[alt={},max width=\textwidth]{c08a2212-3104-425e-8aee-7f2d46f23924-06_531_991_701_248}
    \end{figure} Fig. 3.1
  3. Describe the shape of the distribution. The data are summarised in the frequency table in Fig. 3.2. \begin{table}[h]
    Number of portions of fruit012345
    Number of adults1834261174
    \captionsetup{labelformat=empty} \caption{Fig. 3.2}
    \end{table}
  4. For the data in Fig. 3.2, use your calculator to find
    Give your answers correct to 2 decimal places. A second researcher chooses a proportional stratified sample of 100 children from years 5 and 6 in a certain primary school. There are 220 children to choose from. In year 5 there are 125 children, of whom 81 are boys.
  5. How many year 5 girls should be included in the sample? The second researcher found that the mean number of portions of fruit consumed per day by the children in this sample was 1.61 and the standard deviation was 0.53 .
  6. Comment on the amount of fruit consumed per day by the children compared to the amount of fruit consumed per day by the adults.