NCFE Maths Level 2 Past Papers 2023 Section B

Fiona is on a work placement in a hotel.
The hotel has a loyalty programme for the guests.
There are three million, four hundred thousand and nineteen guests currently
signed up to the loyalty programme worldwide.

Write three million, four hundred thousand and nineteen as a number.

There are 216 guests currently staying at the hotel.
81 of these guests are signed up to the loyalty programme.
Fiona thinks that more than ⁴/₁₀ of these guests are signed up to the loyalty
programme.

Is she correct?

The table below shows information about the 216 guests staying at the hotel on Sunday.

Every Sunday and Monday, guests who will be staying for more nights than the mode are given a voucher for £10 off food and drink in the restaurant.

The total value of the vouchers given to guests on Monday was 4% more than the total value of the vouchers given on Sunday.

What was the total value of the vouchers given on Monday?

Fiona uses this formula to work out the number of loyalty points earned by each guest last year.

L = 300 (s + ^r/₂)

Where L = number of loyalty points collected in a year
s = number of nights stayed in a suite
r = number of nights stayed in a regular room

She then uses this table to put each guest into one of five tiers based on the number of loyalty points they earned.

Last year, Mrs Jones stayed 3 nights in a suite and 7 nights in a regular room.

Which tier should Fiona put Mrs Jones into?

A luxury room in the hotel has a bathtub 60.3 inches long.
What is the length of the bathtub in centimetres?
Use the conversion 1 inch = 2.54 cm

Give your answer correct to 1 decimal place.

Fiona helps with organising an event at the hotel.
The diagram below shows the dimensions of the dance floor.
The shape of the dance floor has one line of symmetry.

On the dance floor, each person must have at least 0.9 m2 of floor space.
Work out the maximum number of people who can use this dance floor at one time.

Calista is a product designer at a toy factory.
The diagram shows a metal part in a toy robot.

What is the name of this shape?
Tick the correct answer.

Calista designs a plastic piece for a game.
The piece is in the shape of a cone.
The diagram shows the dimensions of the piece.

Work out the surface area of the piece.

Use A = 𝜋r² + 𝜋rs
where A = surface area of a cone
r = radius of the circular base
s = slant height of the cone

Use 𝜋 = 3.14

Calista mixes three colours to make teal-coloured paint for the plastic game pieces.
She mixes blue, green and yellow paint in the ratio 4 : 2 : 1
Calista wants to make 14 litres of teal-coloured paint.
She thinks she needs 1.6 litres of yellow paint.

Is she correct?

The graph below shows the information about the settings and fault rate of a machine in the toy factory.

What was the highest fault rate when the machine was set to make 1600 toys per hour?

The graph below shows the information about the settings and fault rate of a
machine in the toy factory.

Calista is writing a report.
She uses a line of best fit to find the fault rate when the machine setting is 2500

Calista writes, “The fault rate when the machine setting is 2500 as a percentage
of the median fault rate when the machine setting is 2600 is more than 90%.”

Is she correct?

Calista has this data about the volume of plastic used to make the toys she has
designed.

She works out an estimate of the mean volume of plastic used for each toy.
She wants to reduce this mean by 8%

If she is successful, what will the new mean be?
Give your answer correct to 1 decimal place.

Abdul wants to build an extension to his house.
The coordinate grid below shows the plan of his back garden where the extension will be.

Points A and B are two corners of the extension.
The line AB shows one wall of the extension.
The floor of the extension will be a square.

Write down a set of possible coordinates for the other two corners of the extension.

The diagram below shows the dimensions of the extension.

Abdul wants to work out the power of the heater needed for the extension.
First, he needs to find the volume (V) of air inside the empty extension by using this formula:
V = 0.5 × w × l × (a + b)
where a = greatest height (m)
b = smallest height (m)
w = width (m)
l = length (m)

Abdul then uses this formula to work out the power of the heater needed for the extension.
P = 40V+ 100n
where P = power of the heater (watts)
V = volume of air inside the empty extension (m³)
n = the number of windows
There will be 2 windows.

Work out the power of the heater needed for Abdul’s extension.

Abdul needs to make a planning application.
He must include a scale drawing of the garden and the extension.
The width of the garden is 11.8 metres.
The drawing will use the scale 1 : 200
Abdul thinks that the width of the garden in the scale drawing is 5.4 cm long.

Is Abdul correct?

Abdul finds this information about planning applications to his local council in 2020.

Abdul thinks that, overall, residential applications are more likely to be granted than commercial applications.

Is he correct?

Abdul finds this information about planning applications to his local council in 2020.

What is the probability that one of these applications chosen at random is a declined commercial application?