Eduqas GCSE Maths Component 1H Higher November 2017 question paper

1. (a) Write 360 as a product of prime factors using index notation.

In index notation, 315 = 3² × 5 × 7.

Find the highest common factor of 315 and 360.

Write 5·4 × 10^{– 4} in decimal notation.

Give your answer in standard form.

2. (a) Tina is carrying out a survey to find out how people use their mobile phones.

Tina surveyed 205 students about the cost of their monthly phone bills. The table shows this information.

Comment on how reliable the data about Monthly contracts are likely to be.

Using the data in the table, Tina compares the cost of Pay-as-you-go with the cost of SIM only. Tina says that students who use Pay-as-you-go have both the lowest and highest bills.

Make further comments to explain why Tina may think • SIM only is a better deal,

• Pay-as-you-go is a better deal.

Complete each of the following statements.

SIM only could be a better deal because_........

Pay-as-you-go could be a better deal because_........

Work out the column vector 2p – q.

The grid shows the vector q.

On the same grid, draw the vector –3q.

5. (a) Expand and simplify (x – 5)(x + 2).

Simplify 3a² × 6a^–1.

Circle the correct statement.

x is inversely proportional to 25
x is directly proportional to y

y is inversely proportional to x
y is directly proportional to x

Find the value of x when y = 100.

The distance-time graph shows the start of a journey.

Work out the speed of this part of the journey in metres per second.

Simplify 15 – .

Work out 12 ÷ 3.

The diagram shows a circle inside a square. The circumference of the circle touches all four sides of the square.

The perimeter of the square is 24 cm.

Work out the area of the circle.

Give your answer as a multiple of .

Three two-digit integers a, b and c are in the ratios

a: b = 4: 5 and b: c = 7: 11.

Find the integers a, b and c.

A length of string has been cut into two pieces in the ratio 3: 5. The longer piece measures 205 cm.

What was the original length of the string?

9. (a) In a warehouse, 4 workers can load 5 tonnes of goods into a vehicle in 3 hours.

How long would it take 6 workers to load 10 tonnes of goods into a vehicle?

You may assume that all workers work at the same rate.

State one other assumption you have made in your answer to part (a).

How would your answer to part (a) change if this assumption were not correct?

10. (a) Olly is trying to solve this inequality.

Here is Olly’s solution.

Is Olly’s solution correct?

Show clearly how you decide.

Sketch the graph of y = x² –4 for values of x between –3 and 3 on the axes

opposite. Mark any intercepts with the x-axis.

Solve x² –4 0.

11. (a) Battery life is the length of time for which a battery can be used before it needs to be recharged.

One hundred users of the Litestar A tablet computer each recorded the battery life of their tablet. The diagram shows the distribution of the battery lives recorded, in hours.

Cumulative Frequency

How many of these Litestar A tablet computers had a battery life of more

than 9·5 hours?

Use the diagram to complete the table for these Litestar A tablet computers.

For the Litestar A tablet computers: • The shortest battery life recorded was 8 hours. • The longest battery life recorded was 10·4 hours.

Using this information and the information from part (a), draw the box plot

for the Litestar A tablet computers on the grid above.

Neena wants to buy one of these tablet computers. She wants the best battery life possible.

Should Neena buy a Litestar A or Litestar B tablet computer?

Give a reason for your decision.

Mahima works in a biscuit factory.

She uses a trolley to move sacks of flour and boxes of chocolate. It is not safe to have more than 215 kg on the trolley. Each sack of flour weighs 10 kg, correct to the nearest kilogram. Each box of chocolate weighs 8·4 kg, correct to the nearest 200 grams. Mahima thinks it is always safe to use her trolley to move 4 sacks of flour and 20 boxes of chocolate at the same time. Is Mahima correct?

Justify your answer with calculations.

Rearrange the formula

to make x the subject.

Fifty people order food and drink for a party.

They each order one main course and one drink from the menu.

28 people order cola. 24 people order a burger. 8 people order a kebab and none of these order cola. The 5 people who order water all order a kebab. Of the people who order a burger, twice as many order cola as order juice.

A person is selected at random from the group.

Using the table to help you, find the probability that this person orders either a burger and cola or a pizza and juice.

You must show all your working.

In the diagram, • ACE is a triangle, • BCDFG is a regular pentagon.

Prove that triangle ABG is congruent to triangle EDF.

Give a reason for each statement you make in your proof.

Conclusion:

The area of the rectangle is 22 cm².

The diagram shows a circle with centre O. The gradient of the radius OA is OA = 10 units.

The tangent to the circle at A meets the x-axis at B.

Explain why the coordinates of A are (6, 8).

Find the coordinates of B.

The diagram below shows a sketch of the graph of y = f (x).

Sketch the graph of y = f(x) + 1 on the axes below.

You must indicate the coordinates of the new positions of the points A and B.

Sketch the graph of y = f(–x) on the axes below.

You must indicate the coordinates of the new positions of the points A and B.

How many different 5-digit whole numbers can be made using the digits

2, 3, 4, 5, and 6 when each digit can be used once only?

What proportion of the 5-digit whole numbers are odd?

How many different 7-digit even whole numbers can be made using the digits

3, 4, 5, 6, 7, 8 and 9 when each digit can be used once only?

f(x) = 5x + 2 g(x) = x³

Solve f^–1 (x) = 10.

Show that gf(x) = 125x³ + 150x² + 60x + 8.

Find gf(–1).

State the coordinates of the turning point of the curve y = x² – 6x + 30.