Eduqas GCSE Maths Component 1H Higher June 2019 question paper

Cherie is in charge of marketing for a tourist attraction.

One weekend, she collects some data about the value of ice cream sales from the café. She records her data in a table and uses it to draw a pie chart.

State one criticism of the use of a pie chart to display her data.

Cherie also records the number of visitors to the tourist attraction each season for 4 years. Her results are shown in the table.

Comment on the trend in the annual number of visitors shown by the data in the table.

2. (a) Solve 19 – 4 x = 11.

Solve 3x + 2 5.

Huw is paid a weekly wage.

Every week he:

• spends 70% of the money he has left on his living expenses,

• spends all that remains on his social life.

One week, Huw saves £40.

How much does Huw spend on his social life?

What percentage of his weekly wage does Huw spend on his social life?

4. (a) 120 = 2³ × 3^k × 5

Find the value of k.

Write 168 as a product of its prime factors.

LoWatts Ltd makes light bulbs that are identical in size.

They have regular orders from Company A for 120 light bulbs and from Company B for 168 light bulbs.

LoWatts Ltd uses one size of box to supply both Company A and Company B. Each box used contains the same number of light bulbs and is full. The number of boxes used is as few as possible.

How many light bulbs does each box hold?

When Jenna was measured recently she was 127 cm tall,

State an assumption that you have made in your answer to part (a).

Comment on the effect that your assumption has had on your decision.

The table shows some of the values of y = x² + x – 1 for –2 x 1.

Complete the table above.

On the graph paper below, draw the graph of y = x² + x – 1 for –2 x 1.

State the equation of the line of symmetry of the curve y = x² + x – 1.

Use your graph to solve x² + x – 1 = 0.

Jon bought a car.

The price of Jon’s car had been reduced by 20%. Jon paid £7680 for his car.

What was the price of the car before the reduction?

Rearrange 6(x + y) = 8 x – 5 to make x the subject.

Sam needs to catch the 8 a.m. bus to get to work on time.

The probability that Sam oversleeps is 0·6.

When Sam oversleeps, the probability that he misses the bus is 0·8. When Sam does not oversleep, the probability that he misses the bus is 0·3.

Calculate the probability that Sam oversleeps and misses the bus.

Calculate the probability that Sam catches the bus.

You must show all your working.

11. (a) Find the value of (3 × 10¹⁷) × (8 × 10⁹).

Give your answer in standard form.

In a particular country for one year: • the total energy consumption was 5·4 × 10¹¹ kilowatt hours, • the average energy consumption per person was 6000 kilowatt hours.

Work out the population of the country.

Give your answer in standard form.

12. (a) Find the value of each of the following.

0·8^–1

13. (a) Shabana is moving to a new house and is using boxes to pack.

Shabana has two different square-based boxes where: • the ratio of the lengths of the sides of the squares is 1: 3, • the ratio of their heights is 1: 4.

How many of the small boxes can the large box hold?

Shabana’s new house is further away from her workplace. She estimates that there will be a 15% increase in the cost of getting to work.

From her old house, she: • drove 945 miles per month, • used petrol at the rate of 9 miles per litre, • paid 120p per litre for petrol.

How much more will it cost her to get to work each month after she has moved?

Increased cost of getting to work £_{…………........ ……………}

A garden centre sells fish.

This box plot summarises data about the length, in cm, of a sample of 50 black and white Japanese koi they have for sale.

What is the length of the longest black and white koi?

What is the median length of the black and white koi?

The garden centre also sells red and white Japanese koi. The table shows information about the length, in cm, of a sample of 50 of the red and white koi they have for sale.

Draw a box plot to represent this data on the grid below.

A, B, C and D are points on a circle. The line PQ is a tangent to the circle at B. PBA = 51°, ACD = w° and BAD = 2w°.

Find the value of w.

You must show all your working.

Ravi needs to choose a 5-character passcode for a door lock.

He chooses to use 5 of these 7 characters:

1 9 6 7 R P #

Each chosen character is used only once.

Find the number of different 5-character passcodes Ravi can make.

Find the probability that Ravi’s 5-character passcode starts with R and ends with P.

The functions f(x) and g(x) are defined for x 0 by

g(x) = x + 5.

Find and simplify an expression for ff(x).

Using your answer to part (a), or otherwise, explain the relationship between f(x)

and f^–1(x).

Solve g^–1f(x) = 11.

Paula is baking biscuits for a charity fundraiser.

She makes biscuits in batches of 12.

Paula’s weighing scales are accurate to the nearest gram. She needs to weigh 8 grams of baking powder to make 12 biscuits.

She has 220 grams of baking powder, correct to the nearest 10 grams. She has plenty of all the other ingredients she needs.

She plans to sell her biscuits at £2 for a pack of 3.

What is the greatest amount of money that Paula could raise for her charity?

You must show all your working.

The diagram shows an arc of a circle with centre O and equation x² + y² = 50. P (5, p) lies on the circle. The arc meets the x-axis at Q. The tangent to the circle at P meets the x-axis at R.

Find the value of p, the y-coordinate of P.

Show that the equation of the tangent to the circle at P is y = mx + 10, where m is a

constant.

Find the exact length of QR.

Complete this proof to show that OE = 6a + 3b.

Proof:

OE = OA + AE = 6a + kb for some positive scalar k

OE = nOD, for some positive scalar n

What does the proof in part (a) also tell you about the point E?