1. 1
   A quality-control log lists seven measurement readings: -15, 0, 17, 21, 27, 90, 100.

   (a)

   Which of these readings is a prime number?

   [1 mark]

   • A21
   • B17
   • C27
   • D90

   (b)

   Which of these readings is a cube number?

   [1 mark]

   • A27
   • B21
   • C90
   • D100

   (c)

   Which of these readings is a square number?

   [1 mark]

   • A90
   • B21
   • C100
   • D27

   Total for question 1: 3 marks

2. 2
   A baker has 168 chocolate cookies and 210 vanilla cookies. She wants to pack them into identical boxes, with only one type of cookie per box, using the greatest possible number of cookies per box and no cookies left over.

   (a)

   Express 168 and 210 as products of their prime factors.

   [2 marks]

   (b)

   Hence find the highest common factor (HCF) of 168 and 210, and state the greatest number of cookies that can go in each box.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A laboratory records the mass of a virus particle as $3.2\times10^{-17}$ kg and the mass of a bacterium as $8\times10^{-13}$ kg.

   (a)

   Calculate the total mass of one virus particle and one bacterium, giving your answer in standard form correct to 3 significant figures.

   [3 marks]

   (b)

   The bacterium's mass is how many times greater than the virus particle's mass? Give your answer in standard form.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   Aisha inherits 18000 dollars and decides to split it between three investments in the ratio 2 : 3 : 4. The first part is placed in a savings account paying 3% simple interest per year. The second part is placed in an account paying 4% compound interest per year.

   (a)

   Work out the amount placed in each of the three investments.

   [4 marks]

   (b)

   Calculate the total simple interest earned on the first investment after 5 years, and hence find the total value of this investment after 5 years.

   [4 marks]

   (c)

   Calculate the value of the second investment after 2 years at 4% compound interest, giving your answer correct to the nearest dollar. Hence determine whether the second investment (over 2 years) or the first investment (over 5 years, from part (b)) has earned the greater amount of interest, and by how much.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   Four runners' fastest lap times are compared as fractions of an hour: Runner A takes $\frac{3}{8}$ of an hour, Runner B takes 0.4 hours, Runner C takes 35% of an hour, and Runner D takes $\frac{9}{25}$ of an hour.

   (a)

   Which runner recorded the fastest (smallest) lap time?

   [1 mark]

   • ARunner A ($\frac{3}{8}$)
   • BRunner B (0.4)
   • CRunner C (35%)
   • DRunner D ($\frac{9}{25}$)

   (b)

   Which runner recorded the slowest (largest) lap time?

   [1 mark]

   • ARunner A ($\frac{3}{8}$)
   • BRunner B (0.4)
   • CRunner C (35%)
   • DRunner D ($\frac{9}{25}$)

   (c)

   What is Runner D's lap time, $\frac{9}{25}$ of an hour, written as a percentage?

   [1 mark]

   • A9%
   • B90%
   • C3.6%
   • D36%

   Total for question 5: 3 marks

6. 6
   A designer is calculating dimensions for a triangular logo. Two side lengths are given as $\sqrt{75}$ cm and $\sqrt{27}$ cm.

   (a)

   Simplify $\sqrt{75}$ and $\sqrt{27}$, each in the form $k\sqrt3$.

   [2 marks]

   (b)

   Hence find the exact difference between the two side lengths, in its simplest surd form.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A cyclist travels 63 km in 3.5 hours at a constant average speed. A separate delivery van travels the same 63 km route later and takes 2.25 hours.

   (a)

   Calculate the cyclist's average speed in km/h.

   [3 marks]

   (b)

   Calculate the van's average speed, and state how many km/h faster the van travelled compared with the cyclist.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   A tour group flies from Dubai to Tokyo. The flight departs Dubai at 23:40 (24-hour clock) and takes 9 hours 35 minutes; Tokyo is 5 hours ahead of Dubai time. Each passenger converts 1850 UAE dirhams (AED) to Japanese yen (JPY) at a rate of 1 AED = 29.63 JPY, then rounds the total to the nearest 10 yen. Passenger luggage is weighed as 23.5 kg, correct to 1 decimal place.

   (a)

   Find the arrival time in Tokyo local time, giving your answer using the 24-hour clock and stating whether it is the same day or the next day (Dubai date).

   [4 marks]

   (b)

   Calculate the number of yen each passenger receives for 1850 AED, using the given exchange rate, and round your answer to the nearest 10 yen.

   [4 marks]

   (c)

   The passenger's luggage of mass 23.5 kg is measured correct to 1 decimal place. Write down the lower and upper bounds of the actual mass, and hence calculate the maximum possible total mass of 3 identical pieces of luggage measured this way.

   [5 marks]

   Total for question 8: 13 marks

End of questions