Pearson Edexcel Level 3 GCE Further
Mathematics Advanced PAPER 3C:
Further Mechanics 1 question paper
june 2026
Section A: Simplifying Ratios (Q1–Q10)
Q1. Simplify 8 : 12
A1. 2 : 3 (divide both by 4)
Q2. Simplify 15 : 25
A2. 3 : 5 (divide both by 5)
Q3. Simplify 14 : 21
A3. 2 : 3 (divide both by 7)
Q4. Simplify 27 : 36
A4. 3 : 4 (divide both by 9)
Q5. Simplify 24 : 30 : 18
A5. 4 : 5 : 3 (divide all by 6)
Q6. Simplify 56 : 88
A6. 7 : 11 (divide both by 8)
,Q7. Simplify 42 : 49 : 70
A7. 6 : 7 : 10 (divide all by 7)
Q8. Simplify 36 : 48 : 60
A8. 3 : 4 : 5 (divide all by 12)
Q9. Simplify 2.5 : 5.0
A9. 1 : 2 (multiply by 2 then divide by 5, or just divide both by 2.5)
Q10. Simplify 0.6 : 1.2
A10. 1 : 2 (divide both by 0.6)
Section B: Dividing Quantities in a Given Ratio (Q11–Q20)
Q11. Share £60 in the ratio 2 : 3
A11. 1 part = £60 ÷ 5 = £12 → £24 : £36
Q12. Share 120 apples in the ratio 1 : 4
A12. 1 part = 120 ÷ 5 = 24 → 24 : 96
Q13. Share 150 km in the ratio 2 : 3 : 5
A13. Total parts = 10, 1 part = 150 ÷ 10 = 15 km → 30 : 45 : 75
km
Q14. Share £84 in the ratio 5 : 7
A14. Total parts = 12, 1 part = 84 ÷ 12 = 7 → £35 : £49
Q15. Share 360 marbles in the ratio 3 : 4 : 5
A15. Total parts = 12, 1 part = 360 ÷ 12 = 30 → 90 : 120 : 150
Q16. Share 400 g of flour in the ratio 2 : 3
A16. 1 part = 400 ÷ 5 = 80 g → 160 g : 240 g
, Q17. Share 500 ml of juice in the ratio 1 : 2 : 7
A17. Total parts = 10, 1 part = 500 ÷ 10 = 50 ml → 50 : 100 : 350
ml
Q18. Share £280 in the ratio 3 : 4
A18. 1 part = 280 ÷ 7 = 40 → £120 : £160
Q19. Share 48 sweets between two children in the ratio 5 : 3
A19. Total parts = 8, 1 part = 48 ÷ 8 = 6 → 30 : 18 sweets
Q20. Share 600 kg in the ratio 2 : 3 : 5
A20. Total parts = 10, 1 part = 600 ÷ 10 = 60 kg → 120 : 180 : 300
kg
Section C: Finding Missing Values (Q21–Q30)
Q21. If x : 9 = 2 : 3, find x.
A21. x/9 = 2/3 → 3x = 18 → x = 6
Q22. If 5 : y = 15 : 27, find y.
A22. 5/y = 15/27 → cross multiply: 5 × 27 = 15y → 135 = 15y → y
=9
Q23. If 4 : 7 = 20 : x, find x.
A23. 4/7 = 20/x → 4x = 140 → x = 35
Q24. If 9 : 12 = x : 16, find x.
A24. 9/12 = x/16 → 12x = 144 → x = 12
Q25. If x : 14 = 6 : 7, find x.
A25. x/14 = 6/7 → 7x = 84 → x = 12
Mathematics Advanced PAPER 3C:
Further Mechanics 1 question paper
june 2026
Section A: Simplifying Ratios (Q1–Q10)
Q1. Simplify 8 : 12
A1. 2 : 3 (divide both by 4)
Q2. Simplify 15 : 25
A2. 3 : 5 (divide both by 5)
Q3. Simplify 14 : 21
A3. 2 : 3 (divide both by 7)
Q4. Simplify 27 : 36
A4. 3 : 4 (divide both by 9)
Q5. Simplify 24 : 30 : 18
A5. 4 : 5 : 3 (divide all by 6)
Q6. Simplify 56 : 88
A6. 7 : 11 (divide both by 8)
,Q7. Simplify 42 : 49 : 70
A7. 6 : 7 : 10 (divide all by 7)
Q8. Simplify 36 : 48 : 60
A8. 3 : 4 : 5 (divide all by 12)
Q9. Simplify 2.5 : 5.0
A9. 1 : 2 (multiply by 2 then divide by 5, or just divide both by 2.5)
Q10. Simplify 0.6 : 1.2
A10. 1 : 2 (divide both by 0.6)
Section B: Dividing Quantities in a Given Ratio (Q11–Q20)
Q11. Share £60 in the ratio 2 : 3
A11. 1 part = £60 ÷ 5 = £12 → £24 : £36
Q12. Share 120 apples in the ratio 1 : 4
A12. 1 part = 120 ÷ 5 = 24 → 24 : 96
Q13. Share 150 km in the ratio 2 : 3 : 5
A13. Total parts = 10, 1 part = 150 ÷ 10 = 15 km → 30 : 45 : 75
km
Q14. Share £84 in the ratio 5 : 7
A14. Total parts = 12, 1 part = 84 ÷ 12 = 7 → £35 : £49
Q15. Share 360 marbles in the ratio 3 : 4 : 5
A15. Total parts = 12, 1 part = 360 ÷ 12 = 30 → 90 : 120 : 150
Q16. Share 400 g of flour in the ratio 2 : 3
A16. 1 part = 400 ÷ 5 = 80 g → 160 g : 240 g
, Q17. Share 500 ml of juice in the ratio 1 : 2 : 7
A17. Total parts = 10, 1 part = 500 ÷ 10 = 50 ml → 50 : 100 : 350
ml
Q18. Share £280 in the ratio 3 : 4
A18. 1 part = 280 ÷ 7 = 40 → £120 : £160
Q19. Share 48 sweets between two children in the ratio 5 : 3
A19. Total parts = 8, 1 part = 48 ÷ 8 = 6 → 30 : 18 sweets
Q20. Share 600 kg in the ratio 2 : 3 : 5
A20. Total parts = 10, 1 part = 600 ÷ 10 = 60 kg → 120 : 180 : 300
kg
Section C: Finding Missing Values (Q21–Q30)
Q21. If x : 9 = 2 : 3, find x.
A21. x/9 = 2/3 → 3x = 18 → x = 6
Q22. If 5 : y = 15 : 27, find y.
A22. 5/y = 15/27 → cross multiply: 5 × 27 = 15y → 135 = 15y → y
=9
Q23. If 4 : 7 = 20 : x, find x.
A23. 4/7 = 20/x → 4x = 140 → x = 35
Q24. If 9 : 12 = x : 16, find x.
A24. 9/12 = x/16 → 12x = 144 → x = 12
Q25. If x : 14 = 6 : 7, find x.
A25. x/14 = 6/7 → 7x = 84 → x = 12
