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5 (a) Rearrange the equation to make x the subject - OCR - GCSE Maths - Question 5 - 2017 - Paper 1

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5 (a) Rearrange the equation to make x the subject. y = 7x - 3 (b) Factorise. (i) x² - xy (ii) x² + 8x + 12

Worked Solution & Example Answer:5 (a) Rearrange the equation to make x the subject - OCR - GCSE Maths - Question 5 - 2017 - Paper 1

Step 1

(a) x =

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Answer

To rearrange the equation to make x the subject, we start with:

y=7x−3y = 7x - 3

  1. Add 3 to both sides: y+3=7xy + 3 = 7x
  2. Divide both sides by 7: x=y+37x = \frac{y + 3}{7}

Step 2

(b)(i) x² - xy

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Answer

We need to factorise the expression:

  1. Observe that both terms share a common factor of x: x2−xy=x(x−y)x² - xy = x(x - y)

Step 3

(b)(ii) x² + 8x + 12

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Answer

To factorise this quadratic expression, we look for two numbers that multiply to 12 (the constant term) and add up to 8 (the coefficient of x).

  1. The numbers 2 and 6 satisfy these conditions:
  2. Therefore, we can write: x2+8x+12=(x+2)(x+6)x² + 8x + 12 = (x + 2)(x + 6)

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