In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Southend Pier is the longest pleasure pier in the world. It is 1∙34 miles long. Gareth walks at a steady pace along Southend Pier. He walks 84 metres every minute. He starts walking along the length of the pier at 2 p.m.
At what time does Gareth reach the end of the pier? Give your time correct to the nearest minute.
You must show all your working.
[7]
The table gives the heights of the 27 musicians in the Camwen Youth Orchestra.
| Height, hcm | Frequency |
150  h  158 | 3 |
158  h  166 | 10 |
166  h  174 | 9 |
174  h  182 | 4 |
182  h  190 | 0 |
| 190 h 198 | 1 |
In which group does the median height of a musician lie?
You must give a reason for your answer.
[2]
Layla has been set a target by her fitness trainer.
Every day, Layla has to increase the number of steps she does.
Today, Layla did 1800 steps.
Layla’s target for the number of steps per day:
Increase by 2% every day for the next 28 days
Calculate the number of steps Layla’s trainer is expecting her to do on the last of these
28 days.
[4]
Paper comes in standard sizes.
| Paper size | A0 | A1 | A2 | A3 | A4 | |
| Length (cm) | 118.9 | 84.1 | 59.4 | 42.0 | 29.7 | |
| Dimensions: | Width (cm) | 84.1 | 59.4 | 42.0 | 29.7 | 21.0 |
Which paper size has an area of approximately 500 000 mm2?
Circle your answer.
A0 A1 A2 A3 A4
[1]
The mass of paper is measured in grams. The quality of paper is given by its mass per square metre of paper.
The quality of a sheet of A2 paper used for printing is stated as 120 g/m2.
Complete the following statement.
‘This sheet of A2 paper has a mass of........ g.’
[4]
Sheets of A4 and A5 paper are mathematically similar.
Calculate the length of the diagonal of a sheet of A5 paper.
You must show all your working.
[5]
The measurements for the A1 sheet of paper in the table are correct to the nearest mm.
Calculate the greatest possible perimeter of an A1 sheet of paper.
[3]
Delta Metals makes aluminium chimneys in the shape of open cylinders.
Each chimney has a height of 2.5 m. The external diameter of each chimney is 0.18 m.
Calculate the external curved surface area of one of these chimneys.
Give your answer correct to 3 significant figures.
[4]
The frequency table below shows the monthly rainfall in Porthislwyn for the 5-year period from January 2010 to December 2014.
| Rainfall, r (mm) | Number of months | Frequency density |
| 0 r 50 | 6 | 0∙12 |
| 50 r 75 | 10 | 0∙4 |
| 75 r 100 | 10 | .............................................. |
100  r  125 | 7 | .............................................. |
| 125 r 150 | 12 | .............................................. |
| 150 r 200 | 8 | .............................................. |
200  r  300 | 7 | .............................................. |
Complete the table above and the histogram below to illustrate this data.
Frequency density
[3]
A wet month is classified as one where the monthly rainfall is greater than 60 mm. Calculate an estimate for the percentage of wet months in Porthislwyn in this 5-year period.
You must show all your working.
[3]
Central Pivot Irrigation is a method of watering crops.
The sprinkler arm, supported by wheeled towers, rotates around a central pivot. For each complete rotation, the watered region forms a circle as shown below.
A typical Central Pivot Irrigation system waters a circular region of radius 400 m. The sprinkler arm rotates through an angle of 30º per hour.
Calculate the area of the region that is watered in one hour.
[2]
The outer tower is 400 m from the pivot. During one watering session, the outer tower moves 1067∙6 m.
Calculate the angle the sprinkler arm has turned through.
[3]
The part of the sprinkler arm furthest away from the pivot delivers water at a faster rate than the part of the sprinkler arm closest to the pivot.
Give one reason why the system has been designed in this way.
[1]
On 1st April 2023, Caitlin invested £10 000 into a savings account. The account had a nominal annual interest rate of 3%, with interest paid on the last day of every month. Caitlin did not plan to make any further payments into the account or make any withdrawals.
Calculate the date when Caitlin will first have over £10 500 in her account.
Date when Caitlin will first have over £10 500 in her account is
[4]
Calculate the AER for Caitlin’s savings account.
Give your answer as a percentage, correct to 2 decimal places.
[2]
Evan will need to put strips of lead from B to C and from B to F. This is to ensure rainwater does not enter the room.
Calculate the total length of lead that Evan will need.
[5]
The roof of the structure is to be tiled. For the top edge, Evan has chosen to use half-round clay tiles.
The cross-section of a tile is shown below.
The length of each tile is 30 cm. XY is a semi-circular arc of radius 8 cm. Each tile has a uniform thickness of 1∙2 cm.
The tile manufacturer covers all 6 surfaces of each tile with a protective glaze.
Calculate the total surface area of one tile that is glazed.
[5]
Evan has bought roof tiles for the structure from Tuff Tiles.
Tuff Tiles makes 2000 of these roof tiles every hour. They randomly sample some of these 2000 tiles to check their quality.
Use the following list of random numbers to select the first 7 tiles for the sample. You must start with the first number in the list, explaining clearly how you are using the
numbers to select the sample.
3205 2002 1924 1521 2735 1205
0114 9533 9507 3969 4941 1521
8377 1098 3473 0769 1003 5421
5533 4788 1003 6432 5630 2483
The tiles selected will be
[3]
The paper as printed
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