NCFE Maths Level 2 Practice Paper 2 Section B

An allotment is a piece of land that people can rent to grow fruit, flowers and vegetables.
A residents’ association has an allotment so that people can grow their own vegetables.
This is a plan of the allotment:

What is the area of the allotment?

Give your answer to 3dp.

There is an oval pond in the allotment.
The pond is 7 m long, 5 m wide and 80 cm deep.
The pond is to be filled in with soil.

The formula to find the volume (in m³) of the pond is: π × ^L/₂ × ^W/₂ × D

Where:
L is the length (in m)
W is the width (in m)
D is the depth (in m)
Use 𝜋 = 3.14

Soil can be bought in two sizes of bag.

The pond should be filled as cheaply as possible.
How much will it cost?

If 3 people work together, it would take them 8 hours to fill in the pond.
How long would it take 5 people working at the same rate?

Asif finds some trial results about two types of potato, Cara and Desiree.

Yield is the weight of potatoes that can be produced from one potato plant.
Asif wants to plant the type of potato with the higher yield.
He will grow 20 potato plants.
Use the trial data to recommend which type of potato Asif should plant and estimate the expected total weight of potatoes, in pounds, that he will get.
Use the conversion: 1 kg = 2.2 pounds

Pete is a catering student.
He has been given a project testing fruit juicers.

Pete is testing the SuperJuicer and the Blitz-It juicer.

Pete juices 100 g of strawberries in the Blitz-It juicer.
He repeats this 7 times.

Calculate the median volume of strawberry juice produced by the Blitz-It juicer.

Pete tests the SuperJuicer.
The manufacturer claims that 300 g of apples will produce ²/₅ of a pint of juice.
Pete tests this claim by juicing different weights of apples and measuring the amounts of juice they produce.
He uses his results to draw this scatter diagram:

Is the manufacturer’s claim correct? Show how you decide.
Use the conversion: 1 pint = 568 ml

The Blitz-It juicer’s information states that the weight of juice produced from oranges is around 30% of the weight of the fruit.
If Pete wants to produce 150 g of juice, what weight of oranges should he use?

Pete asks a group of college students which machine’s juice they prefer.
This table shows their responses:

A student from the group is chosen at random.
What is the probability that the student is under 19 and preferred juice from Blitz-It juicer?

Pete makes a smoothie using juice from pineapples and mangoes.
He wants the volume of pineapple juice to mango juice to be as close as possible to a 3 : 2 ratio.
Typical volumes of juice produced from 1 fruit are:

What is the cost of the fruit that Pete needs to buy to make 8 litres of smoothie?

When Pete goes to buy the fruit, he finds that pineapples have increased in price to £1.75 each.
By what percentage has the price of pineapples increased?
Give your answer to 1 decimal place.

The cylinder has radius 1.5 m and height 1.25 m
Calculate the volume of the cylinder in m³
Give your answer to 1 decimal place.
Use 𝜋 = 3.14

Jan needs to cover a ball with glitter.
The ball’s radius is 60 cm
The formula to find the surface area (A) of a sphere is: A = 4 πr²
Jan buys the glitter in bottles.
She needs to use 300 g of glitter per square metre.
Each bottle holds 254 g of glitter.
Calculate the number of bottles of glitter needed to cover the sphere.
Show your working.
Use 𝜋 = 3.14

The theatre director wants a spotlight that will give a circle of light on the stage with a diameter of approximately 2.15 m
The formula for working out the diameter of the light on the stage is:

D = ^{B × H × 18}/₁₀₀₀

Where:
D is the diameter of the circle of light (in m)
B is the beam angle (in degrees)
H is the vertical distance from the spotlight to the stage (in m

This table shows the available spotlights:

Which spotlight should be chosen to get the diameter closest to 2.15 m?

The theatre needs new stage curtains.
Jan has been asked to order the fabric for the new curtains.
The total width of fabric needs to be 1³/₅ times the width of the stage front.
Write 1³/₅ as a decimal number.

This is a diagram of the stage:

The total width of fabric needs to be 1³/₅ the width of the stage front.
Curtain fabric is sold in widths of 1.4 m

Several widths of fabric are sewn together to make the curtains.
The length of the curtains needs to be 5.8 m to allow for hems.
What length of fabric does she need?