The cumulative frequency curve represents the distribution of heights of 120 seedlings.

Use the curve to estimate:
(i) the median height
(ii) the upper quartile range
(iii) the 90^th percentile

The probability that it rains (R) on the first day is ³⁄₄.
The probability that it does not rain (NR) on the second day is ³⁄₅.
(a) Complete the tree diagram.

(b) Find the probability that:
(i) It rains on both days
(ii) It does not rain on exactly one day

A coin is thrown once.
(a) On the probability Scale, mark with an X, the probability of getting a tail.

(b) A fair die is also thrown once. Find the probability of getting an odd number and a head.

The pie chart shows information about 60 fruit trees in an orchard.

(a) Find the modal fruit tree.
(b) Find the number of apple trees in the orchard.

(a) The table shows the number of students who attended given number of games.

Number of games	0	1	2	3
Number of students	4	5	2	t

Find
(i) The greatest value of t for which the median is 1,
(ii) An expression, in terms of t, for the mean.

(b) Consider the multiplication table given.

×	1	2	3
4	4	8	...........
5	5	...........	15
6	...........	12	18

(i) Complete the table.
(ii) A product is randomly chosen from the table. Find the probability that the product is
(a) An odd number,
(b) Either a prime number or a multiple of 4.
(iii) A product row is chosen at random from the table and deleted.

Find the probability that the product, randomly chosen from the remaining table, is a multiple of 4.

Here is a list of numbers: 8, 0, 3, 1, 7, 4, 3, 4, 2
(a) Find:
(i) The range
(ii) The mode
(iii) The median
(b) A number is chosen at random from the ten and replaced, and a second number is chosen at random from the ten numbers. Find the probability that both chosen numbers are equal to three.

The mean of 12, 18, 21, x and 13 is 17. Find the value of x.

Here is a list of numbers: 36, 29, 41, 45, 15, 10, 13
(a) Find:
(i) The range
(ii) The median
(b) Calculate the mean of the numbers.
(c) Find the probability that a number chosen at random from this list is prime.

The table shows part of a pattern of numbers and the sum of the numbers in each row.

Row Number	Numbers	Sum
1	1	1
2	3, 5	8
3	7, 9, 11	27
4	13, 15, 17, 19	t
5	....	....

(a) Write down the value of t.
(b) Complete row 5 in the table.
(c) The table is continued to row n.

    (i) How many numbers would appear in row n?
    (ii) Write, in terms of n, an expression for the sum of numbers in row n.

Four identical cards are numbered 1, 4, 6 and 9 respectively. A card is chosen at random.
Find the probability that the card is numbered:
(a) 9

(b) Even or odd

(c) At least 4

There are eight cards each with one letter of the word PAPERONE as follows.

These cards are placed in a bag. A card is taken at random from the bag.
(a) Find the probability that the card is not labelled P.
(b) The card is replaced and another taken at random.
This is repeated 200 times.
Find the number of times that the taken card would be labelled E.

In a Form A class, students were asked to indicate their favourite colours. The results are shown in the bar chart.

(a) How many students are there in the Form A class?
(b) Which colour is liked best by the students?
(c) Find the fraction of students whose favourite colour is white.

The diagram shows the possible outcomes when a die is thrown and a coin is tossed. (T = tails, H = heads)

(a) Complete the diagram.
(b) Find the probability of obtaining:
(i) A tail and an odd number less than 4
(ii) A number less than three with a head or tail.

The table shows the shoe size of a group of students.

Shoe size	Number of students
3	7
4	4
5	1
6	2
7	3
8	1

(a) How many students are in the group?

(b) Find the median shoe size.

The minimum temperatures (°C) in Mokhotlong for 10 consecutive days are:
3, 1, 0, −2, 4, 1, 2, 1, −1, −3
Find
(a) The range,
(b) The median,
(c) The mode.

The bar chart shows the number of children per family in a small village.

(a) Calculate the total number of families in the village.
(b) Find the median number of children per family.
(c) A family is chosen at random. Find the probability that it has more than 3 children. Give your answer in its simplest form.

The pie charts show the favourite sports of students from Cheche High Scholl and Mofifi High School.

There are 125 students in each school who have their favourite sport as soccer.

(a) Find the number of students at Cheche high school whose favourite sport is volley ball.

A bag contains 8 beads. There are 5 blue beads, 2 red beads and 1 green bead.
(a) A bead is chosen at random. Find the probability that the bead is red.

(b) Two more green beads are put in the bag. Find the probability of choosing a green bead.

The table shows the results of 45 students who took part in a quiz.

Number of correct answers	3	4	5	6	7	8	9	10
Number of students	5	3	7	8	10	5	4	3

(a) Find:
(i) The number of students who have more than 7 correct answers,

(ii) The median,

(iii) The mean.

(b) Find the probability that a student chosen at random from the club has less than 6 correct answers.

(c) A pie chart is to be drawn to represent the information in the table. Calculate the sector angle that would represent the number of students who has 7 correct answers.

(a) The diagram shows the frequency distribution of the marks obtained by students in a test.

(i) What is the name given to this type of diagram?

(ii) Find the total number of students who wrote the test.

(iii) Calculate the mean mark.

(b) The table shows the distribution of the ages of guardians of 40 students in a class.

Age of guardian	43	45	49	54	56	60	67	77
Number of students	1	4	8	11	10	3	1	2

(i) (a) Find the range of the distribution.

(b) Write the mode of the distribution.

(ii) A student is chosen at random from the class. Find the probability that the student has a guardian aged between 44 and 61 years.

(iii) 20 percent of the class have a guardian aged 'm' years. Find the value of m.

(iv) Tanki draws a pie chart to represent the information in the table. Calculate the sector angle representing the number of students whose guardians are aged 54.

A survey counts the number of cars travelling at various speed levels. The table shows the results.

Speed levels (km/h)	50	60	70	80	90
Number of cars	12	5	4	4	7

(a) Find:
(i) The total frequency,

(ii) The range,

(iii) The mode,

(iv) The median,

(v) The mean.

(b) Draw a bar chart to represent the information on the table.

(c) A car is chosen at random from these counted. Find the probability that it was travelling at speed level 90 km/h.

The table shows the number of items bought by 50 students.

Number of items bought	5	6	7	8	9	10	11	12
Number of students	5	6	8	7	10	6	5	3

(a) Find the number of students who bought:
(i) 10 items,

(ii) less than 11 items.

(b) Find the median number of items bought.

(c) Calculate the mean number of items bought.

(d) A bar chart is drawn to represent the results. The height of the bar for the number of students who bought 5 items is 2.5 cm. Find the height of the bar for the number of students who bought 9 items.

(e) Find the probability that a student chosen at random bought at least 10 items.

Two football teams, Moea and Linkoe, participated in a tournament. The table shows the results of 30 games played by Moea in the tournament.

Result	win	draw	loss
Frequency	12		8

(a) Complete the frequency table.

(b) Draw and label a pie-chart to represent the information in the table.

(c) What is the mode of the result for Moea?

(d) The results for Linkoe are represented in the bar chart.

In the tournament, a team is awarded 3 points for a win, 1 point for a draw and 0 points for a loss.
Which of Moea or Linkoe finished with more points?
Show the working to support your answer.

(e) Sebolelo watched only one of the games played by Linkoe.
Find the probability that it was a game in which the result was:
(i) A draw,

(ii) A win or loss.

The table shows some values of x and y for $y=(3-x)(3+x)$.

$x$	$0$	$1$	$1.5$	$2$	$2.5$	$3$	$3.5$	$4$
$y$	$9$	$8$	$6.8$	$5$	$2.8$	$0$	$\mathrm{}$	$-7$

(a) Complete the table.

(b) On the grid provided plot the points in the table and join them with a smooth curve.

(c) Use your graph to find the value of y when x = 3.8.

(d) On the same axes, draw the graph of $y=2x$.

(e) Write the x value at which the line $y=2x$ intersects the curve.

The table shows information about the number of computers in the offices in an institution.

Number of computers per office	1	2	3	4	5	6
Number of offices	18	10	2	15	8	2

(a) Find the:
(i) modal number of computers per office,

(ii) range for the number of computers per office,

(iii) mean number of computers per office.

(b) An office is chosen at random from the record.
Find the probability that the chosen office has:
(i) 3 computers,

(ii) 15 computers,

(iii) at least 5 computers. Give your answer in its simplest form.

(c) Two offices are chosen at random without replacement.
Find the probability that one office has 2 computers and the other office has 5 computers.

(d) x more offices are added to the record.
None of these x offices has 4 computers.
A pie chart is drawn from the new record.
Write, in terms of x, an expression for the sector angle representing offices with 4 computers.

(a) Six balls of different colours and four coins are placed in a bag.
The possibility space diagram shows the possible outcomes when a ball and a coin are picked at random from the bag.

A ball and a coin are picked at random from the bag. Find the probability that it is a:
(i) white ball and M1 coin,

(ii) red ball and a coin worth at least M2.

(b) The table shows the marks obtained by 25 students in a quiz that was marked out of 5.

Marks	0	1	2	3	4	5
Number of students	1	2	6	8	5	3

(i) Find the modal mark.

(ii) Calculate the mean mark.

(iii) Calculate the sector angle that would represent 2 marks if these data were to be presented in a pie chart.

(a) Complete the table of the values for $y=x^2-2x-3$.

x	−2	−1	0	1	2	3	4
y			−3	−4			5

(b) On the grid, draw the smooth curve of $y=x^2-2x-3$, for $-2\le x\le 4$.

(c) (i) On the same grid, draw the line y = 2.

(ii) Write the x-coordinates of the points where the two graphs intersect.

(a) The table shows the temperature at Litau in winter for one week.

Day	Mon	Tue	Wed	Thur	Fri	Sat	Sun
Temperature (°C)	3	1	−2	−9	−1	4	7

(i) Write down the coldest day.

(ii) Calculate the mean temperature for the week.

(b) The number of hours of sunshine at Litau was also recorded each day during one month.
The results are displayed on the bar chart below.

(i) Find the mode.

(ii) How many days are there in this month?

(iii) Complete the frequency table from the bar chart.

(iv) Find the median.

(v) If the information on the chart is to be represented on a pie chart, find the angle of the sector representing 3 hours of sunshine.

(vi) What is the probability that a day, chosen at random, has more than 4 hours of sunshine?
Give your answer as a fraction in its simplest form.

Eight people are weighed. Their masses (kg) are as follows:
75, x, 92, 46, 71, 84, y, 97
Two masses are unknown and are given as x and y. The mean of the eight masses is 74 kg, the median is 73 kg and the range is 51 kg. Calculate a possible pair of values for x and y.