Magdalen College School 11+ Maths Sample Paper

These questions test arithmetic fluency. Be careful with carrying and borrowing.

• a) 153 + 78 = 231
• b) 185 - 43 = 142
• c) 532 - 85 = 447
• d) 53 × 9 = 477
• e) 37 × 23 = (37×20) + (37×3) = 740 + 111 = 851
• f) 238 ÷ 7 = 34
• g) 442 ÷ 17 = 26

• Perimeter: Sum all outer sides.
  9 + 6 + 4 + 5 + 5 + 1 = 30 cm
• Area: Split the shape into two rectangles.
  Rectangle 1: 4cm × 6cm = 24 cm²
  Rectangle 2: 5cm × 4cm = 20 cm²
  Total Area: 24 + 20 = 44 cm²

• a) 5/12 + 4/12 = 9/12. Simplify by dividing by 3 = 3/4
• b) 1/6 + 1/3. Convert to common denominator (6).
  1/6 + 2/6 = 3/6. Simplify = 1/2

• a) 10% of £70 is £7. So 30% is £7 × 3 = £21
• b) One fifth means dividing by 5. £70 ÷ 5 = £14
• c) Half of £70 is £35.
  10% of 35 is 3.5.
  80% is 3.5 × 8 = £28

• a) Angles on a straight line add to 180°. 180° - 100° = 80°
• b) Exterior angle equals sum of interior opposite, or calculate interior first. 150°
• c) Angles in a triangle add to 180°. 180° - (30° + 32°) = 118°
• d) Alternate angle (Z-angle) corresponds to the 62° shown. 62°

• a) Rule: +4. Next numbers: 23, 27
• b) Rule: ×2. Next numbers: 48, 96
• c) Rule: Add increasing even numbers (+2, +4, +6, +8...).
  23 + 10 = 33; 33 + 12 = 45. 33, 45
• d) Numerators: +2 (odd numbers). Denominators: Add increasing odd numbers (+5, +7, +9...).
  Next: 9/37, 11/50

Convert all values to Fraction, Decimal, and Percentage.

• 50% = 0.5 = 1/2
• 0.75 = 3/4 = 75%
• 3/5 = 0.6 = 60%
• 17/20 = 0.85 = 85%

• a) Edinburgh (13:43) to Kircaldy (14:18) = 35 minutes
• b) Add the standard travel times to the 15:34 departure:
  Haymarket: 15:34 + 23m = 15:57
  Kircaldy: 15:57 + 12m = 16:09
  Ladybank: 16:09 + 5m = 16:14
• c) Express takes 44m. Stopping takes 55m. Difference = 11 minutes
• d) Arrival time at station: 13:05 + 27m + 45m = 14:17. Next train is 14:24. Wait = 7 minutes

Count the total square units inside the given shape. Then, draw a simple rectangle with the same area.
Example: If the shape has an area of 6 squares, draw a 3x2 rectangle.

• a) 5 pens (£6.25) + 7 pencils (£5.60) = £11.85.
  £15.00 - £11.85 = £3.15
• b) 5 pencils cost £4.00. Leaves £11.00.
  £11.00 ÷ £1.25 = 8.8. Max pens = 8
• c) Money spent: £15 - £2.80 = £12.20.
  Trial and error or logic leads to: 4 pens and 9 pencils.

• a) To eat double the loaves (60) in the same time, you need double the scouts. 24 scouts
• b) Half the scouts (6) will take double the time to eat the same amount. 8 days
• c) 1 scout eats 30 ÷ (12×4) = 0.625 loaves/day.
  3 scouts in 8 days = 3 × 8 × 0.625 = 15 loaves

Convert everything to decimals to compare:

• 60% = 0.60
• 17/25 = 0.68
• 2/3 = 0.666...
• 0.66 = 0.66

Order: 60% < 0.66 < 2/3 < 17/25

Using the logic of means (Mean × Count = Total Sum):

• Sum of 2 smallest = 6. (Must be 1 and 5 as they are odd and different).
• Sum of 3 smallest = 15. (1 + 5 + x = 15, so x = 9).
• Sum of all 4 = 28. (15 + y = 28, so y = 13).

The numbers are: 1, 5, 9, 13

There are 10 bottles. The first falls at 5:10 am. There are 9 intervals remaining for the other bottles.

• 9 intervals × 5 minutes = 45 minutes.
• 5:10 am + 45 minutes = 5:55 am

This is a visual symmetry question. You must reflect each line of the shape across the diagonal dotted line carefully, counting squares to ensure the reflection is accurate.

Using cards: 2, 4, 6, 7, 8

• a) Largest odd: Must end in 7. Arrange others high to low. 86427
• b) Closest to 50,000: 48762 (closer than 62478).
• c) Largest Prime (2 cards): 67
• d) Largest multiplication: 876 × 42 (or check combinations). 66793248

• a) Divisible by 4 and 5 (must be 20, 40, 60, 80...).
  Check ÷ 7 remainder 6.
  20 ÷ 7 = 2 r 6. Answer: 20
• b) Divisible by 6 and 7 (must be 42, 84...).
  Check ÷ 5 remainder 4.
  84 ÷ 5 = 16 r 4. Answer: 84
• c) Divisible by 5 (ends in 0 or 5).
  Leaves remainder 1 when divided by 2 (must be odd, so ends in 5).
  Check 5, 15, 25... 85 works for all conditions. Answer: 85

You must place digits 1–8 into the grid so all equations work horizontally and vertically.
Hint: Start with the division (e.g., 8 ÷ 2 = 4 or 6 ÷ 3 = 2).