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CAPE Applied Mathematics Unit 1 · 2017 · Paper 1

44 multiple-choice items from this paper. Open one to see it in full, then practise it on Quelpr and get it marked against the mark scheme.

Practise this paper
  1. Q11 mark · multiple choiceWhich of the following variables is discrete?
  2. Q21 mark · multiple choiceWhich of the following comparisons is correct for a NEGATIVELY skewed distribution?
  3. Q31 mark · multiple choiceFor data arranged in order of size, the LOWER quartile is the value
  4. Q41 mark · multiple choiceItem 4 refers to the following table which shows the distribution of the time, in minutes, that 90 patients waited before being seen by a doctor. \begin{tabular}{|l|c|c|c|c|c|} \hline Waiting Time (min) & 0--6 & 7--13…
  5. Q51 mark · multiple choiceFor a population divided into strata, under which condition is it preferable to use stratified random sampling rather than simple random sampling?
  6. Q61 mark · multiple choiceItems 6--7 refer to the following table which shows the scores obtained by Jack in a game. The mean score is 5. \begin{tabular}{|l|c|c|c|c|} \hline Score & 1 & 2 & 4 & x \\ \hline Frequency & 2 & 5 & 7 & 6 \\ \hline…
  7. Q71 mark · multiple choiceItems 6--7 refer to the following table which shows the scores obtained by Jack in a game. The mean score is 5. \begin{tabular}{|l|c|c|c|c|} \hline Score & 1 & 2 & 4 & x \\ \hline Frequency & 2 & 5 & 7 & 6 \\ \hline…
  8. Q81 mark · multiple choiceThe secretary of a club wants to obtain the opinions of the members about the club's facilities. The club has 339 members of whom 113 are males. The secretary decides to conduct a survey using a random sample of 42…
  9. Q91 mark · multiple choiceItem 9 refers to the following frequency distribution. \begin{tabular}{|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline f & 15 & 22 & 11 & 7 & 3 & 2 \\ \hline \end{tabular} Which of the following is/are…
  10. Q101 mark · multiple choiceThe heights of 100 pea trees are measured to the nearest centimetre. The measurements are put into a frequency table. The diagram that will BEST illustrate this information is a
  11. Q111 mark · multiple choiceItem 11 refers to the following table which shows the daily sales (in thousands of dollars) of 2 outlets of a company in a given five-day period. \begin{tabular}{|l|c|c|c|c|c|} \hline & \multicolumn{5}{|c|}{Day} \\…
  12. Q121 mark · multiple choiceIn a pie chart drawn to illustrate the yearly expenditure for an adult, the sector representing transport measures 80^\circ. If the expenditure for transport is…
  13. Q131 mark · multiple choiceItem 13 refers to the following pie chart (not drawn to scale) which shows the distribution of four animals on a farm. If there are 16 turkeys on the farm, the total number of animals on the farm is
  14. Q141 mark · multiple choiceItems 14--15 refer to the following box-and-whisker plot. The interquartile range is
  15. Q151 mark · multiple choiceItems 14--15 refer to the following box-and-whisker plot. The distribution is
  16. Q161 mark · multiple choiceA and B are mutually exclusive events such that P(A) = 0.2 and P(B) = 0.1. P(A \cup B') =
  17. Q171 mark · multiple choiceA football team has a \frac{3}{5} probability of winning whenever it plays. If the team plays 8 games, the probability of winning exactly 5 games is
  18. Q181 mark · multiple choiceIf events X and Y are independent and P(X) = \frac{1}{9}, P(X \cap Y) = \frac{1}{15}, then P(Y) =
  19. Q191 mark · multiple choiceIf X is a random variable with distribution \text{Bin}(n, 0.4) such that E(X) = 30, then n =
  20. Q201 mark · multiple choiceIf events A and B are independent, which of the following conditions are true? I. P(A \cap B) = 0 II. P(A \cap B) = P(A) \times P(B) III. P(A|B) = P(A)
  21. Q211 mark · multiple choiceIf Z \sim N(0, 1), then P(-3 < Z < -1) is
  22. Q221 mark · multiple choiceItems 22--23 refer to the following information. Ten per cent of bulbs produced by a factory are defective. A sample of 400 bulbs is taken. The mean number of defective bulbs is
  23. Q231 mark · multiple choiceItems 22--23 refer to the following information. Ten per cent of bulbs produced by a factory are defective. A sample of 400 bulbs is taken. The variance for the distribution of defective bulbs is
  24. Q241 mark · multiple choiceIf Z \sim N(0, 1), the figure illustrating P(Z > a) = 0.35 is
  25. Q251 mark · multiple choiceIf A and B are two events such that P(A|B) = 0.6, P(A) = 0.2 and P(B) = 0.3, then P(A \cap B) =
  26. Q261 mark · multiple choiceAn unbiased tetrahedral die is rolled twice. The faces are marked 1, 2, 3 and 4. What is the probability of getting a TOTAL score of 4?
  27. Q271 mark · multiple choiceIn each round of a game of cards, a player can either win or lose the round. The probability of winning the first round is p and the probability of losing the second round is \frac{2}{5}, independent of the first…
  28. Q281 mark · multiple choiceA courier service team has a \frac{3}{5} probability of completing its assigned deliveries in a day. If the team is assigned 8 deliveries on Wednesday, the probability of making exactly 5 deliveries, to 2 decimal…
  29. Q291 mark · multiple choiceIt is estimated that about 30\% of the population of a country holds university degrees. If 10 citizens of this country are drawn at random, the probability that at least one of them holds a university degree is…
  30. Q301 mark · multiple choiceIf X \sim N(20, 16), and P(X > w) = 0.119, then the value of w is
  31. Q311 mark · multiple choiceItems 31--32 refer to the following contingency table which shows the observed results used to investigate whether the variables X and Y are independent. \begin{tabular}{|c|c|c|c|} \hline & X_1 & X_2 & X_3 \\…
  32. Q321 mark · multiple choiceItems 31--32 refer to the following contingency table which shows the observed results used to investigate whether the variables X and Y are independent. \begin{tabular}{|c|c|c|c|} \hline & X_1 & X_2 & X_3 \\…
  33. Q331 mark · multiple choiceIn a one-tailed z-test, the null hypothesis H_0 : \mu = 12 is tested against the alternative hypothesis H_1 : \mu > 12. At the 5\% significance level, the critical z region is
  34. Q341 mark · multiple choiceThe t-test statistic is used to test the population mean when the variable X is
  35. Q351 mark · multiple choiceItem 35 refers to the following scatter diagram. The product-moment correlation coefficient of the data shown is
  36. Q371 mark · multiple choiceThe time, x minutes, taken for an air conditioning unit to reach its desired temperature, y\ ^\circ\text{C}, when switched on on 9 different occasions is summarized by \Sigma x = 68.8, \Sigma x^2 = 753.9,…
  37. Q381 mark · multiple choiceThe parameter of a \chi^2 distribution is the
  38. Q391 mark · multiple choiceThe grades given by 3 teachers at a school are displayed in a 3 \times 5 contingency table. A \chi^2 test, at the 5\% level of significance, is carried out to test the hypothesis that there is no association…
  39. Q401 mark · multiple choiceWhen 60 random samples of size 45 are taken, a 90\% confidence interval for the population mean, \mu, is found for each sample. The expected number of samples that do NOT contain \mu is
  40. Q411 mark · multiple choiceThe regression line of y on x passes through the point (0, 2). The means of x and y are 6 and 8 respectively. The equation of the regression line is
  41. Q421 mark · multiple choiceThe regression line y = 0.95x + 0.4 provides a linear model for the cost, y hundred dollars, associated with producing x components. What is the practical interpretation of the coefficient 0.95?
  42. Q431 mark · multiple choiceIn hypotheses testing, the probability of committing a Type I error is called the
  43. Q441 mark · multiple choiceItem 44 refers to the following information which shows the scores obtained by a sample of 40 students in a class quiz. 25 31 33 17 20 19 39 32 33 12 40 22 25 23 29 15 15 17 27 40 31 35 26 19 29 29 39 33 35 37 32 31 21…
  44. Q451 mark · multiple choiceTo construct a confidence interval for the population proportion, p, which of the following must be true for a sample of size n?

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