OCR GCSE Maths Paper 5: Non-calculator Higher November 2023 question paper J560/05

Write 60 as a product of its prime factors.

By writing each number correct to 1 significant figure, find an estimate for this calculation.

Simplify.

3a² × 4a⁵

Factorise fully.

4x² - 12x

A sales representative and a manager discuss this graph of sales over the last year.

The sales representative says

I can tell from the graph that, over the last year, sales have risen every month.

Is the sales representative correct? Give a reason for your answer.

The manager says

I can tell from the graph that sales are now more than double what they were at the start of the year.

Is the manager correct? Give a reason for your answer.

Work out.

+

- 2

Triangle A and triangle B are drawn on the coordinate grid.

Describe fully the single transformation that maps triangle A onto triangle B.

A motorist wants to buy a new car but does not have enough money.

The price of the car is £16 000.

The motorist sees this notice for a deal on the car they want to buy. The number of equal monthly payments is hidden.

Pay 15% of the price of the car now

Work out the number of monthly payments if the total cost of the car to the motorist is £17 400. You must show your working.

The density of some concrete is 2.4 g/cm³. A lump of this concrete has a volume of 400 cm³.

Work out the mass of the lump of concrete.

A box contains only red, green and black pens. The ratio of red pens to green pens to black pens is 1: 4: 11.

Work out the percentage of the pens that are green.

There are 24 more green pens than red pens.

Work out the total number of pens in the box.

Find the next term of this sequence.

1 3 9 27 81........

In the Fibonacci sequence below, the next term is found by adding the two previous terms. The third term is 0.83 and the fourth term is 1.29.

Complete the first, second and fifth terms of the sequence.

Work out.

0.8 ÷ 0.004

A carpenter has a plank of wood of length w metres. The carpenter cuts of the plank of wood into 20 equal pieces. Each piece has length 0.06 metres.

Work out the value of w, the original length of the plank of wood. You must show your working.

Write down an equation for the line that is parallel to y = 3 x - 5 and passes through the point (0, 1).

Complete the table for y = x³ + 4x².

Draw the graph of y = x³ + 4x² for -5 ⩽ x ⩽ 1.

The equation x³ + 4x² = k, where k is an integer, has exactly one solution for -5 ⩽ x ⩽ 1.

Find the greatest possible value of k.

A teacher is planning a theme day for the 500 pupils at their school. The teacher asks a sample of 20 pupils from year 8 which theme they would prefer.

The results are shown in the table.

Describe two disadvantages of the teacher’s sampling method.

Using the results from the table the teacher estimates that 175 pupils in the school would prefer a sport theme.

Here is the teacher’s method.

Write down one assumption the teacher has made when making their estimate.

Using ruler and compasses only, construct the road from town T to the road AB.

The new road costs £200 000 per kilometre to build. The road constructor says

The new road will cost over £600 000 to build.

Show that the road constructor is incorrect.

The box plot shows the distribution of the times, in seconds, taken by class 11P to complete a

The times, in seconds, taken by class 11Q to complete the same problem are summarised below.

• median = 52

• lower quartile = 42

• interquartile range = 18

• range = 70

• highest score = 86

Show the distribution of 11Q’s times as a box plot on the diagram above.

Which class has the more consistent times? Give a reason for your answer.

y is directly proportional to the cube of x.

Complete the table.

Work out.

Give your answer as a fraction in its simplest form.

The graph of y = x is drawn on the grid.

The region R satisfies the following inequalities.

y ⩾ x y ⩽ 2 y < - 2 x - 3

By drawing two more straight lines on the grid, find and label the region R.

Work out.

The graph of y = x² is shown below for -2 ⩽ x ⩽ 2.

Find the equation of the image when y = x² is reflected in the line y = 2.

Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 6x - 5.

In this question all angles are given in degrees.

A, B, C and D are points on the circumference of a circle, centre O.

Find the size of angle BCD.

Find the size of angle DAB. Give a reason for your answer.

In the diagram,

• ABC is a right-angled triangle

• ACD is the sector of a circle with centre A.

Show that the area of the sector ACD is m².

Work out the total area of the shape ABCD.

The x-coordinates of the intersections of the graphs of y = x² + ax + 7 and y = 3x + b are the solutions to the equation x² + 8x + 13 = 0.

Find the value of a and the value of b.

Riley has a set of cards. Each card has a triangle or circle drawn on it and is coloured red or blue.

The table gives some information about the number of each type of card.

Riley chooses three of these cards at random without replacement. All three of these cards have a circle drawn on them.

Riley says The probability that two of these three cards are blue and one is red is less than Is Riley correct? You must show your working.