The table shows the mass of 90 carrots grown by a gardener.
| Mass, m (grams) | Number of carrots |
30  m  60 | 9 |
| 60 m 90 | 33 |
| 90 m 120 | 38 |
| 120 m 150 | 8 |
| 150 m 180 | 2 |
Calculate an estimate for the mean mass of these carrots.
[4]
Jan, Freda and Pieter share some money.
Freda gets 3 times as much as Jan. Pieter gets half as much as Freda.
Write down the ratio of the amounts of money that they each get.
Give your answer in its simplest form.
Jan: Freda: Pieter =........ :........ :........
[2]
What fraction of the money does Pieter get?
[1]
Samir buys this digger and expects to use it for 1250 hours each year. The digger will decrease in value at a yearly rate of 18% of its value at the end of the previous year.
Use this information to calculate the decrease in value of Samir’s digger when it has been used
for 10 000 hours.
[5]
A circular wheel makes 42 complete turns each minute.
How many degrees does it turn through in one second?
[3]
State one assumption you have made in your answer to part (a).
[1]
How would your answer to part (a) change if this assumption was not correct?
[1]
Solve 2x + 5 = 11 + 5x.
[2]
Solve 8x –(3x + 1) = 2.
Give your answer as a fraction.
[3]
Tansy is trying to solve 1 
x + 2 
5 where x is a whole number. Here is her work.
Ali says, “You have made an error.”
Is Ali correct?
Yes No
Show clearly how you decide.
[1]
Represent the inequality x 
–2 on the number line below.
[1]
In an experiment, a scientist records the temperature, y °C, of an object as it is heated for x seconds.
The scientist thinks that the equation y = mx + c is a good fit for this data.
The diagram shows his results on a scatter graph and his line of best fit.
Estimate the number of seconds for which the object has been heated when its
temperature is 27 °C.
[1]
When x = 70 seconds, the scientist measures the value of y to be 52 °C.
Use this information to decide whether the line of best fit is likely or unlikely to give reliable predictions for values of y when x is greater than 50 seconds.
Likely Unlikely
Explain how you decide.
[1]
The line of best fit passes through the points (0, 15) and (10, 22). Find the equation of the line of best fit.
Give your answer in the form y = mx + c.
[3]
Explain what the gradient of the line of best fit represents in this context.
[1]
[5]
A wedge is cut from a cylinder of cheese of radius 7 cm and height 5 cm. The volume of this wedge is 154 cm3.
What percentage of the whole cheese is this wedge?
[4]
Bronny takes part in a triathlon.
In this race she:
• cycles at an average speed of 27 km/h for 1 hour and 30 minutes,
• runs 9 km in 1 hour.
The average speed of the winner of the triathlon is 16·1 km/h.
Show that Bronny does not win the race.
[4]
[5]
Describe the single transformation that maps triangle ABC to triangle PQR.
[2]
[2]
Find the next term of the following sequence.
0, 7, 26, 63, 124,........
[1]
Find the nth term of the following sequence.
3, 9, 19, 33, 51,........
[2]
A cuboid of copper has a mass of 2150·4 grams and a volume of 240 cm3.
A sphere of copper has a radius of x cm.
Show that the mass, in grams, of the sphere is less than 38x3.
[4]
[3]
Jim squeezes 1 pink grapefruit. He obtains 250 ml of juice, correct to the nearest 50 ml.
Jim thinks he will obtain a maximum of 900 ml of juice if he squeezes 3 pink grapefruit.
Assuming each pink grapefruit is the same size, is Jim likely to be correct?
Yes No
Show how you decide.
[2]
Calculate the minimum mass of the orange.
[3]
As part of an experiment two groups of people, A and B, took the same general knowledge test.
The test had a maximum of 100 marks.
The first two columns of the table summarise the results of the test for the 45 people
| Mark | Frequency | Cumulative Frequency |
0 p  20 | 0 | 0 |
| 20 p 40 | 3 | 3 |
| 40 p 60 | 20 | |
| 60 p 80 | 15 | |
| 80 p 100 | 7 |
Complete the cumulative frequency column.
[1]
Explain why 60 is a reasonable estimate of the median mark.
[1]
This box plot shows the distribution of the marks of the people in Group B.
For the people in Group A:
| Minimum mark | Range | Lower Quartile | Median | Upper Quartile |
| 23 | 76 | 49 | 60 | 75 |
Draw the box plot for Group A on the grid above.
[3]
Make two comments to compare the results of Group A and Group B. One comment must include an appropriate average.
The other comment must include a measure of spread.
Comment 1........
Comment 2........
[2]
On the graph paper below, draw the region which satisfies all of these inequalities.
Indicate clearly the region that is your answer.
[4]
One of these guests is chosen at random. Find the probability that this guest ticked
statement A or statement C but not statement B.
[1]
Given that a guest ticked at least one statement, find the probability that this guest ticked
statement B.
[2]
Find the equation of the line parallel to 4x = 5 –y which passes through the point (1, – 1).
Give your answer in the form y = mx + c.
[3]
[2]
When P is 50, R is 0·02.
Find a formula for R in terms of P.
[3]
Find the positive value of P for which R is 0.
[2]
There are 8 seats in the front row of a theatre.
8 friends sit down in this row.
When each friend can sit in any of the 8 seats, find the number of different seating
arrangements possible.
[2]
Liesa and Todd are 2 of the 8 friends.
Find the probability that Liesa is sitting in the first seat on the left and Todd is sitting
next to her.
[3]
A solution, x, of the equation x3 + x –1 = 0 lies in the interval ‘between 0·5 and 1’.
Kate uses the method of interval bisection to find the solution correct to one decimal place.
Show that Kate’s second interval for x is ‘between 0·5 and 0·75’.
[2]
[1]
Continue Kate’s method of interval bisection to show that the solution is x = 0·7 correct
to one decimal place.
[2]
Debra buys a total of 4 kg of flour and butter at a market.
She pays £7 for her flour and £9 for her butter.
She buys x kg of flour.
Complete this table.
| Total cost (£) | Number of kg bought | Cost per kg (£) | |
| Flour | 7 | x | 7x |
| Butter | 9 | 4 – x |
[1]
The cost per kilogram of her butter is £5 more than the cost per kilogram of her flour.
Use this information and the table in part (a) to show that
5x2 – 4x – 28 = 0.
[5]
Use an algebraic method to find the cost of a kilogram of her flour.
You must show all your working.
[4]
ABC
is acute. The area of triangle ABC is 45·0 cm2. Show that ABC
= 50° correct to the nearest integer and hence calculate ADC
.
[9]
The paper as printed
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