OCR GCSE Maths Paper 4: Calculator Higher November 2021 question paper J560/04

Calculate.

(6² + 5)³

Write your answer correct to 3 significant figures.

Calculate the area of this trapezium.

Simplify.

x¹² ÷ x⁴

Li throws two fair four-sided dice, each numbered 1, 2, 3 and 4. Li multiplies together the two numbers that the dice land on to produce a score.

Find the probability that Li’s score is a prime number.

Fountain A squirts water every 24 minutes. Fountain B squirts water every 42 minutes. They squirt water together at 15:19.

Find the next time they squirt water together.

A school sends 60 students from Year 8 and 105 students from Year 9 to a museum.

The school divides these students into groups using the following rules.

• The groups must all be the same size.

• All students in any group must be from the same year.

• There should be as few groups as possible.

Find the size of each group and the total number of groups.

A shop sells the same milk in three different sized cartons. The diagram shows the price of each carton.

Which carton is the best value for money? Show how you decide.

A student only buys milk on a Saturday morning. They use 120 ml of milk each day. Any unused milk has to be thrown away at the end of the following Friday.

Show that it is cheaper for the student to buy the milk they need in 300 ml cartons than in

500 ml cartons.

Over a long period of time, it is found that the probability of a train from Bewford to London being late is 0.2.

One morning there are two trains from Bewford to London.

Use the information to complete the tree diagram.

Work out the probability that both trains are not late.

Give a reason why the probabilities used in the tree diagram for the second train may not be reliable.

Morgan takes a train from London to Bewford and then another train to Agon. The tree diagram shows the probabilities of Morgan’s trains being late or not late.

Morgan will not catch the train to Agon if the train to Bewford is late and the train to Agon is not late.

Work out the probability that Morgan will catch the train to Agon.

Jamie invests £6000 at a simple interest rate of r % each year. After 6 years the value of their investment is £7170.

Find the value of r.

The price of a plane ticket is increased by 15% to £1426.

Find the original price of the plane ticket.

Alex, Blake and Charlie play a computer game.

Alex goes first and scores n points.

• Blake scores 8 points less than 3 times the number of points scored by Alex.

• Charlie scores 25 more points than Blake.

• The three people score a total of 618 points.

Work out how many points they each score. You must show your working.

The diagram shows triangles ABC and ADE.

B lies on AD and C lies on AE. BC is parallel to DE.

Complete these statements to show that triangles ABC and ADE are similar.

Angle ABC = angle ADE because they are corresponding angles.

Angle ACB = angle........ because........

Triangles ABC and ADE are similar because........

The region R is shown on this grid.

Region R is defined by four inequalities. One of the inequalities is x ⩾ 0.

Use the symbols ⩽ and ⩾ to complete the other three inequalities.

x ⩾ 0

x + 2 y........ 24

The inequality x ⩾ 0 is replaced by a new inequality. Region R is then a kite.

Write down the new inequality.

The height, h cm, of each member of a tennis club is recorded. The histogram shows some of the results.

40% of the members have a height in the interval 160 ⩽ h < 170. 30% of the members have a height in the interval 170 ⩽ h < 180. 100% of the members have a height in the interval 140 ⩽ h < 200.

Complete the histogram for the intervals 170 ⩽ h < 180 and 180 ⩽ h < 200.

Find the coordinates of the turning point of the graph of y = x² + 6x + 17.

Here are the first four terms of a quadratic sequence.

- 1 3 13 29

The nth term is an² + bn + c.

Find the values of a, b and c.

The formula

P = 6800 × 1.045ⁿ

is used to predict the population, P, of an island n years after 2018.

Write down the population of the island in 2018.

Write down the percentage growth rate used in the formula.

Work out the population predicted by the formula for the year 2030.

Give one reason why the answer to (c)(i) may not be reliable.

The diagram shows triangle ABC.

AC = 48 mm, BC = 85 mm and angle BAC = 53°.

Calculate length AB. You must show your working.

For each graph below, select its possible equation from this list.

Here is a sketch of y = x³.

On the axes below, sketch the graphs of

y = -x³

y = x³ - 8, showing the values of any intercepts with the axes.

ABC is an isosceles triangle. The sides of the triangle ABC are all tangents to a circle of radius 6 cm, centre O.

Angle BAC = 70° and BA = BC.

Show that length BO is 17.54 cm, correct to 2 decimal places.

Find the area of triangle ABC. You must show your working.

Solve algebraically.

y = x + 3 (x - 3)² + y² = 50

You must show your working.