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Mathematics Problem Solving Flashcards

6 cards from real 11+ practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A clock shows 15:45. What is the angle between the hour and minute hands?

    Answer: 157.5°

    At 15:45, minute hand is at 9 (270°). Hour hand: 3 o'clock = 90°, plus 45/60 × 30° = 22.5°, so hour hand is at 112.5°. Angle = 270° - 112.5° = 157.5°.

  2. If x + 7 = 3x - 5, what is the value of x?

    Answer: 6

    x + 7 = 3x - 5. Rearranging: 7 + 5 = 3x - x, so 12 = 2x, therefore x = 6.

  3. Three consecutive odd numbers add up to 63. What is the largest of the three?

    Answer: 23

    Let the numbers be n, n+2, n+4. Sum: 3n + 6 = 63, so 3n = 57, n = 19. The largest is 19 + 4 = 23.

  4. A recipe for 4 people needs 300g of flour. How much flour is needed for 10 people?

    Answer: 750g

    For 1 person: 300 ÷ 4 = 75g. For 10 people: 75 × 10 = 750g.

  5. A regular octagon has a perimeter of 96 cm. What is the length of each side?

    Answer: 12 cm

    A regular octagon has 8 equal sides. Side length = 96 ÷ 8 = 12 cm.

  6. What is the prime factorisation of 180?

    Answer: 2² × 3² × 5

    180 = 2 × 90 = 2 × 2 × 45 = 2 × 2 × 9 × 5 = 2² × 3² × 5.