OCR GCSE Maths Paper 6: Calculator Higher November 2023 question paper J560/06

Beth completes some jigsaw puzzles and records the following information.

• The number of pieces in the jigsaw puzzle.

• The time taken to complete the jigsaw puzzle, in minutes.

Beth shows this information in a scatter diagram.

Beth completes two more jigsaw puzzles.

• A 3000 piece jigsaw puzzle taking 460 minutes.

• A 1300 piece jigsaw puzzle taking 320 minutes.

Show this information on the scatter diagram.

Describe the type of correlation shown on the scatter diagram.

One of Beth’s jigsaw puzzles was described as “the most difficult jigsaw puzzle you will ever try”.

Circle the most likely jigsaw puzzle on the scatter diagram.

Give a reason why you chose this jigsaw puzzle.

Draw a line of best fit on the scatter diagram.

Use your line of best fit to estimate how many pieces are in a jigsaw puzzle that takes Beth 500 minutes to complete.

Explain why Beth should not use her scatter diagram to estimate how long it will take to complete a jigsaw puzzle containing 8000 pieces.

A restaurant menu has 4 main courses and 3 side dishes. For their meal, each customer chooses 1 main course and 1 side dish.

Work out the percentage of possible meals that cost less than £8.

Write these numbers in order of size, starting with the smallest.

smallest

Casey’s mobile phone gives a weekly report showing the amount of time they use their phone.

This week the report says that the phone was used

• for 217 minutes

• 24% more than last week.

Calculate Casey’s phone usage last week.

A sheet of A4 card weighs 1.19 × 10^-2 kg.

Work out the weight of 500 sheets of the A4 card.

Card is classified using W, the weight in grams per square metre (gsm).

A sheet of A4 card is a rectangle that is 21 cm by 29.7 cm.

Calculate W for this A4 card.

The area of this rectangle can be written as ax² + bx - 10.

Find the values of a, b and c. You must show your working.

Here are two functions.

5 is input into Function A. 5 is also input into Function B. The output of Function A is 10 times the output of Function B.

Work out the value of k. You must show your working.

The diagram shows four triangles that are joined together.

• Points A, B, C and D lie on a straight line.

• Triangles ABF and CDE are equilateral triangles.

• Triangle BCF is an isosceles triangle with BF = BC.

Show that triangle CEF is a right-angled triangle. Give a reason for each stage of your working. Use the template below to help present your work. You may not need all of the lines.

Angle........ =........ ° because........

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A large box of chocolates contains dark, milk and white chocolates. When Riley opens the box, the ratio of dark to milk to white chocolates is 3: 2: 4. Riley’s family eat 6 of the dark chocolates, none of the milk chocolates and all of the white chocolates. The ratio of dark to milk chocolates is now 9: 8.

How many white chocolates did Riley’s family eat?

x and y are related by the equation xy = 36.

Tick the correct statement.

y is inversely proportional to x⁴. y = 2.5 when x = 2.

Find a formula linking x and y.

The diagram shows a cone and a cube. The cone has radius 8 cm and height 10 cm.

The volume of the cone is equal to the volume of the cube.

Work out the length of one side of the cube. [The volume V of a cone with radius r and height h is V = r²h.]

A cafe owner recorded information about customer orders for coffee. They recorded whether the customer asked for milk (M) and whether the customer asked for sugar (S).

The results are shown in this Venn diagram.

One of the customers is chosen at random.

Find the probability that the customer asked for sugar.

One of the customers is chosen at random.

Find the probability that the customer asked for sugar given that they asked for milk.

The graph of y = 3^x is sketched below.

On the same axes, sketch the graph of y = 2^x.

Charlie sketches this graph.

Charlie says

The equation of my graph is y = sinx.

Explain how you know that Charlie is not correct.

Write down a possible equation for Charlie’s graph.

Here is a right-angled triangle.

The area of the triangle is 100cm², correct to the nearest 10cm². The length of the base of the triangle is 8 cm, correct to the nearest cm.

Calculate the largest possible height of the triangle.

Sasha and Taylor are asked to find how many solutions the equation 5(x + 2)² = 45 has.

Here is Sasha’s answer.
Here is Taylor’s answer.

Decide who is correct, Sasha or Taylor, and give the reason for your decision.

........ is correct because........

Solve this equation algebraically. Give your answers correct to 2 decimal places. You must show your working.

x² - 5x + 3 = 0

The graph of y = x⁵ - 70x - 150 is sketched below. The root of the equation x⁵ - 70x - 150 = 0 is p.

Show that 3 < p < 4.

Find a smaller interval that contains the value of p. You must show calculations to support your answer.

Hiro invests £2500 for 2 years in a bank account paying r % per year compound interest. At the end of 2 years, the amount in the bank account is £2704.

Calculate r.

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

Points C and D lie on a tangent to the circle at C. Angle BCD = 45 °. Angle ACB = 58°. AB = 8cm.

Find the length of BC.

A fitness centre records how long each customer spends in the gym. This cumulative frequency table summarises the results.

Calculate an estimate of the mean time the customers spend in the gym. You must show your working. You may use the table above to help present your work.

This shape is formed from a rectangle and two sectors of circles.

Points A, B and C lie on a straight line. Angle CB D = 3 5 °. DE = 5 t and EF = 2 t.

Explain why BC = 2 t. Give a reason for each step of your explanation.

Show that the perimeter of the shape is t + 14t.

Simplify fully.

x³ + 8₃x² + 15x x - 9x