WJEC GCSE Mathematics Unit 1: Non-calculator Higher November 2020 question paper 3300U50-1

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

The first four diagrams in a sequence are shown below.

Diagram 1 Diagram 2 Diagram 3
Diagram 4

Complete the following subtraction.

The first three diagrams in another sequence are shown below.

Give an expression, in terms of n, for the number of dots (●) in Diagram n.

You must simplify your expression.

On each Venn diagram, shade the region that represents the given set.

The table below shows some of the values of y = x² − 4x − 3 for values of x from –2 to 5.

Complete the table by finding the value of y for x = −2 and the value of y for x = 2.

On the graph paper opposite, draw the graph of y = x² − 4x − 3 for values of x from

–2 to 5.

Draw the line y = 1 on the graph paper.

Write down the values of x where the line y = 1 cuts the curve y = x² − 4x − 3.

Values of x are_........ and_........

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

A sum of money is shared in the ratio 3: 4: 7. The smallest share is £210.

What is the total amount of money shared?

You must show all your working.

Find four different positive whole numbers so that:

• their mean is 8, • their range is 8, • their median is 8.

Write your four numbers in the boxes below.

Factorise x² – 7x + 12, and hence solve x² – 7x + 12 = 0.

Expand and simplify (5x – 2)².

Alice works for an engineering company.

A working day is chosen at random. From keeping a record over the last year, Alice knows that, for this working day,

• the probability that she travels to work by car is 0·7, • the probability that she arrives at work before 8:00 a.m. is 0·4, • her time of arrival is independent of how she travels to work.

Using the above information, draw and fully label a complete tree diagram.

You must include all probabilities.

What is the probability that, on the randomly-chosen working day, Alice travels to work by

car and arrives before 8:00 a.m.?

A circle, centre O, has a radius of 4 cm. A and B are points on the circumference of the circle. Lines PA and PB are both tangents to the circle. PB = 12 cm.

What is the length of PA?

State the circle theorem you have used to find your answer.

Circle theorem:_{……........ ……..}

What is the size of PAO ?

State the circle theorem you have used to find your answer.

Circle theorem:_{……........ ……..}

Calculate the area of the quadrilateral PAOB.

A farmer knows that the time, t, taken by goats to eat all the grass in a particular field is inversely proportional to the number of goats, g, in the field.

When there are 25 goats in the field, the time taken to eat all the grass is 36 days.

You may assume that all the goats eat grass at the same rate.

Find a formula for the time, t, in terms of the number of goats, g.

Hence, find the time taken for all of the grass to be eaten when there are 20 goats in the

field.

The farmer needs the grass to last for at least 40 days.

What is the greatest number of goats that should be allowed in the field?

Express the following as a single fraction in its simplest form.

Two similar cones have volumes of 20 cm³ and 1280 cm³.

The radius of the base of the smaller cone is 2·3 cm.

Calculate the radius of the base of the larger cone.

In the triangle EFH below:

• G is the midpoint of FH, • EG and FH are perpendicular.

Prove that EFG and EHG are congruent triangles.

You must state the condition of congruence.

Make y the subject of the following formula.

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

The curve is transformed, as shown below.

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.

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

A circle has radius r cm, where r is an integer.

The side of a square is of length xcm.

If the circle and square have the same area, explain why x cannot be an integer.

You should consider algebraic expressions in your answer.

Dewi has a box containing eleven socks.

Six of the socks are red, four are green and one is yellow.

Early one morning, without switching on the light, Dewi selects two socks at random.

Calculate the probability that the first sock selected is yellow and the second is red.

Calculate the probability that Dewi selects two socks of the same colour.

Calculate the probability that at least one green sock is selected.