Fractions, decimals, percentages and ratioIB MYP Maths Extended: Subtopic test

1. 1
   In a survey at a school in Lagos, $\frac{7}{20}$ of the students walk to school and the rest travel by other means.

   (a)

   Write $\frac{7}{20}$ as a percentage.

   [1 mark]

   • A$35\%$
   • B$3.5\%$
   • C$70\%$
   • D$14\%$

   (b)

   Find the ratio of students who walk to students who do not walk, in its simplest form.

   [1 mark]

   • A$7:20$
   • B$7:13$
   • C$13:7$
   • D$13:20$

   (c)

   A total of $480$ students took part in the survey. Find how many of them do not walk to school.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A laptop has a price of $\$850$ before a sale.

   (a)

   In the sale the price is reduced by $12\%$. Find the sale price.

   [1 mark]

   • A$\$102$
   • B$\$838$
   • C$\$952$
   • D$\$748$

   (b)

   A month later the sale price is increased by $12\%$. Find the new price.

   [1 mark]

   • A$\$850.00$
   • B$\$760.00$
   • C$\$837.76$
   • D$\$89.76$

   (c)

   The price of the laptop is $\$850$ before the sale. Find the overall percentage change from $\$850$ to the new price after the two changes. State whether it is an increase or a decrease.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A bicycle shop in Dubai sells a bicycle for AED $1440$ after a $20\%$ discount.

   (a)

   Find the original price of the bicycle.

   [3 marks]

   (b)

   The shop paid AED $1080$ for the bicycle. (i) Find the ratio cost to profit, in its simplest form. (ii) Find the profit as a percentage of the cost.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Sofia puts $\$8000$ into a savings account that pays $2.5\%$ interest at the end of each year, and the interest stays in the account. Her brother Daniel puts $\$8000$ into a fund whose value rises by $6\%$ in the first year and then falls by $4\%$ in the second year.

   (a)

   (i) Find the value of Sofia's account after two years. (ii) Find the value of Daniel's fund after two years. (iii) Daniel says: 'Up $6\%$ then down $4\%$ is a net rise of $2\%$, so my fund is worth $8000\times1.02=\$8160$.' Explain why he is wrong.

   [6 marks]

   (b)

   Sofia wants her account to reach at least $\$9000$. (i) Find the smallest whole number of years this takes. (ii) Prices rise by $3\%$ each year. Sofia says her savings will keep their buying power over that time. Justify whether she is correct.

   [6 marks]

   Total for question 4: 12 marks

End of questions