Join TSR
 
 About Us | FAQs | Sign in
 
HomeForumsArticlesRevision NotesPersonal StatementsUniversity GuidesHealth & RelationshipsPostgraduate StudyCareersFreshers
Join the UK's largest student community  
Advanced
Search

Join The Student Room Today

Be part of the UK's largest and fastest growing student community.

It's free to join and a lot of fun - Get inspired, express your ideas, interact and share

Join The Student Room Today

Revision:M1 Maths

From The Student Room

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > M1 Maths

Here are some basic notes on the content needed for M1 A Level maths exams.


Contents

SUVAT

SUVAT equations are only used when acceleration is constant

  • \displaystyle v = u + at
  • \displaystyle s = \frac{u + v}{2} \times t
  • \displaystyle s = ut + \frac{1}{2}at^2
  • \displaystyle s = vt - \frac{1}{2}at^2
  • \displaystyle v^2 = u^2 + 2as


s = height, distance, displacement
u = initial velocity
v = final velocity
a = acceleration
t = time


\displaystyle \mathsf{acceleration} = \frac{\mathsf{change\ in\ velocity}}{\mathsf{time}}


Acceleration (ms-2) Velocity (ms-1)


  • displacement = how far out of place something is from any position (vector quantity)
  • position = displacement from a fixed origin
  • velocity = rate of change of position (vector quantity; its magnitude is speed)
  • acceleration = rate of change of velocity (vector quantity; as in above equation)
  • distance = how much ground an object has covered during its motion (scalar quantity)
  • speed = magnitude of velocity (scalar quantity)

Types of forces

  • weight (w)
  • friction (f)
  • push and pull (p)
  • normal reaction (r)
  • tension (t) such as in a string, springs, rods
  • thrust (s) such thrust in a spring or rod, but in opposite direction


Force = mass x acceleration

Weight = mass x gravitational pull


Tension is the same on both sides of a pulley

Rope in tension, not thrust


Newton's First Law - A resultant force is required to produce an acceleration

\displaystyle R - mg = ma


Calculating tension

\displaystyle T - mg = ma


A few equations of motion of a car

  • \displaystyle D - T = ma
  • \displaystyle T - mg = ma
  • \displaystyle R - mg = ma
D = driving force,
T = tension,
R = normal reaction or resistance


If a body is moving at a constant speed, the forces are in equilibrium


If a question includes air resistance, the equation for motion is

\displaystyle mg - R = ma


If the air resistance is proportional to the area perpendicular to motion, air resistance is kA

\displaystyle mg - kA = ma


When combining forces, you are finding the resultant force

  • A rough surface causes friction
  • Smooth surface causes no friction


Forces on a car for example will be reduced by

  • driving force (forwards)
  • braking force (backwards)
  • resistance (to motion) air or water act in opposite direction to velocity


Graphs

  • Position - Time
    • Gradient = Velocity
    • Area = Nothing
  • Velocity - Time
    • Gradient = Acceleration
    • Area = Displacement
  • Distance - Time
    • Gradient = Speed
    • Area = Nothing
  • Speed - Time
    • Gradient = Magnitude of acceleration
    • Area = Distance


(DISTANCE is NOT negative, ONLY POSITIVE)


Velocity at an instant can be found by drawing a tangent at the curve of the point


If you have a position, differentiate once for the velocity and differentiate twice for acceleration


Comments

Originally written by ixnayonthehombre on TSR Forums.

Retrieved from "http://thestudentroom.co.uk/wiki/Revision:M1_Maths"
Article Tools:  Create New Article  |  Report This Article  |  This Article's History  |