OCR GCSE Maths Paper 4: Calculator Higher November 2019 question paper J560/04

Carol makes birthday cards. Each card takes the same amount of time to make.

She makes 3 cards in 48 minutes. She has an order for 80 cards.

Can she complete this order in 3 days if she works 8 hours each day? Show how you decide.

Use the formula F = to find the value of F when

Give your answer in standard form, correct to 2 significant figures.

At a railway station, trains are either eastbound or westbound. An eastbound train leaves the station every 25 minutes. A westbound train leaves the station every 45 minutes.

An eastbound train and a westbound train both leave the station at 8 am.

When is the next time that two trains leave the station together?

Bob makes dry concrete by mixing cement, sand and stone in the ratio 1: 2: 3 by weight. He buys the cement, sand and stone in bags as shown in this table.

He packs the dry concrete into 30 kg bags.

Bob buys just enough cement, sand and stone to make 50 bags of dry concrete.

Show that Bob buys 500 kg of sand.

Bob sells the 50 bags of dry concrete for a total of £396.

Calculate Bob’s percentage profit.

Multiply out and simplify.

(4 x + y)(x - 3 y)

A bag of sweets contains only mints, sherberts and toffees.

The ratio of the number of mints to sherberts is 2: 3. The ratio of the number of sherberts to toffees is 7: 5.

What fraction of the sweets are sherberts?

12 students take two tests. Each test is out of 60. The scatter diagram shows the results for 10 of the students.

The table shows the results for the other 2 students.

Plot these results on the scatter diagram.

Describe the type of correlation shown in the scatter diagram.

Draw a line of best fit on the scatter diagram.

Another student was absent for Test 2. The student scored 40 marks on Test 1.

Use your line of best fit to estimate a result for this student on Test 2.

Work out the percentage of the 12 students whose result on Test 1 is lower than their result on Test 2.

The diagrams show the price paid by two groups of people visiting a funfair.

Assume each adult pays the same price and each child pays the same price.

Find the price for an adult and the price for a child.

Here is function A.

A number, k, is input into function A. The output is also k.

Find the value of k.

The output of function A is y.

Write an algebraic expression, in terms of y, for the input of function A.

The diagram shows a composite function with an input, n, and an output of 96.

Find the value of n.

The value of a house, £ H, is given by the formula

H = 165 000 × 1.03^t

where t is the number of years after 1st January 2010.

Write down the value of the house on 1st January 2010.

Write down the annual percentage increase in the value of the house.

Show that the value of the house is over £200 000 on 1st January 2017.

Are these two triangles definitely congruent? Give a reason.

Prove that these two triangles are congruent.

The cumulative frequency graph summarises the annual salary, p (£ thousands), of the 60 workers in a factory.

Use the graph to estimate the median annual salary.

(a) £........ thousands

Complete this cumulative frequency table.

Use the information in the cumulative frequency table to calculate an estimate of the mean annual salary.

(c) £........ thousands

Explain why your estimate of the median is more reliable than your estimate of the mean.

A transport lorry consists of a cab and a trailer. The trailer has a volume of 90 m³. Alfie makes a model of this lorry using a scale of 1: 72.

Work out the volume of the trailer in Alfie’s model, giving your answer in cm³.

Alfie paints his model lorry. He has eight colours available.

He decides to paint the cab in one colour and the trailer in a different colour.

He then wants to paint his name on the trailer. The name must be in a different colour to the trailer.

In how many different ways can Alfie paint his model lorry?

The diagram shows a circle with centre (0, 0) and a tangent at the point (– 12, 16).

The tangent crosses the y-axis at the point (0, p).

Find the value of p.

Calculate length DF in this triangle.

Calculate angle ACB in this triangle.

Show that + can be written in the form , where a is an integer.

Sketch the graph of y = 3^x. Give the value of the y-intercept.

The diagram shows a right-angled triangular prism ABCDEF.

Length AD = 11 cm, length CD = 10 cm and length CF = 6 cm.

Calculate the volume of the prism.

Use trigonometry to show that angle FDC = 31°, correct to the nearest degree.

Calculate the exact length of AF.

The graph shows the distance travelled by a particle over 8 seconds.

Estimate the speed of the particle at 5 seconds.