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Maths for Technicians

This modular Maths course equips technicians with essential mathematical skills including algebra, statistics, geometry, and calculus. You'll learn to solve linear and quadratic equations, process statistical data using averages and graphs, and apply geometric principles for area and volume calculations. Additionally, the calculus module covers integration techniques to find areas under curves. The course also introduces mechanics and the mathematics of forces and motion. Develop the analytical skills necessary for examining electrical and mechanical systems and understanding fluid dynamics.

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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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