1. 1
   A gym surveys its 90 members about which of two classes, yoga and spin, they attend. In a Venn diagram, set Y represents yoga and set S represents spin, within a universal set of 90 members. Region Y only contains 34 members, region S only contains 21 members, and the region where the two sets overlap contains 15 members.

   (a)

   How many members attend neither class?

   [1 mark]

   • A20
   • B70
   • C35
   • D15

   (b)

   What is the probability, as a fraction in its simplest form, that a randomly selected member attends spin only (not yoga)?

   [1 mark]

   • A$\frac{1}{6}$
   • B$\frac{17}{45}$
   • C$\frac{7}{30}$
   • D$\frac{49}{90}$

   (c)

   What is $n(Y \cup S)$, the number of members who attend yoga or spin (or both)?

   [1 mark]

   • A90
   • B49
   • C56
   • D70

   Total for question 1: 3 marks

2. 2
   A school allocates a grant of $960 between three clubs, chess, debate and robotics, in the ratio 5:3:4.

   (a)

   Calculate the amount of money received by the robotics club.

   [2 marks]

   (b)

   The debate club is then given an extra $45 on top of its original share. Express the debate club's new total as a percentage of the original $960 grant, giving your answer to 1 decimal place.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Deepa invests $2500 in a savings account paying compound interest at 3.5% per year. Separately, she buys office equipment for $4000 that depreciates in value by 12% per year.

   (a)

   Calculate the value of Deepa's savings account after 4 years, giving your answer to the nearest cent.

   [3 marks]

   (b)

   Calculate the value of the office equipment after 3 years, and hence find the total depreciation, in dollars, over the 3 years.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A laboratory technician records the mass of a chemical sample as 8.4 grams, correct to 2 significant figures, and its volume as 3.5 cm$^3$, correct to 2 significant figures. The number of molecules in a similar sample of the same substance is separately estimated as $2.6\times10^{22}$, correct to 2 significant figures.

   (a)

   Find the upper bound and the lower bound of the sample's density, in g/cm$^3$, given that density = mass ÷ volume. Give each bound to 3 significant figures.

   [4 marks]

   (b)

   Using the mass 8.4 g and the estimated $2.6\times10^{22}$ molecules, calculate the average mass of one molecule, giving your answer in standard form to 2 significant figures.

   [4 marks]

   (c)

   By rounding each value to 1 significant figure, estimate the value of $\frac{8.4\times2.6\times10^{22}}{3.5}$, showing your rounded values. State, with a reason, whether your estimate is an overestimate or an underestimate of the exact value.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   The time, $T$ hours, taken to build a wall varies inversely with the number of bricklayers, $n$, working at the same rate. When 4 bricklayers work, the wall takes 15 hours to build, so $Tn=60$.

   (a)

   How long would the wall take if 6 bricklayers work at the same rate?

   [1 mark]

   • A22.5 hours
   • B10 hours
   • C9 hours
   • D60 hours

   (b)

   How many bricklayers, working at the same rate, are needed to complete the wall in 5 hours?

   [1 mark]

   • A12
   • B3
   • C75
   • D16

   (c)

   If the number of bricklayers working is doubled, what happens to the time taken to build the wall, at the same rate?

   [1 mark]

   • AIt doubles
   • BIt stays the same
   • CIt increases by 50%
   • DIt halves

   Total for question 5: 3 marks

6. 6
   A warehouse packs two types of box onto pallets. Type P boxes are packed in groups of 84, and Type Q boxes are packed in groups of 90.

   (a)

   Express 84 and 90 as products of their prime factors.

   [2 marks]

   (b)

   Hence find the highest common factor (HCF) of 84 and 90.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A chemistry teacher is preparing a revision handout that simplifies surd expressions arising from a titration calculation.

   (a)

   Simplify fully $\sqrt{50}+2\sqrt{18}-\sqrt{8}$, giving your answer in the form $a\sqrt{2}$.

   [3 marks]

   (b)

   Rationalise the denominator of $\frac{12}{\sqrt{18}}$ and simplify fully.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   A bookshop runs a spring sale. Hardback books are reduced by 15%. Paperback books are sold in a bundle deal, and the shop also reviews its overall sale revenue by category.

   (a)

   A hardback book has its original price reduced by 15% in the sale, giving a sale price of $29.75. Find the original price of the book.

   [4 marks]

   (b)

   A paperback bundle of 3 books costs $\frac{2}{5}$ less than buying the 3 books separately at $8 each. Calculate the bundle price.

   [4 marks]

   (c)

   The bookshop's total spring-sale revenue was $18\,000$. Hardback sales made up $\frac{7}{20}$ of this revenue. This year's hardback revenue was 8% more than last year's spring-sale hardback revenue. Calculate last year's hardback revenue, giving your answer to the nearest dollar.

   [5 marks]

   Total for question 8: 13 marks

End of questions