WJEC GCSE Mathematics Unit 1: Non-calculator Higher November 2023 question paper 3300U50-1

The Geometric Mean is a special type of average.

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.

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.

Calculate the size of angle x.

You must show all your working.

Complete the following table to give the set of inequalities that describes the shaded region shown above.

One inequality has already been written for you.

y is inversely proportional to the square of x.

y = 16 when x = 5.

Find an expression for y in terms of x.

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

In the following diagram:

• CB and DE are parallel • CE and BD are straight lines • CA = AE.

Prove that triangles ABC and ADE are congruent.

You must show all your working and explain your reasoning.

Circle the correct answer for each of the following statements.

Give an example of an irrational number that lies between 6 and 7.

My example of an irrational number is_........

Make t the subject of the following formula.

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

The point where the curve has a gradient of 0 is labelled A and has coordinates (8, –1).

On the axes below, sketch the curve y = f (x + 3). You must: • indicate the coordinates of any point where the new curve crosses an axis

• complete the coordinates of the point on the curve where the gradient is 0.

The coordinates of the point on the curve where the gradient is 0 are (_{……........ …..……},_{………........ …..……}).