WJEC GCSE Mathematics Unit 1: Non-calculator Intermediate November 2023 question paper 3300U30-1

Write down the next two numbers in the following sequence.

Simplify the expression 5y + 7m − 3y −10m.

Write 0·41, and 45% in descending order.

You must show all your working.

Here is a net of a cuboid.

The net is folded to form a cuboid.

The volume of the cuboid is 90 cm³.

What is the value of p?

Give your answer in metres.

Express 25 minutes as a percentage of 2 hours 5 minutes.

The mean of four numbers is 9.

What is the total of the four numbers?

Find a set of four numbers such that: • their mean is 9 • their mode is 11.

Write your four numbers in the boxes below.

There are many socks in a drawer.

The socks are red, green, blue or pink.

A sock is chosen at random from the drawer.

Complete the table below.

In the drawer, there are 20 pink socks.

How many red socks are there in the drawer?

A cup contains some tea.

Elsie drinks of the tea. There are 44 ml of tea left in the cup.

How much tea was in the cup before Elsie drank any?

The Geometric Mean is a special type of average.

To find the Geometric Mean of two numbers, you must:

• multiply the two numbers together, and

• then find the square root.

Find the Geometric Mean of 250 and 0·4.

To find the Geometric Mean of three numbers, you must:

• multiply the three numbers together, and

• then find the cube root.

Find the Geometric Mean of 100, 0·3 and 0·9.

The Geometric Mean of three numbers is 10. Two of the numbers are 8 and 25.

Find the third number.

Write down an expression for the n th term of the following sequence.

11, 15, 19, 23,....

The nth term of a different sequence is given by n² − 5.

Write down the first three terms of this sequence.

First three terms are_........ ,_........ ,_........

Express 495 as a product of its prime factors in index form.

Explain how your answer to part (a) tells you that 495 is not a square number.

Find the Highest Common Factor (HCF) of 495 and 60.

£285 is decreased by 4%. This is done 3 times in total. Each time, the previous value is decreased by 4%. What calculation would you use to find the value after the 3 decreases?

Circle your answer.

£285×1⋅04³ £285×0⋅04³ £285×0⋅96³ £285×0⋅6³ £285×0⋅96²

A number has been decreased by 10% to give an answer of 34·2.

What was the original number?

Explain why Rectangle A is not mathematically similar to Rectangle B.

Alun changes only one of the measurements of Rectangle B to make the two rectangles mathematically similar.

Write down a possible length and width of Alun’s new rectangle.

You must show all your working.

Beti walks her dog to a local park and back home every day.

She can either walk along a footpath or along a pavement at the side of a road. The probability that Beti walks to the park along the footpath is The probability that Beti walks home from the park along the road is Her decisions on which routes to walk to and from the park are independent of each other.

Complete the tree diagram below.

Find the probability that Beti walks to and from the park along the footpath.

Factorise x² −8x − 20, and hence solve x² −8x − 20 = 0.

The points B, C, D and E lie on the circumference of a circle, with centre O. AF is a tangent to the circle. AO is a straight line.

Explain how you know that AOB is a right-angled triangle.

Calculate the size of angle x.

You must show all your working.