WJEC GCSE Mathematics Unit 1: Non-calculator Higher November 2022 question paper 3300U50-1

In a group of 200 people:

• 105 people do not have black hair and do not wear glasses • 20 people have black hair and wear glasses • 70 people have black hair.

Triangle ABC is shown in the diagram below.

Using only a ruler and a pair of compasses, construct an accurate drawing of triangle ABC. Side AC has been drawn for you.

All construction lines and arcs must be shown.

Express 1575 as a product of its prime factors in index form.

Simplify the following expressions.

7a(a + 5) − 2(3a² + 6a − 7)

The diagram below shows the graph of a straight line for values of x from –1 to 3.

Write down the gradient of the line above.

Write down the equation of the line in the form y mx c.

Show that the lines

y = 3 x − 8 and 2 y − 6 x = 23

are parallel to each other.

In the following formulae, each measurement of length is represented by a letter. Consider the dimensions implied by each formula. For each case, write down whether the formula could be for a length, an area, a volume or none of these.

The first one has been done for you.

7a³− abc
volume

5abc 6bc b² _........

4a²b 4b²a_........

3a 8b 2c _........

a²− abc _........

Which complete method, using Pythagoras’s Theorem, can be used to find x ?

Circle your answer.

Which of the following calculations can be used to find y?

Circle your answer.

P, Q and R are points on the circumference of a circle with centre O.

Calculate the value of x. You must state all the angle properties that you use.

You must show all your working.

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

On Monday morning, Twm picked n apples from a tree. Ceri picked 5 times as many apples as Twm.

On Monday afternoon, Twm picked 19 more apples. Ceri gave 7 of her apples to Twm.

Ceri still had more apples than Twm.

Write down an inequality in terms of n to show the above information. Use your inequality to find the least possible number of apples Twm picked on Monday morning.

You must show all your working.

Given that y is directly proportional to x³ and that y = 108 when x = 3,

find an expression for y in terms of x.

Use the expression you found in part (i) to complete the following table.

It is known that e is inversely proportional to f.

Describe what happens to e when f is doubled.

Describe fully the single transformation that transforms shape A onto shape B.

In the following diagram, the lines AC and BD bisect each other.

Prove that triangles ABE and CDE are congruent.

You must state the condition of congruence.

Using the axes below, find the region which satisfies the following inequalities.

You must clearly indicate the region that represents your answer.

A cone and a cylinder have equal volumes. The cone has a base radius of rcm and a height of hcm. The cylinder has a base radius of rcm and a height of cm. Find h in terms of r.

You must express your answer in its simplest form.

Evaluate the mean of the following three numbers:

Ffion has some blue cards and some yellow cards. She takes 7 of the blue cards and 3 of the yellow cards and puts them in a box.

Ffion removes one card from the box at random and replaces it with two cards of the other colour.

Then she removes a second card from the box at random.

Calculate the probability that the two cards that Ffion removed are of different colours.

The highest point of a curve is called a maximum point.

The diagram below shows a sketch of the curve with equation y f x. The maximum point of this curve has coordinates (–5, 4).

For each of the following, write down the coordinates of the maximum point of the curve with the given equation.

y 2 f x

The coordinates of the maximum point are (_........ ,_........ ).

y f x 7

The coordinates of the maximum point are (_........ ,_........ ).

The curve with equation y f x is reflected in the y-axis. Write down the equation of the transformed curve.

You should use function notation.

The equation of the transformed curve is

The following diagram shows a sketch of y cosx for values of x from 0° to 360°.

Given that cos25 0 9063, correct to 4 decimal places, write down all the solutions of the equation

for values of x from 0° to 360°.

Solve the following equation.

Do not use a trial and improvement method.