iGCSE Mathematics (0580) : C2.1 Use letters to express generalised numbers and express basic arithmetic processes algebraically.. iGCSE Style Questions Paper 1

Question

Balavan has n marbles.
He gives his sister \( \frac{n}{5} \) marbles.
He gives his cousin \( \frac{n}{2} \) marbles.

Write an expression, in terms of n, for the number of marbles that Balavan has now.
Give your answer in its simplest form.

▶️ Answer/Explanation

Answer: \( \frac{3}{10}n \)

Solution:
1. Total marbles given away: \[ \frac{n}{5} + \frac{n}{2} = \frac{2n}{10} + \frac{5n}{10} = \frac{7n}{10} \] 2. Marbles remaining: \[ n – \frac{7n}{10} = \frac{10n}{10} – \frac{7n}{10} = \frac{3n}{10} \] Simplified expression: \( \frac{3}{10}n \)

Question

Zaid has a non-calculator method for working out if a number is a multiple of 11. He shows his method for the number 919281.

Show that the number 918271937 is a multiple of 11 by using Zaid’s method.

▶️ Answer/Explanation

Solution

Ans: The number is a multiple of 11.

Apply Zaid’s method: Alternate signs for each digit and sum them.

For \(918271937\), compute \(9 – 1 + 8 – 2 + 7 – 1 + 9 – 3 + 7\).

The sum is \(33\), which is divisible by 11 (\(33 = 3 \times 11\)).

Thus, \(918271937\) is a multiple of 11.

iGCSE Mathematics (0580) : C2.1 Use letters to express generalised numbers and express basic arithmetic processes algebraically.. iGCSE Style Questions Paper 1

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