WJEC GCSE Mathematics Unit 1: Non-calculator Intermediate June 2019 question paper 3300U30-1

Twenty-five balls have numbers printed on them.

Some of the balls are coloured yellow (Y), the others are coloured blue (B). The list below shows both the colour of each ball and the number printed on it.

Y 76 Y 217
B 54 B 126
Y 21 Y 438
Y 32 B 561
B 194
Y 69 B 37 B 518
Y 94 Y 157
Y 208 Y 382
B 56 B 234
Y 72 B 84 Y 68 Y 271
Y 53 B 100
Y 321

Complete the frequency table.

How can you use your table to check that all the balls have been counted?

The 25 balls are placed in a box. One ball is chosen at random.

What is the probability that it is a yellow ball numbered less than 100?

Shade one square so that the diagram below has rotational symmetry of order 2.

Shade two squares so that the diagram below has rotational symmetry of order 4.

Shade two squares so that the diagram below has rotational symmetry of order 3.

Write down the next two numbers in the following sequence.

−19 −15 −11 −7 ……. ………

Rods are used to make a sequence of patterns as shown below.

Pattern 1 uses six rods.

How many rods are required to draw Pattern 4?

Pattern 37 requires 186 rods.

How many rods are required to draw Pattern 38?

Describe in words the rule used in the following sequence.

243 81 27 9 …….

In this question, you must use only the numbers 3 and 7 to make other numbers.

You must only add or subtract.

For example, if we wanted an answer of 11, we could write

7 + 7 – 3 = 11.

Show how you can get each of the following answers.

2

Write your solution in the box below.

8

Write your solution in the box below.

19

Write your solution in the box below.

A Venn diagram is used to show the following information:

• The Universal set, ε, is the set of numbers from 10 to 20 inclusive. • Set A = {11, 13, 14, 18, 20}. • Set B = {multiples of 3}.

Draw the Venn diagram that shows the above information.

Factorise 10 a – 15.

Solve the following equations.

13f + 2 = 6f + 5.

n is an integer.

Tick the correct statement below.

You must give an explanation for your decision.

ABCD is a rectangle.

AB is parallel to EF. AC, CE and DG are straight lines.

Find the size of each of the angles a, b and c.

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

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

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

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

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?

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.