• The Earths Changing Magnetic Field

    The inside of the Earth is not solid. It is actually part viscous fluid, part solid. The innermost core is solid, but the outermost core and the mantle are both fluid. The Earth's magnetic field is actually generated by the outermost part of the core,...

    https://astarmathsandphysics.com/igcse-physics-notes/432-the-earths-changing-magnetic-field.html

  • Locus of Points Equidistant Between Two Points

    Intuitively the set of points equidistant from two given points is the set of points halfway between them. The locus will be a straight line halfway between the two points. We can construct this line by drawing circles of equal radius centred at A and...

    https://astarmathsandphysics.com/igcse-maths-notes/483-locus-of-points-equidistant-between-two-points.html

  • Optimisation - Maximising a Function

    As a race we need the most from our limited resources. Every manager must decide what or who to send where so as to get the job done with the least effort and risk, and at the least cost, or decide what products to make and sell, subject to the...

    https://astarmathsandphysics.com/igcse-maths-notes/491-optimisation-maximising-a-function.html

  • Bisecting an Angle

    We can bisect an angle using only compasses. Put the point of the compass at O and draw arcs that crosses both lines that constitute the angle. From each point where an arcs just drawn cross a line construct other arcs to cross as shown. Now draw a...

    https://astarmathsandphysics.com/gcse-maths-notes/562-bisecting-an-angle.html

  • Gradients and Equations of Lines

    The general equation of a line may be wriiten as (1) where m is the gradient and is the – intercept, or where is again the gradient. We may be asked: Find the equation of the line which passes through the two points and we have to find the gradient We...

    https://astarmathsandphysics.com/gcse-maths-notes/599-gradients-and-equations-of-lines.html

  • Locus of Points Equidistant Between Two Points

    Intuitively the set of points equidistant from two given points is the set of points halfway between them. The locus will be a straight line halfway between the two points. We can construct this line by drawing circles of equal radius centred at A and...

    https://astarmathsandphysics.com/gcse-maths-notes/605-locus-of-points-equidistant-between-two-points.html

  • Natural Logairthms

    One number raised to the power of another is called a base. In the expression 3^4 the base is 3. The most common base is 10 – we count and measure things in multiples of 10 because we have 10 fingers on which to count. There is however, one base which...

    https://astarmathsandphysics.com/ib-maths-notes/logarithms/988-natural-logairthms.html

  • Calculations Involving The Normal Distribution - Finding Probabilities

    If you look at the tables for the normal distribution, along the top and left borders there are z – values. If we have a Normal distribution and we want to find then we can use the – transform to find a – value then find the probability for this –...

    https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1042-calculations-involving-the-normal-distribution-finding-probabilities.html

  • Calculating Regression Lines

    Many variables are related by a straight line, or more strictly, over a certain range for both variables the relationship between them can be expressed as a straight line. Often we have to find the equation of the line from a table of raw data. This...

    https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1064-regression-lines.html

  • Proof That the Square Root of 2 is Irrational

    Rrational numbers are fractions where both numerator and denominator are integers. Irrational numbers are conversely, any number that cannot be written as a fraction with one integer divided by another. Suppose then we want to prove that is irrational....

    https://astarmathsandphysics.com/ib-maths-notes/proofs/1083-proof-that-the-square-root-of-2-is-irrational.html

  • Arithmetic and Geometric Mean

    The terms 'arithmetic mean' and 'geometric mean' are derived naturally from the definition of arithmetic series and geometric series respectively. Successive terms in an arithmetic sequence are defined by where is the common difference. We add to each...

    https://astarmathsandphysics.com/ib-maths-notes/sequences-and-series/1113-arithmetic-and-geometric-mean.html

  • Formula for the Area of a Triangle

    The area of a triangle is where is the base and is the perpendicular height. This formula is a bit artififical because we can take any side as the base and the height will be the perendicular distance of the opposite vertex from this chosen base. There...

    https://astarmathsandphysics.com/ib-maths-notes/trigonometry/1124-formula-for-the-area-of-a-triangle.html

  • Finding the Vector Equation of a Line Passing Through Two Given Points

    The general equation of a line passing through two points and is given by where and can be in two or three dimension ie or t is a parameter – the value of determines a unique point on the line. Any point on the line can be found by substituting a...

    https://astarmathsandphysics.com/ib-maths-notes/vectors-lines-and-planes/1163-finding-the-vector-equation-of-a-line-passing-through-two-given-points.html

  • Types of Star

    The type of star is due mainly to it's age and mass. A brown dwarf is a very low mass star. (less than about 0.08 solar masses). It does not have a core temperature high enough for nuclear reactions to start in the core, and the heat it generates is...

    https://astarmathsandphysics.com/ib-physics-notes/astrophysics/1211-types-of-star.html

  • Half Life

    The process of radioactive decay has a particular mathematical property. The rate of radioactive decay is proportional to the number of undecayed atoms present. We can write where is the decay rate, is the number of undecayed atoms present is the decay...

    https://astarmathsandphysics.com/ib-physics-notes/atomic-and-nuclear-physics/1219-half-life.html

  • The Equation of a Straight Line Graph

    The general equation of a line is where and are the variables that label the axes and m and c are constants. is called the independent variable. It is the variable that can be controlled in an experiment. is called the dependent variable. It changes in...

    https://astarmathsandphysics.com/ib-physics-notes/measurements-units-uncertainty-and-principles/1348-the-equation-of-a-straight-line-graph.html

  • Weight

    Weight and mass are often taken to be synonymous. In fact they are very different concepts, but people are easily confused because although weight is actually a force measured in newtons and mass is the amount of matter measured in kg, people often say...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1383-weight.html

  • The Diffraction Grating

    The diffraction grating is Young's double slit writ large. Young's double slit has two slits, and the diffraction grating has many slits, each separated by the same distance. Additional slits with a constant separation will not affect the condition for...

    https://astarmathsandphysics.com/ib-physics-notes/optics-and-light/1411-the-diffraction-grating.html

  • Einstein's Model of Light

    The question of whether light was a particle or a wave is an old one. Newton thought light was made up of particles, Young that it was made up of waves. The argument seemed to be settled in favour of the wave theory until the photoelectric effect and...

    https://astarmathsandphysics.com/ib-physics-notes/quantum-and-nuclear-physics/1423-einstein-s-model-of-light.html

  • Temperature Scales

    The temperature of a body is a measure of how hot or cold it is. If two bodies are placed in thermal contact then heat will be transferred from the hotter to the colder until both are at the same temperature. When they are at the same temperature they...

    https://astarmathsandphysics.com/ib-physics-notes/thermal-physics/1479-temperature-scales.html

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