Questions — Edexcel FS2 AS (30 questions)

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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 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 Mechanics 1 PURE Pure 1 S1 S2 S3 S4 Stats 1 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 SPS SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics 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
Edexcel FS2 AS 2024 June Q5
  1. A random sample of 24 adults is taken. The height, \(h\) metres, and the arm span, \(s\) metres, for each adult are recorded.
These data are summarised below. $$\mathrm { S } _ { h h } = 0.377 \quad \mathrm {~S} _ { s h } = 0.352 \quad \bar { s } = 1.70 \quad \bar { h } = 1.68$$ The least squares regression line of \(h\) on \(s\) is $$h = a + 0.919 s$$ where \(a\) is a constant.
  1. Calculate the product moment correlation coefficient. A doctor uses the least squares regression line of \(h\) on \(s\) as a model to predict a person's height based on their arm span.
  2. Use the model to predict the height of an adult with arm span 1.79 metres. Ewan has an arm span of 1.70 metres and a height of 1.75 metres. His information is added to the sample as the 25th adult.
  3. Explain how the gradient of the regression line for the sample of 25 adults compares with the gradient of the regression line for the original sample of 24 adults.
    Give a reason for your answer.
Edexcel FS2 AS Specimen Q1
  1. In a gymnastics competition, two judges scored each of 8 competitors on the vault.
CompetitorABCDEFGH
J udge 1's scores4.69.18.48.89.09.59.29.4
J udge 2's scores7.88.88.68.59.19.69.09.3
  1. Calculate Spearman’s rank correlation coefficient for these data.
  2. Stating your hypotheses clearly, test at the \(1 \%\) level of significance, whether or not the two judges are generally in agreement.
  3. Give a reason to support the use of Spearman's rank correlation coefficient in this case. The judges also scored the competitors on the beam.
    Spearman's rank correlation coefficient for their ranks on the beam was found to be 0.952
  4. Compare the judges’ ranks on the vault with their ranks on the beam.
Edexcel FS2 AS Specimen Q2
  1. The continuous random variable \(X\) has probability density function
$$f ( x ) = \begin{cases} \frac { 1 } { 18 } ( 11 - 2 x ) & 1 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$
  1. Find \(\mathrm { P } ( \mathrm { X } < 3 )\)
  2. State, giving a reason, whether the upper quartile of \(X\) is greater than 3, less than 3 or equal to 3 Given that \(\mathrm { E } ( \mathrm { X } ) = \frac { 9 } { 4 }\)
  3. use algebraic integration to find \(\operatorname { Var } ( \mathrm { X } )\) The cumulative distribution function of \(X\) is given by $$F ( x ) = \left\{ \begin{array} { l r } 0 & x < 1
    \frac { 1 } { 18 } \left( 11 x - x ^ { 2 } + c \right) & 1 \leqslant x \leqslant 4
    1 & x > 4 \end{array} \right.$$
  4. Show that \(\mathrm { c } = - 10\)
  5. Find the median of \(X\), giving your answer to 3 significant figures. \section*{Q uestion 2 continued}
Edexcel FS2 AS Specimen Q3
  1. A scientist wants to develop a model to describe the relationship between the average daily temperature, \(\mathrm { x } ^ { \circ } \mathrm { C }\), and a household's daily energy consumption, ykWh , in winter.
A random sample of the average temperature and energy consumption are taken from 10 winter days and are summarised below. $$\begin{gathered} \sum x = 12 \quad \sum x ^ { 2 } = 24.76 \quad \sum y = 251 \quad \sum y ^ { 2 } = 6341 \quad \sum x y = 284.8
S _ { x x } = 10.36 \quad S _ { y y } = 40.9 \end{gathered}$$
  1. Find the product moment correlation coefficient between y and x .
  2. Find the equation of the regression line of \(y\) on \(x\) in the form \(y = a + b x\)
  3. Use your equation to estimate the daily energy consumption when the average daily temperature is \(2 ^ { \circ } \mathrm { C }\)
  4. Calculate the residual sum of squares (RSS). The table shows the residual for each value of x .
    \(\mathbf { x }\)- 0.4- 0.20.30.81.11.41.82.12.52.6
    R esidual- 0.63- 0.32- 0.52- 0.730.742.221.840.32\(f\)- 1.88
  5. Find the value of f.
  6. By considering the signs of the residuals, explain whether or not the linear regression model is a suitable model for these data.
Edexcel FS2 AS Specimen Q4
  1. The continuous random variable \(X\) is uniformly distributed over the interval \([ - 3,5 ]\).
    1. Sketch the probability density function \(\mathrm { f } ( \mathrm { x } )\) of X .
    2. Find the value of k such that \(\mathrm { P } ( \mathrm { X } < 2 [ \mathrm { k } - \mathrm { X } ] ) = 0.25\)
    3. Use algebraic integration to show that \(\mathrm { E } \left( \mathrm { X } ^ { 3 } \right) = 17\)