• Constructing a Right Angle

    edge of which is a diameter, is always a right angled triangle. Therefore, start by drawing a circle with a compass. The centre of the circle will be at the position of the compass needle. Draw a diameter of the circle. Put the compass needle on one end...

    https://astarmathsandphysics.com/igcse-maths-notes/460-constructing-a-right-angle.html
  • Mode, Median and Mean

    There are three useful measures of the centre of a data set: The Mode is the most common. The Median is found by writing the list in order. If the list is a list of numbers, write them in order of size from smallest to largest. If the list has an “odd...

    https://astarmathsandphysics.com/igcse-maths-notes/487-mode-median-and-mean.html
  • Proof Length of Tangent Squared Equals Product of Chord With Chord Extended to Meet Tangent

    common to both triangles, so call it Call angle then other angles can be found in terms of and Now draw radii from to the centre of the circle and label the remaining angles. and Hence triangles are similar. Hence

    https://astarmathsandphysics.com/igcse-maths-notes/504-proof-length-of-tangent-squared-equals-product-of-chord-with-chord-extended-to-meet-tangent.html
  • Angles in Three Dimensional Solids

    may cut the base up into six equilateral triangles, so that each angle is 60 and each length is 2 cm The length (O is the centre of the base so FOC is a straight line) is then 4 cm and we may construct the triangle below. The angle is twice the angle...

    https://astarmathsandphysics.com/gcse-maths-notes/557-angles-in-three-dimensional-solids.html
  • Circle Theorems - A Summary

    The angle subtended at the centre of the circle is twice the angle subtended at the edge. The angle at the edge of a circle subtended by a diameter is a right angle. Opposite angles in a cyclic quadrilateral - where all the vertices are an the edge of...

    https://astarmathsandphysics.com/gcse-maths-notes/565-circle-theorems-a-summary.html
  • Constructing an Angle of 45 Degrees

    edge of which is a diameter, is always a right angled triangle. Therefore, start by drawing a circle with a compass. The centre of the circle will be at the position of the compass needle. Draw a diameter of the circle. Put the compass needle on one end...

    https://astarmathsandphysics.com/gcse-maths-notes/571-constructing-an-angle-of-45-degrees.html
  • Constructing a Right Angle

    edge of which is a diameter, is always a right angled triangle. Therefore, start by drawing a circle with a compass. The centre of the circle will be at the position of the compass needle. Draw a diameter of the circle. Put the compass needle on one end...

    https://astarmathsandphysics.com/gcse-maths-notes/574-constructing-a-right-angle.html
  • The Geiger Muller Tube

    The Geiger Muller tube is used to detect and measure radioactivity. It consists of a thin wire down the centre of a metal tube enclosed in a glass container. The apparatus contains gas at low pressure and the whole apparatus is connected to a power...

    https://astarmathsandphysics.com/gcse-physics-notes/857-the-geiger-muller-tube.html
  • The Rutherford Alpha Particle Scattering Experiment

    Rutherford showed that his results could be explained by modelling the atom as containing a very small core at the at the centre of the atom, containing all the positive charge. The electrons orbited the nuclus in a way similar to planets orbiting the...

    https://astarmathsandphysics.com/gcse-physics-notes/872-the-rutherford-alpha-particle-scattering-experiment.html
  • The Scientific Method

    came to science was to argue over ideas but not to test them. For a long time it was thought that the Earth was at the centre of the Universe just because Aristotle had put forward this idea and his ideas were promoted by the Roman Catholic church, and...

    https://astarmathsandphysics.com/gcse-physics-notes/873-the-scientific-method.html
  • The Four Spheres

    As we move out from the centre of the Earth we pass through several sharply defined regions: The core, consisting of liquid iron and nickel surrounding a solid inner core. The core is the origin of the Earth's magnetic field. The mantle, consisting of...

    https://astarmathsandphysics.com/gcse-physics-notes/879-the-four-spheres.html
  • The Sun

    Like other stars, our Sun is a large ball of hydrogen and helium gas. In the centre of the Sun – the core – hydrogen is burning in a nuclear fusion process, turning into helium. Very high temperatures are needed for nuclear fusion. The temperature...

    https://astarmathsandphysics.com/gcse-physics-notes/880-the-sun.html
  • Solving Absolute Value Complex Equations

    out the brackets and collect like terms. Divide by 3 and complete the square. This is the equation of a circle with centre and radius

    https://astarmathsandphysics.com/ib-maths-notes/complex-numbers/953-solving-absolute-value-complex-equations.html
  • Venn Diagrams 1

    Dirty Digger and Daily Trash and 2 read all three. We have to fill out the diagram above. It is best to work out from the centre. 2 people read all three newspapers, so the entry in the central region is 2. Complete the regions in the order shown:1) 2)...

    https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1074-venn-diagrams-1.html
  • Circles

    The equation of a circle with centre and radius is or This equation is a consequence of Pythagoras theorem and is illustrated below. The equation of a circle is a quadratic equation because of the and terms.

    https://astarmathsandphysics.com/ib-maths-notes/quadratics/1087-circles.html
  • Circular Measure

    sector of a circle. These can be easily found by considering fractions of circles. A circular arc subtends an angle at the centre of a circle. The length of the arc is just the angle subtended as a fraction of times the circumference: The perimeter of...

    https://astarmathsandphysics.com/ib-maths-notes/trigonometry/1119-circular-measure.html
  • Knots and Nautical Miles

    the Earths surface that subtends an angle of 1 minute (where 1 minute = 1/60 degree) along any merician measured from the centre of the Earth (a meridian is any circle drarn on the surface of the Earth that passes through both poles). The average radius...

    https://astarmathsandphysics.com/ib-maths-notes/trigonometry/1125-knots-and-nautical-miles.html
  • Binary Stars

    exist in binary systems consisting of two or more stars in orbit around each other (or more accurately, around their common centre of mass). There are different types of binary star – visual, spectroscopic and eclipsing: A visual binary is one that can...

    https://astarmathsandphysics.com/ib-physics-notes/astrophysics/1186-binary-stars.html
  • The Milky Way

    Way is a spiral galaxy, rotating with a period of about years. It is about meters or 100,000 light years across. At the centre, as with many galaxies there is a bulge of gas and stars surrounding a supposed black hole. We can actually look out into the...

    https://astarmathsandphysics.com/ib-physics-notes/astrophysics/1204-the-milky-way.html
  • The Earths Magnetic Field

    It has been known for millennia that the Earth has a magnetic field, as though there were a giant magnet at the centre. It is for this reason that North Pole and South Pole are geographic terms. In fact the Earth's North Pole, the true North Pole is...

    https://astarmathsandphysics.com/ib-physics-notes/electromagnetism/1284-the-earths-magnetic-field.html

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