WJEC GCSE Numeracy Unit 1: Non-calculator Higher November 2022 question paper 3310U50-1

In the north orchard, • Malik has a total of 35 trees • number of apple trees: number of pear trees = 4: 3.

In the west orchard, • Malik has twice as many pear trees as he has pear trees in the north orchard • number of pear trees: number of cherry trees = 5: 11.

How many cherry trees does Malik have?

You must show all your working.

Malik’s crop of apples this year has a total mass of 5280 pounds. He makes apple juice from of the mass of his apple crop. Malik makes 2 litres of apple juice from every 5 kg of apples.

Calculate the number of litres of apple juice Malik makes.

Whales are sometimes spotted in the Irish Sea, off the west coast of Wales.

Scientists decide to search for other whales in the Irish Sea. The search area is the region within 20 km of the position where the minke whale was spotted.

Using the scale given, show this search area on the map above.

This minke whale has a length of 20 feet.

Remember: 1 inch ≈ 2·5 cm, 1 foot = 12 inches

Use these facts to complete the following statement.

The minke whale has a length of_........ metres.

The brain of a minke whale has 12·8 billion neocortical neurons. A female human brain has 19 billion neocortical neurons.

Remember: 1 billion = 1000 million

Calculate an estimate for the number of neurons in a minke whale brain expressed as a percentage of the number of neurons in a female human brain.

You must show all your working.

Approximately_........ %

10% of all neocortical neurons are lost over a human lifespan. Calculate the number of neocortical neurons in a female human brain at the end of a lifespan.

Give your answer in standard form.

The shortest yacht has a length of 3 m. The longest yacht has a length of 22 m.

Use the information above to complete a box-and-whisker diagram on the graph paper

The lengths of the 68 yachts in Clwyd Marina were measured.

For these yachts: • the lower quartile of their lengths is 10 m • 25% have lengths greater than 18 m • the median length is 11·6 m.

Calculate how many of the yachts in Clwyd Marina have lengths greater

than 10 m.

Melin is a company that packages flour for sale in supermarkets.

It packages the flour in cylindrical bags. The area of the cross-section of each of these bags is 25 cm².

Each bag has a volume of 500 cm³.

Currently the bags are filled with flour at a rate of of a bag per second.

Complete the following statement.

Melin packages bags of flour at a rate of_........ cm³ per minute.

A new cylindrical bag is designed to have the same capacity and to be more stable.

Melin decides to increase the area of the cross-section of its original bags by 100%.

Calculate the height of this new bag.

Madeleine is researching the effects of waves. She does this at two different beaches, Llanddawel and Abertig.

She measures the masses of pebbles in a sample taken from each beach.

Look at the histogram below. It shows the masses of the pebbles in the sample taken from Llanddawel beach.

Calculate an estimate for the percentage of pebbles in Madeleine’s sample that had a

mass of less than 70 g.

Look at the histogram below. It shows the masses of the pebbles in the sample taken from Abertig beach.

The scale on the vertical axis is missing.

120 pebbles each had a mass of less than 30 g.

Use this fact to complete the frequency density axis above.

What was the median mass of the pebbles in the sample taken from Abertig beach?

Circle your answer.

30 g 40 g 45 g 50 g 50∙5 g

Luke wants to lay wooden flooring in the living room of his house.

The plan view of his living room floor is shown below.

All the measurements shown on the diagram are correct to the nearest 0∙2 m.

Luke knows that: • each pack of wooden flooring covers exactly 3 m² • 10% needs to be added to the area of the floor that is to be covered, to ensure he has enough wooden flooring.

Calculate the minimum number of packs needed to guarantee that Luke has enough wooden flooring to cover his living room floor.

You must show all your working.

Number of packs is_........

Emma wants to know how much water is in a pond near her house.

She has taken width measurements of the pond every 3 m along its length. These width measurements are shown on the plan view of the pond below.

Emma has used these width measurements to sketch the following graph.

Emma knows that the pond has a uniform depth of 1∙2 m. Use the trapezium rule with 4 strips to calculate an estimate for the volume of water in the

pond.

Gerallt has decided to open a new ice cream shop at his local seafront. He has designed his new ice cream shop to look like half an ice cream cone. The design consists of half a hollow cone connected to half a hollow hemisphere, as shown below.

The radius of the base of the half hemisphere is 3 m. The perpendicular height of the cone is shown as h on the diagram above.

Gerallt designed the shop so that the volume of the half cone is equal to the volume of the half hemisphere.

A rubber ball is dropped from a height of 8 m onto horizontal ground.

After each bounce, the ball reaches a maximum height that is 17% lower than the maximum height reached after its previous bounce.

The diagram below shows the path of the ball for the first few bounces.

Write a formula for the maximum height, H, in metres, reached by the ball after n bounces.