The Logic of Maths

May 26, 2014 § 1 Comment

Part of mathematical ability comes down to logic. People who are logical are able to follow mathematical processes and understand the mechanisms behind the question. This is especially helpful when it comes to solving word problems, a particular obstacle to lots of maths students.

Here’s one of the word problem questions from a GCSE Higher Maths Mock Paper:

Janice asks 100 students if they like biology or chemistry or physics best.
38 of the students are girls.
21 of these girls like biology best.
18 boys like physics best.
7 out of the 23 students who like chemistry best are girls.
Work out the number of students who like biology best.

This question can easily get you in a tangle! It needs to be tackled logically. Often, diagrams and charts are a good way to order your thought processes. For this particular question, a two-way table is helpful. We know that there are 100 students in total. 38 are girls, so 62 are boys. 21 girls like biology, 18 boys like physics, 7 girls like chemistry and 16 boys like chemistry. If we put those numbers into a table, we can then work out the rest.

So, the answer is 49.

Don’t Be Negative – A Common GCSE Maths Mistake!

May 11, 2014 § Leave a comment

Okay so this might be a bit of a boring blog post! But, with the GCSE exams round the corner, I thought I would highlight one of the most common mistakes seen when marking GCSE maths papers.

That problem is negative numbers. They just get students in a right old pickle! And that’s why they crop up every year in the exam papers! But they won’t be obvious . . . . they are often very sneaky and catch people off guard. For instance, you will see minus signs when expanding brackets or in substitution or indices questions.

So, here are the simple rules:

MINUS X MINUS = PLUS

MINUS X PLUS = MINUS

Take this past paper question as an example:

V = 3b + 2b2

Find the value of V when b = –4

First, substitute the number into the equation.

3b + 2b² =   3 x -4 + 2 x -4²

3 x -4 is PLUS x MINUS, so it becomes a MINUS: 3 x -4 = -12

2 x -4² is a bit more complicated because we need to do the squaring first:
-4² = -4 x -4 which is MINUS x MINUS, so it becomes a PLUS. -4 x -4 = 16

2 x 16 = 32

So, 3b + 2b² =   3 x -4 + 2 x -4² = -12 + 32 = 20

Just take it step by step and CHECK YOUR WORK! We wish everyone doing the GCSE exams all the best.

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