CAPE Applied Mathematics Unit 1 · 2014 · Paper 1
43 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.
- Q11 mark · multiple choiceItems 1–2 refer to the following types of data. I. Qualitative II. Quantitative III. Discrete IV. Continuous The number of births at the hospital during the month of January is an example of
- Q21 mark · multiple choiceItems 1–2 refer to the following types of data. I. Qualitative II. Quantitative III. Discrete IV. Continuous The marital status of persons is
- Q31 mark · multiple choiceItem 3 refers to the following frequency distribution.
\begin{array}{|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{array}Which of the following statements… - 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{array}{|l|c|c|c|c|c|} \hline \text{Waiting time (in minutes)}… - 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{array}{|l|c|c|c|c|c|} \hline \text{Waiting time (in minutes)}… - Q61 mark · multiple choiceItems 6–7 refer to the following table which shows the scores obtained by Jack in a game. Jack's mean score is 5.
\begin{array}{|l|c|c|c|c|} \hline \text{Score} & 1 & 2 & 4 & x \\ \hline \text{Frequency} & 2 & 5 & 7 &… - Q71 mark · multiple choiceItems 6–7 refer to the following table which shows the scores obtained by Jack in a game. Jack's mean score is 5.
\begin{array}{|l|c|c|c|c|} \hline \text{Score} & 1 & 2 & 4 & x \\ \hline \text{Frequency} & 2 & 5 & 7 &… - Q81 mark · multiple choiceThe mean of the positive numbers
x_1, x_2, x_3is\bar{x}, and the mean of the positive numbersy_1, y_2, y_3is\bar{y}. The mean of the numbersx_1, x_2, x_3, y_1, y_2andy_3is - Q91 mark · multiple choiceItem 9 refers to the following stem-and-leaf diagram.
\begin{array}{r|llllllllll} 1 & 2 & & & & & & & & \\ 1 & 5 & & & & & & & & \\ 1 & 7 & 7 & & & & & & & \\ 2 & 0 & 0 & & & & & & & \\ 2 & 2 & 2 & & & & & & & \\ 2 &… - Q101 mark · multiple choiceA sampling frame is
- 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{array}{|l|c|c|c|c|} \hline \text{Issue} & \text{January} &… - Q141 mark · multiple choiceItems 14–15 refer to the following box-and-whisker plot. The interquartile range is
- Q151 mark · multiple choiceItems 14–15 refer to the following box-and-whisker plot. The distribution is
- 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…
- Q171 mark · multiple choiceAn unbiased tetrahedral die with faces marked
1, 2, 3, 4is tossed three times and the number on the base is noted each time. A member of the possibility space is - Q181 mark · multiple choiceItem 18 refers to the following information.
Events
XandYare independent andP(X) = \frac{1}{9},P(X \cap Y) = \frac{1}{15}.P(Y) = - Q191 mark · multiple choiceIf
Xis a random variable with distribution\text{Bin}(n, 0.4)such that\text{E}(X) = 30, thenn = - Q201 mark · multiple choiceIf events
AandBare independent, which of the following conditions are true? I.P(A \cap B) = 0II.P(A \cap B) = P(A) \times P(B)III.P(A|B) = P(A)IV.P(A \cup B) = P(A) + P(B) - Q211 mark · multiple choiceThe events
MandNare such thatP(M) = \frac{1}{4},P(N) = \frac{1}{5},P(M \cup N) = \frac{5}{12}.P(M \cap N) = - Q221 mark · multiple choiceThe continuous random variable
Xhas a probability density function given byf(x) = \begin{cases} 0.5, & 0 < x < 2 \\ 0, & \text{otherwise} \end{cases}P\left(X < \frac{1}{2}\right)is - Q231 mark · multiple choiceWhich of the following statements is NOT a condition for the binomial model of probability?
- Q241 mark · multiple choiceThe heights of rose plants follow a normal distribution with mean
215\text{ cm}and standard deviation20.2\text{ cm}. The probability, to 3 significant figures, that the height of a randomly chosen rose plant is… - Q251 mark · multiple choiceItem 25 refers to the following information.
The discrete random variable
Y, whereytakes on only the values1, 2, 3and4, has a cumulative distribution functionF(y)which is represented in the table… - Q261 mark · multiple choiceIf the letters of the word
\text{SCHOOL}are arranged at random, what is the probability that the arrangement begins with the letters\text{OO}? - Q271 mark · multiple choiceWhich of the following activities illustrates a probability?
- Q281 mark · multiple choiceThe random variable
Xhas probability mass functionP(X = x)forx = 3, 4, 5, 6as shown below.\begin{array}{|l|c|c|c|c|} \hline x & 3 & 4 & 5 & 6 \\ \hline P(X = x) & a & 0.5 & 0.2 & 0.1 \\ \hline… - 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… - Q301 mark · multiple choiceIf
X \sim \text{N}(20, 16), andP(X > w) = 0.119, then the value ofwis - Q311 mark · multiple choiceIn a one-tailed hypothesis test, the critical value divides the total region under a sampling distribution into
- Q321 mark · multiple choiceFor a contingency table with 4 rows and 3 columns, the number of degrees of freedom for a
\chi^2test of independence is - Q331 mark · multiple choiceWhich of the following values for the product-moment correlation coefficient,
r, indicates the strongest degree of linear correlation between the two variables? - Q341 mark · multiple choiceThe regression line
yonx - Q351 mark · multiple choiceA
t-test is used to test a company's claims that its watch batteries last an average of 7 years. A sample of 10 of the company's watch batteries has a mean life of 6.75 years and a standard deviation of 0.5 years. The… - Q361 mark · multiple choiceIf
Xis a\chi^2distribution with 12 degrees of freedom, then the value ofP(X < 4.404)is - Q371 mark · multiple choiceThe time,
xminutes, 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 =… - Q381 mark · multiple choiceWhich of the following conditions are satisfied for the use of the central limit theorem?
- Q391 mark · multiple choiceThe cholesterol levels of 8 women are
\begin{array}{cccc} 3.1 & 2.7 & 1.3 & 1.4 \\ 1.7 & 3.3 & 2.4 & 1.9 \end{array}In conducting at-test on the mean, the number of degrees of freedom is - Q401 mark · multiple choiceThe mean age of teachers in a certain country is 30 years. A random sample of 49 teachers yields a mean age of 33.08 years. Using a population standard deviation of 12 years, a
z-test at the5\%significance level… - Q411 mark · multiple choiceGiven a random sample of size
nwith mean\bar{x}and standard deviation\hat{\sigma}, then a90\%confidence interval for the population mean is - Q421 mark · multiple choiceTwo hundred samples are chosen and 90% confidence intervals calculated for each. How many of these samples are NOT expected to contain the population mean? The confidence level used is
- Q431 mark · multiple choiceA chi-squared test does NOT
- Q441 mark · multiple choiceA balloon manufacturing company claims that at least
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… - Q451 mark · multiple choiceThe mass of a bag of potatoes is normally distributed with mean mass
50\text{ kg}and standard deviation6\text{ kg}. Five bags of potatoes are chosen at random. Given…