## Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. |

## 1. | GCSE Higher |

(a) In an election, David Linewhip gained 27 552 votes out of a total of 43 715 votes. Write 27 552 as a percentage of 43 715 giving your answer to the nearest integer.

(b) Goodtrip Travel increases the cost of a holiday by 8%. The holiday originally cost £1245. Find the new cost of the holiday.

## 2. | GCSE Higher |

In 2009 the price of a Big Mac was £2.29.

In 2013 the price of a Big Mac had risen to £2.69.

(a) Work out the percentage increase in the price of this snack over the four years.

(b) Express the price in 2009 as a percentage of the 2013 price.

(c) By what percentage must the 2013 price be discounted to equal the 2009 price?

## 3. | GCSE Higher |

Davy Browning buys a premium skateboard.

He gets a discount of 15% off the normal price.

Davy pays £170 for the skateboard.

(a) Work out the normal price of the skateboard.

Saj invests £8000 in a savings account.

The savings account pays compound interest at a rate of 1.8% for the first year then 1.2% for each extra year.

(b) Work out the value of Saj’s investment at the end of 4 years.

## 4. | GCSE Higher |

(a) Davy Browning earns £54000 per year before paying tax.

He pays tax on his earnings at a rate of 18%.

Calculate the amount Davy has after paying tax.

(b) Patty O’Dawes earns £57810 per year after paying tax at a rate of 18%.

Calculate the amount that Patty earns before paying tax.

(c) Davy opens a savings account with £2500.

The account pays 2.4% per year simple interest.

Calculate the amount in Davy’s account at the end of 5 years.

(d) Patty opens a savings account with £500 at the same time ad Davy.

The account pays 2.1% per year compound interest.

Patty pays another £500 into her account on the same day every year.

Find who has the greater amount in their account at the end of 5 years.

## 5. | GCSE Higher |

The value of a new car is £22 000.

The value of the car decreases by 30% in the first year then 10% in each of the next 5 years.

Work out the value of the car after 6 years.

## 6. | GCSE Higher |

Windthrup bought a car for £9500 which depreciated by 6% in the first year and 3.5% in the second year.

a) Windthrup thinks that in two years his car depreciated by 9.5% over the two years. Show, with any necessary calculations, that Winthrup is wrong.

b) Windthrup's car depreciates by \(x%\) during the third year. At the end of the three years the car is worth £8190. Find the value of \(x\) to three significant figures.

## 7. | GCSE Higher |

Zoe invests £5000 in an account for one year. At the end of the year, interest is added to her account.

Zoe pays tax on this interest at a rate of 25%. After the tax has been taken off she received £25.40 interest.

Work out the percentage interest rate for the account.

## 8. | GCSE Higher |

Montague invests £7000 for six years in a bank offering compound interest at \(x%\) per annum.

The investment is worth £7654.10 at the end of the six years.

Find the value of \(x\).

## 9. | GCSE Higher |

John times how long it takes him to run around Hazelnut Park each Friday afternoon. The last three weeks his times, rounded to the nearest minute are \(p, q \; \text{and} \; r\).

He notices that \(q\) is 5% more than \(p\) and \(r\) is 5% less than \(q\).

Indicate which of the following statements are true:

(a) \( r \lt p \) and \( r \lt q \)

(b) \( r \gt p \) and \( r \gt q \)

(c) \( r = p \) and \( r \lt q \)

(d) \( p \gt q \) and \( p = r \)

(e) \( p =q \) and \( p \gt r \)

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