0580/42 Oct/Nov 2024, Question 3: Simultaneous Equations with a Curve

Part (ai) · 2 marks

Simplify 3m − 5n − 4m + 8n by collecting like terms.

1. 13m − 4m = −m and −5n + 8n = 3n
2. 2= −m + 3n

Answer−m + 3n

Part (aii) · 2 marks

Simplify (3a²c³)⁴, applying the power to each factor.

1. 13⁴ = 81, (a²)⁴ = a⁸, (c³)⁴ = c¹²
2. 2= 81a⁸c¹²

Answer81a⁸c¹²

Part (aiii) · 2 marks

Simplify 4x/5 − 3x/10 + 2x/15 by combining the fractions.

1. 1Use the common denominator 30.
2. 24x/5 = 24x/30, 3x/10 = 9x/30, 2x/15 = 4x/30
3. 3(24x − 9x + 4x)/30 = 19x/30

Answer19x/30

Part (b) · 3 marks

An isosceles triangle has perimeter 35.5 cm, equal sides (3a + 2) cm and base a cm. Find a.

1. 1a + 2(3a + 2) = 35.5
2. 27a + 4 = 35.5
3. 37a = 31.5
4. 4a = 4.5

Answer4.5

Part (c) · 3 marks

Solve 5x² − 4x − 3 = 0 using the quadratic formula, showing all working.

1. 1x = (−(−4) ± √((−4)² − 4 × 5 × (−3)))/(2 × 5)
2. 2x = (4 ± √76)/10
3. 3x = −0.4718… ≈ −0.472 and x = 1.2718… ≈ 1.27

Answer−0.472 or −0.4718 to −0.4717 and 1.27 or 1.271 to 1.272

Part (d) · 5 marks

Solve the simultaneous equations y = x² − 4x + 5 and y = 2x − 3, showing all working.

1. 1x² − 4x + 5 = 2x − 3
2. 2x² − 6x + 8 = 0
3. 3(x − 2)(x − 4) = 0, so x = 2 or x = 4
4. 4y = 2(2) − 3 = 1 and y = 2(4) − 3 = 5
5. 5x = 2, y = 1 and x = 4, y = 5

Answerx = 2, y = 1 and x = 4, y = 5

More past-paper questions on simultaneous equations with a curve

• 0580/22 May/Jun 2026 Q25 · 5 marks
• 0580/42 Feb/Mar 2025 Q22 · 6 marks
• 0580/22 May/Jun 2025 Q24 · 5 marks
• 0580/42 Oct/Nov 2025 Q19 · 6 marks
• 0580/41 May/Jun 2024 Q8 · 15 marks
• 0580/22 Feb/Mar 2023 Q19 · 3 marks