WJEC GCSE Numeracy Unit 1: Non-calculator Higher November 2021 question paper 3310U50-1

The skeleton of a dinosaur was found in Wyoming, USA, in 2008. This skeleton is now on display in a shopping mall in Dubai. Here are some facts about this skeleton. • It was transported 7500 miles from Wyoming to Dubai. • It is over 155 million years old. • It is 80 feet (ft) long and 25 feet tall.

Assume: • the skeleton had been transported complete in one crate, • the crate was in the shape of a cuboid.

Which of the following would be the best estimate of the volume of the crate?

Circle your answer.

Which of the following is 155 million written in standard form?

Circle your answer.

Penystrad is a mountain village. The daily rainfall for April 2021 is given in the table below.

Daily rainfall, r (mm)	Number of days
0 r 6	15
6 r 12	11
12 r 18	3
18 r 24	1

Wesley asks,

Explain why it is not possible to answer Wesley’s question using the table shown

above.

Calculate an estimate for the mean daily rainfall for the 30 days of April.

Glanwen is a different village.

During the first 25 days of April in Glanwen, the mean daily rainfall was 4∙4 mm. It did not rain in Glanwen during the last 5 days of April. Calculate the mean daily rainfall in Glanwen for April.

Give your answer correct to 3 significant figures.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Sara makes handmade chocolates. She sells the chocolates in boxes.

Each box contains 4 chocolates. Each chocolate costs Sara 7p to make. She can make 25 boxes from thin card for 50p. Sara makes just enough chocolates and boxes to sell 150 boxes of chocolates.

Sara makes 20% profit from selling all 150 boxes of chocolates. How much profit does Sara make?

You must show all your working.

Bethan works as an office manager at a medical centre.

Last Monday, 60 patients each had an appointment with a doctor. Bethan recorded how long each patient’s appointment lasted. Her results are given in the table below.

Length of time, t (minutes)	0 t 4	4 t 8	8 t 12	12 t 16	16 t 20	20 t 24
Number of patients	4	24	18	6	2	6

Complete the following cumulative frequency table.

Time, t (minutes)	t 0	t 4	t 8	t 12	t 16	t 20	t 24
Cumulative frequency	0	4	28				60

Each patient is given 10 minutes for their appointment. Use your graph to give the best estimate for the number of appointments that lasted longer than 10 minutes.

Give your answer correct to the nearest whole number of appointments.

Of the patients seen last Monday, what percentage spent longer than 20 minutes with

the doctor?

The median length of the appointments last Tuesday was 11.5 minutes. (e) How much shorter was the median length of the appointments on Monday?

Give your answer correct to the nearest minute.

Bethan is considering changing the time given for each patient’s appointment to 12 minutes. She would set a target of 80% of patient appointments taking less than or equal to 12 minutes. Would this target have been met last Monday?

You must show all your working.

Bearing-Up is a company that makes steel spheres to be used in bearings.

PowrUp is a company that makes a certain type of battery.

To find out how long these batteries last, it tests a sample of new batteries. The lifetime of each battery in the sample is recorded. The results are shown in the histogram below.

Frequency density

Use the histogram to answer the following questions:

Calculate the total number of batteries that were in the sample.

PowrUp can advertise the lifetime of these batteries based on the results of these tests. 75% of the sample must exceed this lifetime.

Calculate an estimate of the lifetime of these batteries that PowrUp should use in its adverts.

You must show all your working.

The graph below shows the velocity, v, in m/s, of a particle at time t seconds, for the first

8 seconds of its journey.

Velocity, v (m/s)

At time t = 2 seconds, estimate the acceleration of the particle. Simplify your answer as far as possible.

State the units of your answer.

Use the trapezium rule with 8 strips of equal width to estimate the distance travelled

by the particle in the first 8 seconds.

The actual distance travelled during the first 6 seconds is exactly 144 m. Use this to calculate the average velocity of the particle over the first 6 seconds

Give your answer in miles per hour (mph).