Year 10 Maths Feast 2018 Round 2 - Problems, Problems,... (20 marks)

Size: px

Start display at page:

Download "Year 10 Maths Feast 2018 Round 2 - Problems, Problems,... (20 marks)"

Leona Austin
5 years ago
Views:

1 Year 10 Maths Feast 2018 Round 2 - Problems, Problems,... (20 marks) There are six problems below as a team you will score maximum marks for correct solutions to FOUR of them. You can attempt all six if you wish, but only hand in a maximum of FOUR. You can answer each question as a group or as individuals it s up to you! There is space on some of the sheets for rough working, but you may use further scrap paper if required. Please ensure that your final solution is clearly presented in the answer box below the question. Set out your answers clearly so that the working can easily be followed to score maximum marks. Each question will score up to maximum of 5 marks. The answer on its own will only score 1 mark.

2 Problem A: Jade heats her home using electricity. Typically Jade uses 4000 units of electricity per year. Jade is deciding whether to use Trustpower or Meridian as her provider. Their charges are shown in the table below: Standing Charge Cost per unit Trustpower per year 18p Meridian per year 14p (i) Which company should Jade use as her provider, explaining why? Problem A (i): Answer (explain your solution fully) Jade decides to improve the insulation of the roof space. The upgrade should reduce her consumption of electricity by 30%. (ii) If she upgrades the insulation of the roof space, which electricity provider should she use? Explain why. Problem A (ii): Answer (explain your solution fully)

3 Problem B: Crystal decides to raise funds for a summer camping trip, by selling orange drinks on a stall outside her house. Her Mum suggests that she costs out the project and reminds her that she will need a temporary street trading license. Crystal does some research and finds: The cost of the street sellers license is 75. A 1 litre bottle of squash costs The squash is diluted, 1 part squash to 4 parts water. 50 cups cost Each cup holds 200 ml. Crystal decides to sell each cup of drink for 40 p. How many cups of drink will she have to sell to cover the cost of the license?. Rough working space (will not be marked) Problem B: Answer (explain your solution fully)

4 Problem C: In a kiwi fruit packhouse, kiwi fruit are packed into boxes. You have three boxes in front of you. One contains only green kiwi fruit. One contains only gold kiwi fruit. The third crate contains both green and gold kiwi fruit. Each crate is labelled. One reads 'green', one reads 'gold', and one reads 'green and gold'. Unfortunately the labelling machine is faulty and is now labelling all the boxes incorrectly. If you can only take out and look at just one kiwi fruit from just one box, how can you label all three of your boxes correctly? Rough working space (will not be marked) Problem C: Answer (explain your solution fully)

5 Problem D: An emerald necklace has 11 emeralds, with the largest and most valuable in the middle. Starting from each end, each successive emerald is valued at 200 more than the one before (up to the middle one). The whole necklace is valued at 10,500. What is the value of the middle emerald? Rough working space (will not be marked) Problem D: Answer (explain your solution fully)

6 Problem E: The purity of gold is measured in carats. 24 carat gold is pure gold, 100% gold. 12 carat gold is 50% gold. 18 carat gold is 75% gold. (i) What percentage of gold is 10 carat gold? Give your answer to an accuracy of 1 decimal place. Problem E (i): Answer (explain your solution fully) (ii) A jeweller decides to make a ring by melting 20 grams of 12 carat gold with 30 grams of 18 carat gold. How many carats will the finished ring be, to the nearest whole number? Problem E (ii): Answer (explain your solution fully)

7 Problem F: Martha's Mine, Waihi is an open cast gold mine. This can be modelled as an inverted elliptical cone. a b Volume of the elliptical cone = π abh, 1 3 where h = height of the cone, a = semi-major axis, b= semi-minor axis. h The semi-major axis of the mine is 800 m, the semi-minor axis of the mine is 500 m and the depth is 250 m. (i) Using π = 3, calculate the volume of rock removed from the mine. Problem F (i): Answer (explain your solution fully) The average density of the rock removed is 2.8 tonnes per cubic metre and 1.5 grams of gold is processed from each tonne of rock. (ii) Estimate the mass of gold extracted from the mine. Give your answer in kilograms to 1 significant figure. Problem F(ii): Answer (explain your solution fully)

Using column addition, keep the decimal points aligned one beneath the other to keep the correct place value of the digits.

Q1-5. Using column addition, keep the decimal points aligned one beneath the other to keep the correct place value of the digits. Q1. 1. 6 3 8. 2 + 3. 2 5 4 3. 0 5 [1.6 + 38.2 + 3.25 = 43.05] Q2. 0. 1