NCFE Maths Level 2 September 2020 Section B

Liam searches online for a choice of broadband services.
He finds this graph:

Broadband speed is measured in Mb/s (Megabits per second).
The lettered crosses in the graph represent the different services.
What is the modal speed of these broadband services?

Alice lives in Oldcastle.
She is on a Community Policing course.
The ratio of solved to unsolved crimes in Oldcastle is 2 : 9
¹/₈ of crimes are solved in the whole of the UK.
Alice thinks that a greater proportion of crimes are solved in Oldcastle than in the rest of the UK.

Is she correct?

The value of items stolen in Oldcastle has increased by 8% each year.
The value of stolen items in 2017 was £1.7 million.

What was the value of items stolen in 2019?

Alice attends a workshop about home security.
The tutor tells the group about a house burglary.
The police found a footprint in the garden.
They used a coordinate grid to record where it was:

What are the coordinates of the point marked by ×?

A witness said the suspect is under 5 feet 10 inches tall, and has blonde hair.
Alice is shown 15 photographs:

Alice picks one of the photographs at random.
What is the probability that it is of a person who has blonde hair and is under 5 feet 10 inches tall?

Give your answer as:
• a fraction
• a decimal.

At 20:40 a witness saw the suspect entering the park at Gate A.
Another witness saw the same person leaving the park through Gate B exactly 12 minutes later.
The group are given this map of the park:

The map has a scale of 1 : 25 000
The distance between Gates A and B on the map is 9 cm

What was the average speed of the person seen entering and leaving the park?
Give your answer in metres per second (m/s).

The house had a CCTV camera.
The shaded section of the diagram shows the area covered by the camera:

Calculate the area covered by the camera.
Use 𝜋 = 3.14

Alice has a digital picture of the burglar from the CCTV camera.
The size of the print is 5¹/₂ inches by 3³/₄ inches.

Alice enlarges the picture by doubling both the width and the length.
She wants to print the enlarged picture onto one side of A4 paper.
A4 paper is 21 cm wide and 29.7 cm long.
Will the enlarged picture fit onto one side of A4 paper?
Show how you decide.
Use the conversion: 1 inch = 2.54 cm

Sam is a volunteer for CHAD, a charity that supports children.
Charities are put into categories according to the amount of money they raise each year.
Last year, CHAD raised five hundred and sixty-nine thousand, eight hundred and one pounds.
Which category is CHAD in.

This year, CHAD aim to raise £626 000
The pie chart shows where the funds will come from:

So far, CHAD have raised £95 280 from grants.

How much more money do they aim to raise from grants this year?

Sam asks friends and family to sponsor him for a 10 km run.
A local business offers to donate 25p for every £10 that Sam raises.
In total, Sam raised £2634.25
This included the money that the business donated.

How much did the business donate to Sam?

CHAD are sending a letter to supporters.
They have asked for volunteers to put the letters into envelopes.
Eight people volunteer to help.
Each person works at the same rate.
It takes them 480 minutes to complete the task.

How many minutes would the task have taken 12 people, if each person worked at the same rate?

Some people donate to CHAD by giving a one-off donation.
The table below shows the one-off donations made last year:

Other people donate by paying regular amounts.
Last year, CHAD had 150 of these regular donors who donated £7500 in total.
Sam works out an estimate for the mean of the one-off donations last year.
He compares this with the mean for regular donors last year.
Sam says,
“The mean amount donated last year was higher for the one-off donors than
for the regular donors”.

Is Sam correct?

Emma sells cars.
The original price of a car was £15 400
Its sale price is £13 500
Calculate the percentage discount.

Give your answer to one decimal place.

Emma also buys cars.
Bill wants to sell his old car.
The car is 3 years old and in good condition.
Emma uses a formula to work out the price that she will pay for Bill’s car:
P = 12 000 × C × (0.75)^T

Where:
P is the price the she will pay (in £)
T is the age of the car (in years)
C is the condition of the used car, according to this table:

The scatter diagram below shows the prices paid online for the same model of car in good condition:

How much more would Bill expect to get if he sells his car online instead of selling to Emma?

Bill sees a new car he likes.
The car’s fuel consumption is 16 km per litre.
Bill drives a total of 45 miles each day.
Fuel costs 136.9 pence per litre.
Work out the total cost of fuel Bill would use each day in this car.
Give your answer in pounds and to the nearest penny.

Use this conversion graph to help you:

Emma employs Hans.
She pays Hans a bonus when he sells a car.
The bonus is 1.5% of the price of the car.
The available makes of cars are:

How many cars would Hans have to sell at the modal price to get a bonus of at least £7500?