• A Level Mathematics M1 Revision Notes

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Uniform Acceleration Equations

  • Always remember SUVAT or UVAST - these are the 5 precious pieces of info.
  • S is the displacement (How far it is from where it started.)
  • U is the starting or 'initial' velocity.
  • V is the final velocity.
  • A is the acceleration. (If negative, it is a deceleration.)
  • and T is the time taken.

The equations are:

  • V = U + AT
  • V^2= U^2 + 2AS
  • S=UT + 1/2AT^2 (and sometimes you may need *S= VT - 1/2AT^2)

and finally; *S = 1/2(U + V) T

    • Key point: You will need at least three of the UVAST letters to work out the required one.

For example: "A car starts from rest, at point A, and accelerates uniformly at 2ms^-2 for 3 seconds, until it passes point B. At what speed did it pass point B?"

It started from rest, therefore U = 0. It's acceleration is 2ms^-2, therefore A = 2 We're interested in the first 3 seconds of its movement, so T = 3. We want to know what its final velocity was, i.e. what is V?

Using V= U + AT;

V = 0 + (2x3) = 6 So it passed point B with a velocity of 6ms^-1.


This topic will require basic knowledge of Trigonometry: SOHCAHTOA:

  • Sin = Opposite side/Hypotenuse
  • Cos = Adjacent side/Hypotenuse and
  • Tan = Opposite side/Adjacent side

as well as Arctan in order to calculate angles from resulting vectors.

    • A key point, when drawing vectors, especially when working out what the resulting vector is, is to always draw them NOSE TO TAIL.
  • This then leaves no confusion as to which direction they are pointing. Often, you will asked what angle the resulting vector makes with the horizontal (the x axis in coordinate geometry) (the i axis in vectors); or the vertical (the j axis).
  • Speed = |velocity|

Friction and Inclined Particles

Friction = Coefficient of Friction x Normal reaction of the plane

F(net) = ma ---"The total force in one direction equals the mass times the acceleration in that direction."


  • Moment (Nm) = Force (N) x Perpendicular distance (m) **You may be asked what your units are - these are "Newton metres" (because they are simply Newtons x Metres :) )

and in equilibrium:

  • Total clockwise moment = Total anticlockwise movement

  • It's 90%+ likely that you will be given a diagram of a pulley or a seesaw. They will either have people on, or be held by strings or on a pivot of some sort. Look carefully at the diagram for lengths - start deducing what other lengths are, using the info you've been given.
  • To solve, simply choose a point as your centre, and "take moments about it."
  • "Uniform" rods are easier to calculate for because the centre of mass is always the centre of the rod - a simple case of halving the rod's length. For more awkward questions where the rod is NOT uniform, even if the question does not ask of it, it will more than likely be the turning point of information that you need to answer the question; so keep your eyes peeled and Always read the question!

  • This may the point in the paper where you are asked about your '"Mathematical modeling"' - Remember key vocabulary! You must know the meaning of such terms as: "light"; "inextensible"; "uniform"; "smooth; "rough" e.t.c. and more importantly, why the answer would differ if these assumptions weren't so - e.g. If a surface is "rough" and not "smooth", then there is friction present, which will oppose motion.


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