Here are two pieces of work. Each shows a question and the first line of an incorrect solution. For each part, describe the error made in the first line of the solution. You do not need to complete the solution. (a) Question: Simplify: $$\frac{2}{x-1} + \frac{3}{x+4}$$ Solution: $$\frac{2}{x-1} + \frac{3}{x+4} = \frac{2(x-1) + 3(x-4)}{(x-1)(x+4)}$$ (b) Question: Solve. $x^{2} + 7x + 5 = 0$ Solution: $$x = \frac{7 \pm \sqrt{7^{2}-4\cdot1\cdot5}}{2\cdot1}$$

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Here are two pieces of work - OCR - GCSE Maths - Question 13 - 2023 - Paper 4

Question 13

Here are two pieces of work. Each shows a question and the first line of an incorrect solution. For each part, describe the error made in the first line of the sol... show full transcript

Worked Solution & Example Answer:Here are two pieces of work - OCR - GCSE Maths - Question 13 - 2023 - Paper 4

Step 1

(a) Describe the error made in the first line of the solution.

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Answer

The error in the first line of the solution is that the expression does not correctly add the two fractions. The correct approach should involve finding a common denominator and correctly applying addition rather than incorrectly multiplying through. The expression

\frac{2(x-1) + 3(x+4)}{(x-1)(x+4)}

is necessary to combine the fractions.

Step 2

(b) Describe the error made in the first line of the solution.

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Answer

The first line of the solution is incorrect as it does not apply the quadratic formula correctly. The correct application of the quadratic formula should be

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

, which means for the equation $x^{2} + 7x + 5 = 0$ , $a = 1$ , $b = 7$ , and $c = 5$ . The expression should correctly reference these coefficients.

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