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CAPE Applied Mathematics Unit 1 · 2016 · 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 choiceA sampling frame is defined as
  2. Q21 mark · multiple choiceWhich of the following relationships is TRUE for a negatively skewed distribution?
  3. Q31 mark · multiple choiceWhich of the following statements is TRUE of a histogram?
  4. Q41 mark · multiple choiceItems 4–5 refer 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 \textbf{Waiting Time (minutes)}…
  5. Q51 mark · multiple choiceItems 4–5 refer 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 \textbf{Waiting Time (minutes)}…
  6. Q61 mark · multiple choiceItems 6–7 refer to the following cumulative frequency curve which illustrates the results of an examination. How many students scored less than 70 marks?
  7. Q71 mark · multiple choiceItems 6–7 refer to the following cumulative frequency curve which illustrates the results of an examination. How many students scored higher than the upper quartile?
  8. Q81 mark · multiple choiceThe mean of the positive numbers x_1, x_2, x_3 is \bar{x}, and the mean of the positive numbers y_1, y_2, y_3 is \bar{y}. The mean of the numbers x_1, x_2, x_3, y_1, y_2, and y_3 is
  9. Q91 mark · multiple choiceItem 9 refers to the following stem-and-leaf diagram. \begin{tabular}{c|llllllll} 1 & 2 & & & & & & & \\ 1 & 5 & & & & & & & \\ 1 & 7 & 7 & & & & & & \\ 2 & 0 & 0 & & & & & & \\ 2 & 2 & 2 & & & & & & \\ 2 & 4 & 4 & 4 &…
  10. Q101 mark · multiple choiceItem 10 refers to the following table which shows the daily sales (in thousands of dollars) of two outlets of a company in a given week. \begin{tabular}{|l|c|c|c|c|c|} \hline \textbf{Day} & D_1 & D_2 & D_3 &…
  11. Q111 mark · multiple choiceItem 11 refers to the examination marks recorded in the following table for 20 science students. \begin{tabular}{|c|c|c|c|c|} \hline 6 & 17 & 19 & 20 & 22 \\ \hline 24 & 24 & 27 & 28 & 29 \\ \hline 32 & 36 & 41 & 44 &…
  12. Q131 mark · multiple choiceItem 13 refers to the following table which shows the number of copies of a school magazine circulated in the first four months of the last year. \begin{tabular}{|l|c|c|c|c|} \hline \textbf{Issue} & \text{January} &…
  13. Q141 mark · multiple choiceItems 14–15 refer to the following box-and-whisker plot. The interquartile range is
  14. Q151 mark · multiple choiceItems 14–15 refer to the following box-and-whisker plot. The distribution is
  15. Q161 mark · multiple choiceWhich of the following statements describe the main features of the normal distribution? I. It is bell-shaped. II. It is symmetrical about the mean. III. The total area under the curve is 1. IV. It extends from 0 to…
  16. Q171 mark · multiple choiceAn unbiased tetrahedral die with faces marked 1, 2, 3, 4 is tossed three times and the number on the base noted each time. A member of the possibility space is
  17. 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) =
  18. Q191 mark · multiple choiceA and B are mutually exclusive events such that P(A) = 0.2 and P(B) = 0.1. P(A \cup B') =
  19. Q201 mark · multiple choiceWhen the normal distribution is to be used as an approximation to the binomial distribution, the P(40 < X \le 45) becomes
  20. Q211 mark · multiple choiceA binomial distribution, \text{Bin}(n, p) has n = 250 and p = 0.6. The mean and the variance of this distribution are
  21. Q221 mark · multiple choiceA random variable X has the following probability distribution. \begin{tabular}{|l|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline P(X = x) & 0.3 & 0.1 & 0.4 & 0.2 \\ \hline \end{tabular} P(X \ge 2) =
  22. Q231 mark · multiple choiceItems 23–24 refer to the following tree diagram. P(L) is
  23. Q241 mark · multiple choiceItems 23–24 refer to the following tree diagram. P(L' \mid B) is
  24. Q251 mark · multiple choiceIf X \sim N(24, 36), then P(X > 25) is
  25. Q261 mark · multiple choiceIf the letters of the word SCHOOL are arranged at random, then what is the probability that the arrangement begins with the letters OO?
  26. Q271 mark · multiple choiceWhich of the following activities illustrates a probability?
  27. Q281 mark · multiple choiceThe random variable, X, has a probability mass function P(X = x) for x = 3, 4, 5, 6 as shown in the following table. \begin{tabular}{|l|c|c|c|c|} \hline x & 3 & 4 & 5 & 6 \\ \hline P(X = x) & a & 0.5 & 0.2…
  28. 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…
  29. Q301 mark · multiple choiceTo secure the national championship title, a team must win the remaining two games. The probabilities that the team will win the first and second games are 0.6 and 0.7 respectively. Assuming that the outcomes of the…
  30. Q311 mark · multiple choiceIn a hypothesis test at the 5% level of significance, the null hypothesis is
  31. Q321 mark · multiple choiceWhich of the following conditions will widen the confidence interval for a population mean \mu? I. The level of significance increases. II. The sample size increases. III. The variance increases.
  32. 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
  33. Q341 mark · multiple choiceThe t-test statistic is used to test the population mean when the variable X is
  34. Q351 mark · multiple choiceA t-test is used to test whether solar coils last an average of 7 years. A sample of 10 of these solar coils have a mean life of 6.75 years and a standard deviation of 0.5 years. The value of the test statistic, t,…
  35. Q361 mark · multiple choiceThe cholesterol levels of 5 women are \begin{tabular}{ccccc} 3.1 & 2.7 & 3.3 & 2.4 & 1.9 \\ \end{tabular} When conducting a t-test on the mean at the 5% level of significance using a one-tailed test, the critical…
  36. Q371 mark · multiple choiceThe time, x minutes, taken on 9 different occasions for an air conditioning unit to reach its desired temperature, y\ ^\circ\text{C}, when switched on is summarized by $\sum x = 68.8, \sum x^2 = 753.9, \sum y =…
  37. Q381 mark · multiple choiceWhich of the following conditions are appropriate for the use of the central limit theorem?
  38. Q391 mark · multiple choiceThe cholesterol levels of 8 women are \begin{tabular}{cccc} 3.1 & 2.7 & 1.3 & 1.4 \\ 1.7 & 3.3 & 2.4 & 1.9 \\ \end{tabular} In conducting a t-test on the mean, the number of degrees of freedom is
  39. Q401 mark · multiple choiceItems 40–41 refer to the following information. A \chi^2 test of independence is carried out using a contingency table with 4 rows and 5 columns. The number of degrees of freedom is
  40. Q411 mark · multiple choiceItems 40–41 refer to the following information. A \chi^2 test of independence is carried out using a contingency table with 4 rows and 5 columns. The critical value at the 5% significance level appropriate to this…
  41. Q421 mark · multiple choiceItem 42 refers to the following contingency table which gives the results of a football team over 40 matches. \begin{tabular}{|l|c|c|c|} \hline & \textbf{Good Weather} & \textbf{Bad Weather} & \textbf{Total} \\ \hline…
  42. Q431 mark · multiple choiceThe weights of iron rods manufactured by a certain company are normally distributed with a standard deviation of 3.4\text{ kg}. A random sample of 35 iron rods with mean weight of 40.2\text{ kg} is selected. A 99%…
  43. Q441 mark · multiple choiceA balloon manufacturing company claims that 10% of its balloons are blue. A random sample of 200 of these balloons is taken, and 16 are found to be blue. Which of the following tests would be MOST appropriate for…
  44. Q451 mark · multiple choiceThe mass of a bag of potatoes is normally distributed with mean mass 50\text{ kg} and standard deviation 6\text{ kg}. Five bags of potatoes are chosen at random. Given \bar{X} \sim N\left(50, \frac{36}{5}\right),…

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