## Exam-Style Questions on Number## Problems on Number adapted from questions set in previous exams. |

## 1. | GCSE Higher |

The difference between the areas of the two squares is 51 cm^{2}.

When measured in cm the lengths of the sides of the squares are integers and both less than 20cm.

Find the lengths of the sides of the two squares.

## 2. | IB Studies |

This Venn diagram shows the relationship between the sets of numbers

$$\mathbb N, \mathbb Z, \mathbb Q \text{ and } \mathbb R$$Write down the following numbers in the appropriate place in the Venn diagram.

(a) \(5\)

(b) \(\frac23\)

(c) \(\pi\)

(d) \(0.91\)

(e) \(\sqrt 7\)

(f) \(-0.75\)

## 3. | GCSE Higher |

This expression can be used to generate a sequence of numbers.

$$n^2+n + 5$$(a) Work out the first three terms of this sequence.

(b) What is the smallest value of \(n\) that produces a term of the sequence that is not a prime number?

(c) Is it true that odd square numbers have exactly three factors? Explain and justify your answer.

(d) Seymour is thinking of a number.

- It is a common factor of 144 and 192.
- It is a common multiple of 6 and 8.
- It is less than 100.

Find the two possible numbers that Seymour could be thinking of.

## 4. | GCSE Higher |

(a) Write this list of numbers in order, smallest first.

$$\sqrt{47}, \frac{22}{3}, 3.5^2, 8.64$$(b) Write \((1 + \sqrt5)^2\) in the form \(a + b\sqrt5\) .

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