2026 NORTHBROOKS P2 Q1

2026 NORTHBROOKS P2 Q1

Secondary 4
12 marks
  1. Solve \(\dfrac{2}{x+2}=\dfrac{1}{3x-4}\).[2]
  2. Factorise completely \(3x^2-48y^2\).[2]
  3. Write \(\dfrac{3^{85}\times3^{15}}{3^{15}+3^{15}+3^{15}}\) as a single power of 3.[2]
  4. Solve these simultaneous equations.
    \(\begin{aligned} 3x-2y&=2 \\ 7x+3y&=43 \end{aligned}\)
    You must show your working.[3]
  5. Write \(\dfrac{y^2}{(x+y)(x-3y)}-\dfrac{x-y}{3y-x}\) as a single fraction in its simplest form.[3]

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Answer:(a) \(x=2\). (b) \(3(x+4y)(x-4y)\). (c) \(3^{84}\). (d) \(x=4,y=5\). (e) \(\dfrac{x^2}{(x+y)(x-3y)}\).

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