WJEC GCSE Mathematics Unit 1: Non-calculator Higher June 2019 question paper 3300U50-1

Express 315 as a product of its prime factors in index form.

What is the Highest Common Factor (HCF) of 315 and 42?

Complete the table below.

Draw the graph of y = 3x² – 25 for values of x between −3 and 4. Use the graph paper below.

You must choose a suitable scale for the y-axis.

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

A regular octagon with centre O is shown below.

Calculate the exact size of OAB. You may choose to draw additional lines on the diagram to help you.

You must show all your working.

The Anglesey Show is a two-day event held every August.

On the first day, a random sample of 2000 visitors at the show were asked:

640 of them answered 'Yes'. What was the relative frequency of those who answered ‘Yes’?

Give your answer as a decimal.

On the second day a random sample of 3000 visitors at the show were asked the same question. The relative frequency of those who answered ‘Yes’ on this day was 0·42. Calculate the relative frequency of those who said they lived on Anglesey when the samples for both days were combined.

Give your answer as a decimal.

Which of the following is most likely to give the best estimate for the relative frequency of visitors to the show living on Anglesey? Circle your answer.

You must give an explanation for your choice.

A mass is written as 430 kg, correct to the nearest 10 kg.

Circle the least possible value of this mass.

420 kg 425 kg 429·5 kg 426 kg 424·9 kg

A time period is written as 22 seconds, correct to the nearest second.

Circle the least possible value of this time period.

22 s 20 s 21 s 21·5 s 21·4 s

A population is written as 85 people, correct to the nearest five people.

Circle the least possible value of this population.

83 people 81 people 84 people 82 people 80 people

Leah is visiting Cardiff.

The probability that she will go on a tour bus is 0·3. The probability of Leah seeing a show at the Millennium Centre is independent of her going on a tour bus.

The probability that she goes on a tour bus and sees a show at the Millennium Centre is 0·24.

Complete the following tree diagram.

Calculate the probability that Leah does not go on a tour bus and does not see a show at

the Millennium Centre.

Arthur, Sian and Kezia are all given some £1 coins.

Arthur receives £n. Sian is given five times as much money as Arthur. Kezia receives three times as much money as Arthur, plus an extra £7.

Sian was given less money than Kezia.

Write down an inequality in terms of n that illustrates the fact that Sian received less

money than Kezia.

What was the greatest amount of money that Arthur could have been given?

Rearrange the following formula to make x the subject.

c x – 3 = 4 x + d

In the following diagram, AE and BD are straight lines and BC = CE.

Is it possible to conclude that triangles ABC and DEC are congruent?

You must show all your working and explain your decision.

The diagram shows a cylinder.

The cylinder has a base of radius r and a height of

A sphere has radius R. The volume of the sphere is equal to the volume of the cylinder. Find R in terms of r.

Give your answer in its simplest form.

The following diagram shows a sketch of the curve y = f (x).

The curve is transformed, as shown below. y

Using function notation, complete the equation of the transformed curve.

The following diagram again shows a sketch of the curve y = f(x).

The curve is transformed, as shown below. y

Using function notation, complete the equation of the transformed curve.

A box contains 4 yellow cards and 6 red cards.

Three cards are chosen at random, one at a time, without replacement.

Calculate the probability that the first two cards are yellow and the third card is red.

You must show all your working.

Calculate the probability that at least one yellow card is chosen.

Write the following expression as a single fraction.

Give your answer in its simplest form.

Solve the following equation.