WJEC GCSE Numeracy Unit 2: Calculator-allowed Higher November 2018 question paper 3310U60-1

Tube Cycles makes a large number of bikes each day.

On 1st December 2016, 4000 bikes were made at the Tube Cycles factory. The Tube Cycles factory was working at 80% capacity on that day. This means that only 80% of the maximum possible number of bikes were made.

When the factory works at 95% capacity, how many bikes are made in one day?

In October 2018, the manager of the Tube Cycles factory recorded the number of bikes made each day. Here are her results.

Number of bikes, b	Frequency
1000 b 2000	3
2000 b 3000	12
3000 b 4000	9
4000 b 5000	7

Calculate an estimate of the mean number of bikes made per day during October

2018.

Which group contains the median number of bikes made per day?

Circle your answer.

Use this information to calculate how long Emyr takes to cut his lawn.

Give your answer in minutes.

It takes Emyr_........ minutes.

What assumption have you made?

What impact would this have on the time you calculated in answering (a)(i)?

Emyr cuts his lawn 25 times a year. He uses 4.5 litres of petrol in his lawn mower each year.

How much petrol does the lawn mower use for every 100 metres that Emyr walks?

Give your answer in litres.

Petrol costs £1.30 per litre.

Emyr says, “The petrol for my lawn mower costs me approximately 60p per pint.”

Is Emyr correct?

You must show all your working.

Yes No

Amrit is planning to go to Switzerland.

The table below shows the rates for exchanging British pounds (£) and Swiss francs (CHF) at a money exchange shop.

The exchange shop: • has all possible British notes and coins, • sells and buys CHF notes only (no coins are available or accepted), • has 10 CHF, 20 CHF, 50 CHF, 100 CHF, 200 CHF and 1000 CHF notes.

Amrit has £480 to buy Swiss francs. Calculate • the maximum number of Swiss francs that Amrit can buy, and • how much, to the nearest penny, this will cost him.

You must show all your working.

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Luned’s tent is in the shape of a triangular prism. The cross-section of her tent is an isosceles triangle. She noted a few measurements on a diagram of her tent, as shown below.

Calculate the volume of Luned’s tent. Give your answer in m³.

You must show all your working.

Volume of Luned’s tent is_{.....……........ ……………} m³

Cycle frames are made from steel, aluminium or carbon fibre.

The table below gives the density of steel, aluminium and carbon fibre.

Volume of aluminium in Owain’s cycle frame is_{……........ …………} cm³

Bethan has a cycle frame that is identical to Owain’s cycle frame. However, her cycle frame is made from carbon fibre. Calculate the mass of this frame.

Give your answer in grams.

Mass of this cycle frame is_{……........ …………} g

The diagram below is a sketch of the Eiffel Tower.

The sketch is drawn to scale. The Eiffel Tower is 324 metres tall. Visitors can climb up to the Level 2 viewing platform using the internal steps.

Which of the following is a reasonable estimate of the number of steps from the ground to

the Level 2 viewing platform?

150 650 2500 3500 6500

Calculate the angle of elevation of the top of the Eiffel Tower from the point P.

Danielle is studying the growth of the population of Wales.

She used the 2001 and 2011 Census data to draw these histograms.

Use Danielle’s histograms to answer the following questions:

Circle the earliest decade in which anyone included in the histograms could have

been born.

1890–1899 1900–1909 1910–1919 1920–1929 1930–1939

From Danielle’s histogram, the population of under-50s in Wales was 1 870 000 in 2001. Calculate the increase in the population of under-50s in Wales from 2001 to 2011.

The 60 to 69-year-olds saw the biggest increase in population from 2001 to 2011. Calculate the percentage increase in the number of 60 to 69-year-olds from 2001 to 2011.

Give your answer to the nearest whole number.

The data in this table was also available to Danielle.

Explain why Danielle did not include this data in her histograms.

The number of 40 to 49-year-olds in 2011 was different to the number of 30 to 39-year- olds in 2001.

Give a full explanation for what could have caused this.

Heledd is the captain of a cargo ship. She is planning her next voyage.

Heledd has been employed to deliver 3 × 10⁵ tonnes of sand. (a) Heledd needs to know the volume of the sand before the sand can be loaded on to the ship. She has been given the following information about the sand:

Calculate the number of grains of sand in 3 × 10⁵ tonnes of sand.

Give your answer in standard form.

Calculate the volume of the 3 × 10⁵ tonnes of sand in m³.

Heledd has been given the following instructions for her voyage:

• From port A, sail 200 km due south to port B. • From port B, sail due east to port C. • From port C, sail on a bearing of 318º back to port A.

Use the space below to draw a sketch of the ship’s voyage.

Calculate the distance from port C directly back to port A.

You must show all your working.

Time it will take is_{……........ ……} hours and_{……........ ……} minutes

A train manufacturer has developed a new braking system. The velocity-time graph shows the velocity of a train from when the new brakes are applied until it comes to rest.

Velocity (ms⁻¹)

Estimate the train’s deceleration at time 60 seconds.

Calculate an estimate of the distance travelled by the train from the instant the brakes are applied until it comes to rest.

You must use exactly 4 strips of equal width.

Explain how you could use the graph to gain a more accurate estimate of the

distance travelled.

The base radius of the cone and the radius of the cylinder are both 9 cm. The height of the cylinder is four times the vertical height of the cone.

The bottle has been designed so that it has a capacity of 10 litres.

Calculate the total height of the bottle.

Weedkiller is poured into the bottle at a constant rate. The cone is full of weedkiller after 2 seconds. The bottle as a whole is full after 26 seconds. Using the axes below, sketch a graph of the height of weedkiller in the bottle during the

26 seconds it takes to fill.

Height of weedkiller (cm)