Mathematical Requirements, Notations, Symbols and Formulas

Mathematical Requirements

Bold text is for Higher level only.

1. Use of calculators

Students will be expected to have an electronic calculator conforming to the examination regulations for the duration of the course and when answering the examination paper. It is recommended that students have available the following keys:

In carrying out calculations, students should be advised to show clearly all expressions to be evaluated using a calculator. The number of significant figures given in the answer to a numerical problem should match the number of significant figures given in the question.

ORDINARY LEVEL

+, -, x, ÷, p, x2, sqrtx,1x, x^y, EE or EXP; sine, cosine and tangent and their inverses in degrees and fractions of a degree; memory.

HIGHER LEVEL

as above and log10 x, 10x, ln x.

In carrying out calculations, students should be advised to show clearly all expressions to be evaluated using a calculator. The number of significant figures given in the answer to a numerical problem should match the number of significant figures given in the question.

2. Mathematical requirements

The physics syllabus does not require Higher level mathematics. Higher level physics may include some of the optional work of Ordinary level mathematics. There is no requirement for the use of calculus techniques.

Arithmetic

Students should be able to

• understand the concept of significant figures
• recognise and use significant figures as appropriate
• recognise and use expressions in decimal and standard form (scientific) notation
• recognise and use prefixes indicating multiplication by 10-12, 10-9, 10-6, 10-3, 103, 106, 109
• use an electronic calculator for addition, subtraction, multiplication and division and for finding arithmetic means, reciprocals, squares, square roots, sines, cosines and tangents, exponentials, logarithms, and their inverses
• make approximate evaluations of numerical expressions and use such approximations to check calculator calculations.

Algebra

Students should be able to

• change the subject of an equation
• solve simple algebraic equations
• substitute for physical quantities in physical equations using consistent units
• formulate simple algebraic equations as mathematical models of physical situations
• comprehend and use the symbols >, <, ?, =, x, ?x.

Geometry and Trigonometry

Students should be able to

• calculate the area of right-angled triangles, circumference and area of circles, surface area and volume of rectangular blocks, cylinders and spheres
• use Pythagoras' theorem, similarity of triangles, the angle sum of a triangle
• use sines, cosines and tangents in physical problems
• recall that sin ? ˜ tan ? ˜ ?/radians, and cos ? ˜ 1 for small ?
• translate between degrees and radians and ensure that the appropriate system is used.

Vectors

Students should be able to

• find the resultant of two perpendicular vectors, recognising situations where vector addition is appropriate
• obtain expressions for components of a vector in perpendicular directions, recognising situations where vector resolution is appropriate.

Graphs

Students should be able to

• translate information between numerical, algebraic, verbal and graphical forms
• select appropriate variables and scales for graph plotting
• determine the slope of a linear graph and allocate appropriate physical units to it
• choose by inspection a straight line that will serve as the best straight line through a set of data presented graphically.

Notations and Symbols

Standard units, signs and symbols should be used throughout the syllabus. In this section, selected abbreviations are given. The physical quantities, their symbols and units are given. The common electrical circuit symbols are shown.

Abbreviations

The following abbreviations should be used:

quarks:

antiquarks:

Basic units

The international system of units (SI) should be used. The required base units are given in the table below.

Physical quantities, symbols, and units

The physical quantities, their units and the appropriate symbols required by the syllabus are shown below. Some non-SI units are required. These are indicated by an asterisk*.

Electrical circuit symbols

The use of standard symbols (BS 3939) is recommended.
The common symbols required by the syllabus are given below.

*image* conductors crossing with no connection
*image* junction of conductors
*image* earth
*image* normally open switch
*image* normally closed switch
*image* relay coil
*image* relay contact
*image* primary or secondary cell
*image* battery of cells} electro magnetic relay
*image* power supply}
*image* primary or secondary cell
*image* battery of cells
*image* power supply
*image* neon lamp
*image* signal lamp
*image* filament lamp
*image* voltmeter
*image* galvanometer
*image* ammeter
*image* fuse
*image* fixed resistor
*image* variable resistor
*image* thermistor
*image* potential divider
*image* capacitor
*image* electrolytic capacitor
*image* inductor
*image* inductor with ferromagnetic core
*image* transformer with ferromagnetic core
*image* light-emitting diode LED
*image* photo-voltaic cell
*image* earphone
*image* loudspeaker
*image* microphone
*image* electric bell
*image* motor
*image* diode/rectifier
*image* p n p junction transistor
*image* n p n junction transistor
*image* light-sensitive diode
*image* photodiode
*image* light-dependent resistor LDR
*image* invert or NOT gate
*image* OR gate
*image* AND gate

FORMULAS

Students should know and be able to use the following formulas. At Ordinary level no derivations are required.
Equations in black text apply to Higher level only.
Those marked with † should be derived at Higher level.

Mechanics

Electricity