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

## 2. | GCSE Higher |

Without using a calculator:

(a) Express 68 as the product of its prime factors.

(b) Divide 68 by 5 giving your answer in decimal format.

(c) Multiply 13.06 by 2.1

## 3. | GCSE Higher |

The number, \(N\), can be written as the product of prime factors in index form as:

$$N = 3 × 5^3 × x^4$$Work out \(5N^2\) as a product of prime factors in index form giving your answer in terms of \(x\).

## 4. | 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.

## 5. | 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) \(-0.75\)

## 6. | 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.

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