Information: The total mark for this section is 16.
Gareth sells hot drinks. He sells cups of tea, cups of coffee and cups of hot chocolate.
Of all the hot drinks he sold last week
- 25 were cups of tea
- 13 were cups of coffee.
What fraction of all cups of hot drinks sold were cups of hot chocolate?
(a)Work out 13.4 × 5.2 (2 marks)
(b)Use estimation to show a check of your working. (1 mark)
Mitch works in a fitness centre. He gives one raffle ticket to each of 1000 people that attend the fitness centre.
Mitch starts to complete this two-way table to show information about the people he gives the raffle tickets to.
(a)Complete the two-way table for Mitch. (2 marks)
| age (years) | favourite class | total | ||
|---|---|---|---|---|
| spin | yoga | cardio | ||
| 18 to 24 | 92 | 145 | 322 | |
| 25 to 49 | 107 | |||
| 50 and over | 134 | 318 | ||
| total | 230 | 381 | 389 | 1000 |
(Fill in the seven empty cells.)
Mitch selects a raffle ticket at random.
(b)What is the probability that the ticket he selects belongs to a person aged under 50 whose favourite class is cardio? (2 marks)
Dave is going to paint a wall. Here is a scale diagram of the wall.
Scale: 1 cm represents 0.5 m
Dave will paint this wall twice.
He thinks the total area that he needs to paint is greater than 30 m2.
Is Dave correct? You must show all your working.
Information: The total mark for this section is 48. The total mark for the paper is 64.
Here is a set of data.
(a)Find the median. (2 marks)
(b)Find the mode. (1 mark)
Last year Jim bought 15 prizes for work. The prizes cost £27 each.
This year Jim will buy 18 prizes. He will spend the same total amount of money as he spent last year on the prizes.
Each of the 18 prizes must cost the same amount of money.
Work out the cost of each prize this year.
Steve is writing a report about TV viewing. He has the following information.
| Number of people in the household | 3 | 5 | 5 | 6 | 5 | 2 | 4 | 2 |
|---|---|---|---|---|---|---|---|---|
| Number of TVs in the household | 2 | 3 | 4 | 4 | 5 | 1 | 3 | 2 |
Steve thinks there is a relationship between the number of people and the number of TVs in a household.
(a)Draw a suitable diagram for Steve. (3 marks)
Marks awarded for: (1) Linear scales covering data range. (2) Plotting (allow 1 error). (3) Labels — "(number of) People" and "(number of) TVs" or appropriately detailed title.
(b)Describe the relationship between the number of people and the number of TVs in a household. (1 mark)
Karen invests £2 500 for 3 years.
The investment earns 1.7% compound interest per year.
Work out the value of the investment at the end of 3 years.
Here is a cylinder.
(a)Using y = 11, calculate the area of the curved surface of the cylinder. (4 marks)
Here is a trapezium. The trapezium has one line of symmetry.
(b)Choose the correct calculation to work out the perimeter of the trapezium. (1 mark)
(a)Write 45% as a fraction in its simplest form. (1 mark)
(b)Calculate 5 + 13211 − 9.5 (2 marks)
Kate is making biscuits. She uses flour, butter and sugar in the ratio 5 : 3 : 2.
Kate has:
- 800 g flour
- 550 g butter.
Kate wants to make the maximum number of biscuits possible. She works out how much sugar she needs.
(a)How much sugar does Kate need? You must show your working. (3 marks)
(b)Use a reverse calculation to show a check of your working. (1 mark)
Lou wants to go to a gym. She sees these two offers at the gym.
£44 per month + £30 joining fee
All classes included
£7.75 per class
No joining fee
Lou wants to attend 2 classes each week for one year.
Lou thinks if she uses offer A she will save at least 28% on the total cost of classes compared to using offer B.
Is she correct? Show why you think this.
Here is a grid with points A, B, C and D plotted.
(a)Write down the coordinates of point A. (1 mark)
(b)On the grid, mark with a cross another point and join all five points to form a pentagon with one line of symmetry. (2 marks)
Enter coordinates of your fifth point (must lie on the line of symmetry y = 1):
Rav provides food for events.
Last year 550 people attended an event.
This year there will be 748 people attending the event.
Calculate the percentage increase in the number of people attending.
Meg has a dog. She has this information about dog food.
| Dog size | Daily quantity of dog food in packs |
|---|---|
| Small (up to 12 kg) | 1 to 113 |
| Medium (13 kg to 25 kg) | 113 to 213 |
| Large (26 kg to 45 kg) | 213 to 313 |
| Giant (46 kg to 70 kg) | 313 to 5 |
Meg knows that her dog weighs 29 lbs.
Meg has 24 packs of dog food.
(a)What is the maximum number of days she can feed her dog with the 24 packs? Show why you think this. (3 marks)
Meg needs to replace part of her garden fence to keep her dog safe.
She needs to replace 78 feet of fencing. Meg buys fencing measured in metres.
Meg uses 1 metre = 3.28 feet.
(b)Work out how many metres of fencing Meg needs. (2 marks)
Ria works in a factory making solid steel spheres.
She has this information about the number of spheres made each day for the last 100 days.
| Number of spheres | Number of days |
|---|---|
| 210 to 212 | 4 |
| 213 to 215 | 32 |
| 216 to 218 | 53 |
| 219 to 221 | 11 |
Ria will use this information to estimate the mean number of spheres made each day.
She knows that the volume, v, of a sphere is
Each sphere has a diameter of 15 mm.
Calculate the mean volume of steel used each day to make spheres. Give your answer to the nearest thousand.