1. 1
   An Arctic research station is compiling its daily report. It records an ice-sheet thickness of $4.5 \times 10^3$ mm, a wind speed of $38.472$ km/h, and it needs to evaluate $6.2 \times 10^{-4} \div 4$ for a probability estimate used in the report.

   (a)

   What is the ice-sheet thickness, $4.5 \times 10^3$ mm, written in metres?

   [1 mark]

   • A4.5 m
   • B0.45 m
   • C45 m
   • D450 m

   (b)

   What is the wind speed, $38.472$ km/h, written correct to 2 significant figures?

   [1 mark]

   • A38.5
   • B39
   • C38
   • D40

   (c)

   Using a calculator, $6.2 \times 10^{-4} \div 4$ is worked out and given correct to 2 significant figures. Which value is this?

   [1 mark]

   • A0.0016
   • B0.00016
   • C0.000155
   • D0.000016

   Total for question 1: 3 marks

2. 2
   A print shop starts a week with a full stock of paper. It uses $\frac{2}{5}$ of the stock on Monday and a further $\frac{1}{4}$ of the original stock on Tuesday.

   (a)

   Work out the fraction of the original stock used over the two days. Give your answer in its simplest form.

   [2 marks]

   (b)

   Write the fraction of stock used over the two days, $\frac{13}{20}$, as a percentage.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A small business had total sales of £8,400 in its first year of trading. In its second year, sales increased by 8%. The owner then invests £5,500 of the business's profit into a savings account paying 3.5% compound interest per year, left untouched for 3 years.

   (a)

   Work out the business's sales in its second year of trading.

   [3 marks]

   (b)

   Work out the value of the £5,500 investment after 3 years, correct to the nearest penny.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A plumbing supplier wants to cut two rolls of pipe, 84 m and 126 m long, into pieces of equal length with none left over. Each finished inspection cover in the job is a square with side length $\sqrt{18}$ m. The delivery van uses $(23.6 - 8.9) \div 2 \times 3$ litres of diesel for the round trip, calculated using the correct order of operations, at a cost of £1.48 per litre.

   (a)

   The supplier wants to cut both rolls into the longest possible equal-length pieces with none left over. Using prime factorisation, find this greatest length.

   [4 marks]

   (b)

   Each inspection cover is a square with side length $\sqrt{18}$ m. Show that this simplifies to $3\sqrt{2}$ m, and hence find the exact area of one cover, giving your answer in its simplest form.

   [4 marks]

   (c)

   The delivery van uses $(23.6 - 8.9) \div 2 \times 3$ litres of diesel for the round trip, calculated using the correct order of operations, at a cost of £1.48 per litre. Work out the total cost of the diesel, giving your answer to the nearest penny.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   A pharmaceutical laboratory is compiling a dilution report. It records a chemical sample mass of $3.2 \times 10^{-3}$ g, a concentration reading of $0.04837$ mol/l, and it needs to evaluate $\frac{3.2 \times 10^{-3}}{0.048}$ using a calculator.

   (a)

   What is the sample mass, $3.2 \times 10^{-3}$ g, written in milligrams (1 g = 1000 mg)?

   [1 mark]

   • A0.0032 mg
   • B32 mg
   • C320 mg
   • D3.2 mg

   (b)

   What is the concentration reading, $0.04837$ mol/l, written correct to 2 significant figures?

   [1 mark]

   • A0.048
   • B0.049
   • C0.05
   • D0.04

   (c)

   Using a calculator, $\frac{3.2 \times 10^{-3}}{0.048}$ is worked out and given correct to 2 significant figures. Which value is this?

   [1 mark]

   • A0.67
   • B0.0067
   • C0.067
   • D6.7

   Total for question 5: 3 marks

6. 6
   A charity shop receives a large donation of clothing. Of the total donation, $\frac{3}{7}$ is childrenswear. Of the remaining items, $\frac{2}{5}$ are coats.

   (a)

   Work out the fraction of the total donation that is coats. Give your answer in its simplest form.

   [2 marks]

   (b)

   Write the fraction of the donation that is coats, $\frac{8}{35}$, as a decimal correct to 3 decimal places.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A mobile phone network had 1,200 subscribers on a certain tariff at the start of the year. By mid-year this had increased by 8%. The network also invests £6,200 of its profit into an account paying 2.75% compound interest per year, left untouched for 4 years.

   (a)

   Work out the number of subscribers on the tariff by mid-year.

   [3 marks]

   (b)

   Work out the value of the £6,200 investment after 4 years, correct to the nearest penny.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   A tiling company is laying square tiles in a hallway. Two batches of skirting board measure 108 cm and 144 cm and must be cut into equal-length pieces with none left over. Each tile has a side length of $\sqrt{50}$ cm. The company's delivery cost is $(52.80 - 19.35) \div 3 \times 5$ pounds for labour, calculated using the correct order of operations, plus a call-out fee of £22.40.

   (a)

   The two batches of skirting board are to be cut into the longest possible equal-length pieces with none left over. Using prime factorisation, find this greatest length.

   [4 marks]

   (b)

   Each tile has a side length of $\sqrt{50}$ cm. Show that this simplifies to $5\sqrt{2}$ cm, and hence find the exact area of one tile, giving your answer in its simplest form.

   [4 marks]

   (c)

   The company's delivery cost is $(52.80 - 19.35) \div 3 \times 5$ pounds for labour, calculated using the correct order of operations, plus a call-out fee of £22.40. Work out the total cost, giving your answer to the nearest penny.

   [5 marks]

   Total for question 8: 13 marks

End of questions