Maths Extension Work

This page contains resources for extending your learning and understanding of physics, with more maths involvement.  You may need to request permission by email to access some of the materials.

Note - this page is currently under development, and more resources will appear over time.  Questions come from English GCSE, AS and A Level resources, and I intend to post solutions and hints

Fun problems - mostly mathematical. Try at your own risk - solutions available by emailing me!

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Can you solve it ? some problems which appeared in the Guardian newspaper, October 2022

CGP resources are from a book which is designed for practice in maths, and the questions are not likely to be too demanding. 

Introduction to calculations in physics - 1   2  3  (these are fairly basic)

CGP resources - answers are here (1) and here (2)

AS resources are harder than CGP, and designed to introduce high school physics. Solutions to exercises are on the question sheets.

PIP resources are more demanding. They may include more complicated algebra, trigonometry and geometry.

Grade 7	Topic	Resources	Notes	Solutions
	SI prefixes and units	This is the full list of SI prefixes Exercise on units and prefixes AS Symbols and units info sheet	An understanding of standard form and powers of 10 is useful	Exercise on units and prefixes solutions
	Frequency and period calculations	AS Frequency and Time Period AS Waves AS The Wave Equation AS The Wave Equation 2 Wave properties 1 PIP Wave properties 2 PIP		Wave properties 1  Wave properties 2
	Speed of sound	Question sheet shamelessly found online
	Calculating wavelength, frequency and speed	Waves 1 (CGP) Waves 2 (CGP)		CGP answers are in one of these two links: (A) (B)
	Thermal expansion	Golden Gate Bridge expansion How does a hole expand ?	Detailed info about thermal exapnsion from Openstax University Physics volume 2
	Heat capacity and temperature rise	Heat capacity 1 PIP Heat capacity 2 PIP Heat capacity 3 PIP Heat capacity 4 (CGP) Specific latent heat (CGP)		Heat capacity 1, 2 and 3 Heat capacity 4 and Specific latent heat CGP answers CGP answers are in one of these two links: (A) (B)

Grade 8	Topic	Resources	Notes	Solutions
	Vectors and general mathematics	Reading graphs and charts (CGP) Drawing graphs and charts 1(CGP) Drawing graphs and charts 2 (CGP) Drawing graphs and charts 3 (CGP) Drawing graphs and charts 4 (CGP)		CGP answers are in one of these two links: (A) (B)
	Resolving forces		Knowledge of trigonometry needed
	Resultant forces	AS Forces 1 AS Forces 2 AS Forces 3 Forces causing acceleration 1 PIP Forces causing acceleration 2 PIP Mass and weight 1 (CGP) Mass and weight 2 (CGP) Forces and motion 1 (CGP) Forces and Motion 2 (CGP) Forces and Motion 3 (CGP)	Knowledge of trigonometry and Pythagoras may be needed	Forces causing acceleration 1 solutions p1 Forces causing acceleration 1 solutions p2 Forces causing acceleration solutions 2 CGP answers are in one of these two links: (A) (B)
	Using the equations of motion	AS Distance, speed and time AS Distance, speed and time 2 AS Displacement AS Displacement 2 AS Velocity AS Velocity 2 AS Acceleration AS Acceleration 2 AS Displacement time graphs AS Displacement time graphs AS Velocity time graphs AS Velocity time graphs 2 Speed and velocity 1 PIP Speed and velocity 2 PIP Speed and velocity 3 PIP Speed and velocity 4 PIP Freefall and projectile motion 1 PIP Freefall and projectile motion 2 PIP Freefall and projectile motion 3 PIP Speed and velocity 1 (CGP) Speed and velocity 2 (CGP) Acceleration (CGP) Velocity and acceleration (CGP)		Speed and velocty 1,2,3,and 4 Freefall and projectile motion 1,2 and 3 CGP answers are in one of these two links: (A) (B)
	Average and instantaneous velocity		Tutorial video   which introduces the limit, which will lead on to derivatives which are covered well here.
	Conservation of energy	Kinetic energy and gravitational potential energy 1 PIP Kinetic energy and potential energy 2 PIP Work = force x distance 1 (CGP) Work = force x distance 2 (CGP) Gravitational Potential Energy 1 (CGP) Gravitational Potential Energy 2 (CGP) AS Kinetic and Gravitational Potential Energy 1 AS Kinetic and Gravitational Potential Energy 2 AS Kinetic and Gravitational Potential Energy 3 AS Work 1 AS Work2 AS Power 1 AS Power2 AS Efficiency		Kinetic energy and gravitational potential energy 1 & 2 CGP answers are in one of these two links: (A) (B)

Grade 9 SHORT	Topic	Resources	Notes	Solutions
	Scales and numbers	This is the full list of SI prefixes Exercise on units and prefixes	This is the original 'Powers of 10' video which clearly shows the distances in standard form.	Exercise on units and prefixes solutions
	Half-life and radioactive decay	Atoms and nuclei sheet 1 PIP Atoms and nuclei sheet 2 PIP Laws of radioactive decay PIP AS Nuclear radiation 1 AS Nuclear radiation2 AS The random nature of nuclear decay AS The random nature of nuclear decay 2 Half-life 1 (CGP) Half-life 2 (CGP)		Atoms and nuclei 1 &2 Laws of radioactive decay CGP answers are in one of these two links: (A) (B)
	Special relativity	Exercises in relativity		Ideas for 'Exercises in relativity' question 13 are discussed here (sort of) Exercises in relativity solutions p1, p2,p3,p4

Grade 9 LONG	Topic	Resources	Notes	Solutions
	Simple resistive circuits	AS Current 1 AS Current 2 AS Voltage AS Resistance 1 AS Resistance 2 Resistance 1 PIP Resistance 2 (CGP) Resistance 3 (CGP) Series and parallel resistors 1 (CGP) Charge = current x time (CGP) The infamous resistor cube! If 12 resistors, each of value R, are arranged to make the edges of a cube, what is the equivalent resistance of the combination, as measured from opposite corners ?		Resistance 1 CGP answers are in one of these two links: (A) (B) The resistor cube
	Energy in circuits	Energy in circuits 1 (CGP) Energy in circuits 2 (CGP) AS Power 1 AS Power 2		CGP answers are in one of these two links: (A) (B)
	Energy costs	Energy and cost (CGP)		CGP answers are in one of these two links: (A) (B)
	Calculations with transformers	Tutorial page with worked examples Simple calculations More tricky calculations		Simple calculations and More tricky calculations, answers  online.
	Static electricity and charge	AS Charge AS Explaining electrostatic phenomena 1 AS Explaining electrostatic phenomena 2
	Efficiency	Efficiency 1 (CGP) Effiiciency 2 (CGP)		CGP answers are in one of these two links: (A) (B)