Questions — OCR MEI Paper 2 (129 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 Paper 2 Specimen Q13
6 marks Challenging +1.2
Evaluate \(\int_0^1 \frac{1}{1 + \sqrt{x}} \, dx\), giving your answer in the form \(a + b \ln c\), where \(a\), \(b\) and \(c\) are integers. [6]
OCR MEI Paper 2 Specimen Q14
12 marks Standard +0.3
In a chemical reaction, the mass \(m\) grams of a chemical at time \(t\) minutes is modelled by the differential equation $$\frac{dm}{dt} = \frac{m}{t(1 + 2t)}.$$ At time 1 minute, the mass of the chemical is 1 gram.
  1. Solve the differential equation to show that \(m = \frac{3t}{(1 + 2t)}\). [8]
  2. Hence
    1. find the time when the mass is 1.25 grams, [2]
    2. show what happens to the mass of the chemical as \(t\) becomes large. [2]
OCR MEI Paper 2 Specimen Q15
15 marks Standard +0.3
A quality control department checks the lifetimes of batteries produced by a company. The lifetimes, \(x\) minutes, for a random sample of 80 'Superstrength' batteries are shown in the table below.
Lifetime\(160 \leq x < 165\)\(165 \leq x < 168\)\(168 \leq x < 170\)\(170 \leq x < 172\)\(172 \leq x < 175\)\(175 \leq x < 180\)
Frequency5142021164
  1. Estimate the proportion of these batteries which have a lifetime of at least 174.0 minutes. [2]
  2. Use the data in the table to estimate
    [3]
The data in the table on the previous page are represented in the following histogram, Fig 15. \includegraphics{figure_15} A quality control manager models the data by a Normal distribution with the mean and standard deviation you calculated in part (b).
  1. Comment briefly on whether the histogram supports this choice of model. [2]
    1. Use this model to estimate the probability that a randomly selected battery will have a lifetime of more than 174.0 minutes.
    2. Compare your answer with your answer to part (a). [3]
The company also manufactures 'Ultrapower' batteries, which are stated to have a mean lifetime of 210 minutes.
  1. A random sample of 8 Ultrapower batteries is selected. The mean lifetime of these batteries is 207.3 minutes. Carry out a hypothesis test at the 5% level to investigate whether the mean lifetime is as high as stated. You should use the following hypotheses \(\text{H}_0 : \mu = 210\), \(\text{H}_1 : \mu < 210\), where \(\mu\) represents the population mean for Ultrapower batteries. You should assume that the population is Normally distributed with standard deviation 3.4. [5]
OCR MEI Paper 2 Specimen Q16
20 marks Easy -1.8
Fig. 16.1, Fig. 16.2 and Fig. 16.3 show some data about life expectancy, including some from the pre-release data set. \includegraphics{figure_16_1} \includegraphics{figure_16_2} \includegraphics{figure_16_3}
  1. Comment on the shapes of the distributions of life expectancy at birth in 2014 and 1974. [2]
    1. The minimum value shown in the box plot is negative. What does a negative value indicate? [1]
    2. What feature of Fig 16.3 suggests that a Normal distribution would not be an appropriate model for increase in life expectancy from one year to another year? [1]
    3. Software has been used to obtain the values in the table in Fig. 16.3. Decide whether the level of accuracy is appropriate. Justify your answer. [1]
    4. John claims that for half the people in the world their life expectancy has improved by 10 years or more. Explain why Fig. 16.3 does not provide conclusive evidence for John's claim. [1]
  3. Decide whether the maximum increase in life expectancy from 1974 to 2014 is an outlier. Justify your answer. [3]
Here is some further information from the pre-release data set.
CountryLife expectancy at birth in 2014
Ethiopia60.8
Sweden81.9
    1. Estimate the change in life expectancy at birth for Ethiopia between 1974 and 2014.
    2. Estimate the change in life expectancy at birth for Sweden between 1974 and 2014.
    3. Give one possible reason why the answers to parts (i) and (ii) are so different. [4]
Fig. 16.4 shows the relationship between life expectancy at birth in 2014 and 1974. \includegraphics{figure_16_4} A spreadsheet gives the following linear model for all the data in Fig 16.4. (Life expectancy at birth 2014) = 30.98 + 0.67 × (Life expectancy at birth 1974) The life expectancy at birth in 1974 for the region that now constitutes the country of South Sudan was 37.4 years. The value for this country in 2014 is not available.
    1. Use the linear model to estimate the life expectancy at birth in 2014 for South Sudan. [2]
    2. Give two reasons why your answer to part (i) is not likely to be an accurate estimate for the life expectancy at birth in 2014 for South Sudan. You should refer to both information from Fig 16.4 and your knowledge of the large data set. [2]
  2. In how many of the countries represented in Fig. 16.4 did life expectancy drop between 1974 and 2014? Justify your answer. [3]