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Algebra – Your guide to improving your mathematical working out and increasing your marks!

Now that you’ve got your head around the guidelines surrounding setting out your algebra working out, it’s time to see how we can apply this to some of the types of questions you’ll indefinitely face during your study of Mathematics in High School or even university. I’d like to stress that with setting out mathematical working out it is all about displaying in a coherent fashion what your solution is and how you have reached it. Remember! The more clearer you are and the more you spend on the small details in your working out, the more chance you have of receiving full marks.

In this article, we will explore how to set out mathematical working out for algebra. We will be drawing upon more senior topics in the high school mathematics curriculum and highlighting why marks are awarded the ways they are. Nonetheless, mathematical working out is key to success as once it is mastered and the theory behind it is understood, all questions you will approach in the near future will be much more easier. Most importantly, this creates transparency in your solutions.

To begin with, let’s discuss how to set out working out for algebra questions. Now, I’ll be demonstrating a progression in difficulty from basic algebra questions all the way up to polynomials studied at the Extension Mathematics levels. The key principle is that there isn’t much difference.

Example 1 - Algebraic Working Out Question - Stepping Stones Education - Tutoring Centre

For those who feel that the above question was relatively easy and straight forward, the purpose of mathematical working out is to demonstrate to the marker that you have reached the solution to your own ability. Now, there are some hard workers out there who have reached the skill level of being able to see the solution as listed out in step 4 and unfortunately skip straight from step one to the final one. However, the practical thinkers out there who understand the nature of the question will recognise that this question alone relies heavily on algebra manipulation and thus by skipping the steps will forfeit you marks or credibility. Oh, and don’t forget… work down the page and NEVER continue your working out to the left or right of your equation (as shown above).

If you observe carefully the steps outlined are very straight forward,

  1. Write out the question
  2. Manipulate the equation by -4 to both sides
  3. Re-arrange the equation to make 2x the subject
  4. Make x the subject by dividing both sides by \frac{1}{2}

Arguably, a question like this doesn’t require as many steps as listed above but this is the basic skeleton of setting out algebra. IT IS ALL ABOUT WHAT YOU NEED!

In your mind you should see what steps are required to move towards the solution but always show more than you need and you will always move towards perfect working out for algebra. The purpose of showing you this example is to reinforce that with algebra, there are so many ways to approach the solution but it is all about SHOWING and not assuming that the marker will know what you are doing. If in your mind you wanted to make 2x independent on one side DO THAT STRAIGHT AWAY, don’t do too many processes at the same time as this will immediately mean that your skipping steps and setting yourself up for the fabled ‘silly mistakes’ excuse.

Now, onto a more difficult example. However, before I do move forward, the topic at hand is polynomials Year 11 Mathematics Extension 1 but pay close attention to how everything is set out and you will see the similarities to the example previously.

Example 2 - Polynomial Working Out Question - Stepping Stones Education - Tutoring Centre

The focus of this example is not to teach you what was done or how the solution was reached but for those who do understand will see that this solution was reached very neatly. For those who have no idea what was going on I want you to pay close attention to each line. In Step 1 the question was still written out and in the steps that followed there was no point in time that it was unclear what was going on. This is the goal for mathematical working out and although it appears to get more complex as the topics get increasingly ‘difficult’ the foundations remain the same. In Steps 2 Steps 5 what was shown was everything that was flying through the mind of whoever was solving it. The test was to apply the theorem by substituting values of x until there was a solution of achieved. Although in some cases a student might see almost immediately that a number of x=2 will achieve the required condition, an oblivious student would skip from steps 1 straight to step 6.

If your still wondering what the purpose behind these examples p(x)  =  0 is I want you to see that there are no faults in the answers between each example above. Some markers and students will argue that you can ‘get away’ with less but none can argue that the solution wasn’t reached in a clear and transparent fashion. The overriding message I want to leave with you, using algebra as a case study, is that do more than what you think is required and you will end up doing the ‘correct’ amount. Remember, maintain consistency in your working out and DON’T skip steps just because you knew the answer already, a lot of struggling students will face this problem because as they become more and more proficient at mathematics they sway themselves to believe that they can get away with more when in reality that is the reason why they are seeing more and more ‘silly mistakes’ popping up in their exams.

If you want to practice what is considered enough working out it is always a great idea to pay close attention to the examples given by people who are experienced with the topic as they will always show you what is required in exams for the question. Cross check their examples and working out with the full suggested solutions at the end of a past paper and even some textbooks or even have your work verified by a teacher or a tutor. Setting out mathematical working out is a principle, it will obviously look different from each topic but the foundational qualities of having coherent and tidy work will always stay the same.

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