OCR GCSE Maths Paper 5: Non-calculator Higher November 2021 question paper J560/05

Work out.

Give your answer as a mixed number in its simplest form.

Azmi is given this question.

Write 40 as a product of prime factors. Give your answer in index form.

Azmi’s answer is 2 × 2 × 2 × 5.

Is Azmi correct? Explain your answer.

Find the value of x.

A car mechanic has a tin containing 5 litres of engine oil. Each week they use 450 millilitres of this oil for their vehicles.

The car mechanic says

After 9 weeks I will have used over 80% of the oil in this tin.

Are they correct? Show how you decide.

The table shows the marks obtained by 10 students in spelling tests in January and February.

The marks for the first six students are plotted on the scatter diagram.

Plot the marks for the remaining four students.

Describe the type of correlation shown in the completed scatter diagram.

On the scatter diagram, circle the student that made the greatest improvement in their

marks from January to February.

Work out the percentage change in this student’s marks from January to February.

Another student, Kai, scored 79 marks in the test in January but was absent for the test in February.

Kai says

I could use a line of best fit on the scatter diagram to estimate the marks I may have achieved in the test in February.

Is Kai’s method reliable? Give a reason for your answer.

Work out the volume of this prism.

Here are sketches of five graphs.

Write the letter of the graph that represents the following relationships.

y is directly proportional to x.

y is inversely proportional to x.

Solve the inequality.

4 (x - 3) < x

Show your answer to part (a) on the number line.

Complete the table for y =

Draw the graph of y = for -6 ⩽ x ⩽ 6, x ≠ 0.

A worker received a 10% pay increase in 2017 and a further 10% pay increase in 2018. The worker says

Over these two years, my pay increased by 10% + 10% = 20%.

The worker is incorrect.

Work out the correct percentage increase. You must show your working.

Force is measured in newtons (N). A force of 198.5 N is applied to a rectangular surface of length 4.9 cm and width 4.1 cm.

Work out an estimate of the pressure, in N / cm², applied to this rectangular surface. [The formula for pressure is: Pressure =

The diagram shows a quadrilateral ABCD.

AD = 10 cm, angle BAD = 30° and angle ABD = angle BDC = 90°.

The ratio of length BD to length DC is 1: 2.4.

Work out length BC. You must show your working.

The box plot shows the distribution of the lengths, in cm, of 60 full-grown mice owned by a pet

Find the range.

Work out the number of these mice that have a length of at least 7.2 cm.

Sam owns 5 full-grown mice. Sam picks the third longest mouse and measures its length. Sam then looks at the box plot.

Sam says

This mouse is 7.35 cm long. Therefore, the mice I own are longer than the full-grown mice owned by the pet shop.

Give a mathematical reason to support Sam’s conclusion.

Give a mathematical reason why Sam’s conclusion may be unreliable.

Write as a fraction in its simplest form.

Two solid ornaments are mathematically similar. The larger ornament is twice as tall as the smaller ornament.

The smaller ornament has a volume of 50 cm³.

Work out the volume of the larger ornament.

In a group of 60 students, 40 own a smartphone, 27 own a tablet and 8 own neither.

A student is chosen at random from those that own a tablet.

Find the probability that they also own a smartphone. You must show your working.

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

EF is the tangent to the circle at D.

Angle BDF = 70°.

The ratio angle BCD: angle CBD is 5: 2.

Work out angle CBD. You must show your working.

Find the equation of the circle.

x² - 2y = 5 and 4y + z = 7.

Write z in terms of x. Give your answer in its simplest form.

AOB is a sector of a circle, centre O and radius 10 cm.

The area of the sector is 40π cm².

Work out the perimeter of the sector. Give your answer in the form a + b π, where a and b are integers. You must show your working.

n is a positive integer.

Prove that (2 n + 1)(n - 3)(n + 2) + 3 n (n + 7) is always even.