Credit Diploma in Applied Science (Forensic Science) Assignment: Numbers for Science

Assignment Scenario

As part of your BTEC studies, the college is working to secure you work placement in a range of scientific careers. During this you will be asked to complete mathematical calculations, below are a range of questions from different scientific fields that previous students have faced.

Task 1 -

Your job is to conduct post-mortems on dead bodies to see why they died. An important part of your job is to record the dead person's measurements such as height and weight. 

Keep your answers to 3 significant figures where appropriate.

1) The length of this dead body is 6 feet? What is this length in metres?

2) The length of his hand span is 24 cm. What is this measurement in inches?

3) Give the hand span as a percentage of the length of the body.

4) 5.2 litres of blood was drained from the dead body. How many pints of blood is this?

5) The dead body had a mass of 210 lbs. (pounds). How much is this in kilograms?

6) The stomach contents of the body are 5/8 full. What was the empty proportion of the stomach?

7) The measurements of a normal liver are 21cm length by 15cm width. The liver on this body is removed to check for abnormalities. The measurements are 25cm length by 20cm width. What is the area of the liver?

8) The depth of the liver measures 10cm. Use your answer from question 7 to find the volume of the liver.

9) Density = mass x volume. If the mass of the liver is 200g, use your volume from question 8 to find the density.

10) The body took 2.5 hours to start to decompose. How long did it take in minutes?

11) It turns out that this person was shot. The bullet had mass 0.015kg and travelled with an acceleration of 150m/s. Given that force = mass x acceleration, what was the force of the bullet?

Task 2 -

Solve the following algebra questions:

1) x + 5 = 12

2) 3 - x = 7

3) 2x + 4 = 10

4) 3x - 1 = 1                     

Task 3 -

1) It is estimated that light takes 100 000 years to travel the full distance across our galaxy, the Milky Way. If light travels 3.0 x 10⁸ m in 1 second, how long is the Milky Way in meter? Give your answer in standard form.

2) In an atomic model negatively charged electrons are orbiting around the nucleus. If the masses of neutron, proton and electron are 1.67 x 10^-27 kg, 1.67 x 10^-27 kg and 9.11 x 10^-31 kg respectively, find the total mass of the atom which has 2 protons, 2 neutrons and 2 electrons. Give your answer in standard form.                                                                           

3) The length, the width and depth of the plant cell are 50µm, 10µm and 8µm respectively. Find the surface area and volume of the plant cell and write your answer in standard form.

Task 4 -

1) You are working at the National Blood Service Clinical Studies Unit. You are investigating blood flow in arteries. Use a scientific calculator to answer the following question. A 40mm long section of an artery of cylindrical shape is found to have an inner diameter of about 0.44mm. Find the surface area and the volume of the artery.

2) You are a geologist assigned to estimate the density of the Earth. You know that density is given by: ρ=m / V. You need to first find the volume (V) of the Earth, which can be found by the equation: g=G x m/r². You are given the following values: G=6.67 x 10^-11Nm²kg^-2, m=5.97 x 10²⁴ kg and g=9.81 ms^-2. Calculate the radius of the Earth and then the volume of the Earth. Assume that the Earth is perfect spherical shape and find its surface area.

3) Find the surface area and volume of the Hydrogen atom.

Task 5 -

1) You are working as a clinical chemist in charge of the testing of blood samples. You are required to mix a sodium chloride solution with water in the ratio of 2:5. Starting with 780 ml of the sodium chloride, how much water needs to be added?                                                                                 

2) In one sample, the albumin level was 4.6g/dL. In this sample, the albumin to globulin ratio was 1:1.5. What was the globulin level?                                                  

3) The number of electron of Chlorine atom is 17 and the ratio of electron to neutron is 17:18, find total number of particles in the nucleus.(Use the information in Task 3 Question 2)

4) Physicist use models to work out the pressure inside an aeroplane. The length of a model aeroplane is 16 cm and the length of the real aeroplane is 60 m. Work out the ratio of the length of the model to the real aeroplane.

Task 6 -

1) You are a crime scene investigator at the scene of a murder. From CCTV records you already know that the murderer travelled from Paris to London by Eurostar. The train leaves Gare Du Nord in Paris at 08.35 and arrives at London St Pancras International Station on the same day.

If the distance between two cities is 605 km and the speed of the train is 186 mph, find the earliest time that the murderer and his victim meet at St Pancras Station.

2) The blood splatter from the victim is at a distance of 2.4 metres. If it took 5 seconds to splatter this distance, find the speed of the blood particles.                                                                 

3) If the average mass of blood in the artery section is estimated to be 6.9 x 10¯³g, determine the density of the blood. (Use the information in Task 3 Question 3)

4) If the mass of the Hydrogen atom is 1.67 x 10^-24 g, find the density of the atom. Give your answer in standard form. (Use then information in Task 4 Question 4)

Useful resource materials -

Textbooks:

Foale S, Hocking S, Llewellyn R, Musa I, Patrick E, Rhodes P and Sorensen J - BTEC Level 3 in Applied Science Student Book (Pearson, 2010) ISBN 9781846906800

Johnson T and Clough T - Aim High 2: Aiming for Grade A/A* in Edexcel GCSE Mathematics (Edexcel, 2007) ISBN 9781846901881

Metcalf P - GCSE Edexcel Maths (Revision Guide) (Collins, 2006) ISBN 9780007213610

Parsons R - GCSE Maths Edexcel Modular Revision Guide: Higher (Coordination Group Publications, 2006) ISBN 9781841460932

Pledger K (editor) - Edexcel GCSE Maths: Higher Student Book (Heinemann Educational Secondary Division, 2006) ISBN 9781841465463

Journals:

isquared magazine

Mathematical Association

Mathematical Gazette

Mathematics in Schools

Websites:

www.bbc.co.uk/schools/gcsebitesize - BBC GCSE Bitesize

www.bbc.co.uk/skillswise - BBC Skillswise

www.education.bham.ac.uk/subjects/maths/links - University of Birmingham selection of mathematics education sites

www.gcseguide.co.uk - GCSE guide

www.gcsevise.com - Gcsevise

www.mathstutor.com - Mathstutor