UGANDA ADVANCED CERTIFICATE OF EDUCATION
POST - MOCK EXAMINATIONS September 2023
PURE Mathematics
Paper One
3 Hours
INSTRUCTIONS:
Answer all questions in section A and any five questions in section B
SECTION A (40 MARKS)
1. Solve the equations; 2𝑥 − 𝑦 + 𝑧 = 5
𝑥 + 2𝑧 − 3𝑦 = 2
2𝑥 + 4𝑧 + 𝑦 + 3 = 0 (5 marks)
2. Find the acute angle between the line 𝑥−6
5
= 1 − 𝑦 = 1 + 𝑧 and the plane 7𝑥 − 𝑦 + 5𝑧 +
5 = 0 giving your answer to the nearest degree. (5 marks)
3. Show that 𝑥 + 1 is a factor of the expression; 𝑥
3 − 5𝑥
2 + 2𝑥 + 8 hence solve the equation
𝑥
3 − 5𝑥
2 + 2𝑥 + 8 = 0 (5 marks)
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1. Solve the equations; 2𝑥 − 𝑦 + 𝑧 = 5
𝑥 + 2𝑧 − 3𝑦 = 2
2𝑥 + 4𝑧 + 𝑦 + 3 = 0 (5 marks)
2. Find the acute angle between the line 𝑥−6
5
= 1 − 𝑦 = 1 + 𝑧 and the plane 7𝑥 − 𝑦 + 5𝑧 +
5 = 0 giving your answer to the nearest degree. (5 marks)
3. Show that 𝑥 + 1 is a factor of the expression; 𝑥
3 − 5𝑥
2 + 2𝑥 + 8 hence solve the equation
𝑥
3 − 5𝑥
2 + 2𝑥 + 8 = 0 (5 marks)
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