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Maths for Technicians

Maths for Technicians. Course Overview. Modular Course. You will require to demonstrate ability in: Algebra Statistics Geometry Calculus. Algebra. Linear Equations Quadratic Equations Factorisation (x-3)(x+5) Solving (x-3)(x+5) = 0 hence x = 3 or x = -5

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Maths for Technicians

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  1. Maths for Technicians Course Overview

  2. Modular Course • You will require to demonstrate ability in: • Algebra • Statistics • Geometry • Calculus

  3. Algebra • Linear Equations • Quadratic Equations • Factorisation (x-3)(x+5) • Solving (x-3)(x+5) = 0 hence x = 3 or x = -5 • Using the equation and completing the square

  4. Statistics • The easiest of the modules • Averages • Representing data (Histograms and Cumulative Frequency) • Reasoning what the graph actually is saying about the data set • More ‘why’ than ‘how’

  5. Geometry • Area of scalar triangles using a variety of methods • Hero’s or Heron’s Formula • Using sine and cosine rule • Using radian measure rather than degrees • Using Trigonometric equations • = ? • The Tan curve (shown opposite) • Volumes of regular 3d shapes

  6. Calculus (counting) • Finding the gradient of curved lines • Finding the area under curves exactly • Time for you to do some learning!

  7. Integration (or finding the area) • If the variable is x, note the power here is 1 we can write this as • When integrating, we • raise the power by one and • Divide by that raised power • Hence simples! • How does this help us?

  8. Area under a straight liney = mx+c • between 0 and 5 • = 12.5 • Now recall area of triangle is

  9. Let’s just confirm our knowledge • Integrating • raise the power by one and • Divide by that raised power • So between 0 and 5 • The 2s cancel leaving us with • 52 – 02 = 25 • How does that compare with

  10. Using your sheet now work out the area under each of the lines and then curves • Note when integrating values such as 7 it is actually • 7x0 so when integrated it becomes • 7 x1

  11. Answers • 1. area = between 0 to 3 • So area = 18 • 2. area = between 0 to 3 • So area = 15 • 3. area = 125 • 4. area = 36x - between 0 to 5 • So area = 180- 125/3= 138.3 (1dp) • 5. area = between -3 and 0 + area = between 0 and 5 = 176.5

  12. Mechanics • We will look at how multiple forces can be calculated to see if a system is in equilibrium. • What force T3 is required to keep the load from falling?

  13. Mechanics • What forces exist at Point C on this bridge? • More importantly at the joints?

  14. Kinematic systems • What speed will the truck hit the bottom of the slope when we consider the friction of the tyres and the road? • Hint Pokemon 150 applies here

  15. Overview • You’ll have the skills required to examine electrical and mechanical systems using advanced mathematical techniques. • You’ll have the skills required to examine the forces, and dynamics within structures, and to determine when they might fail. • We’ll also look at fluids and thermodynamics. • Any Questions?

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