National 5 Lifeskills Maths Practice Assessment 2 Geometry and Measures FORMULAE LIST

Transcription

1 National 5 Lifeskills Maths Practice Assessment 2 Geometry and Measures FORMULAE LIST Practice Assessment 2 October

2 1 Lisa is moving to Brisbane, Australia. She has the following information: Distance to Brisbane from London Aircraft speed Time difference Stopover in Hong Kong km 900 km/h +9 hours 3 hours 45 minutes Calculate how long the journey from London to Brisbane will take including a stopover in Hong Kong. Give your answer in hours and minutes (give your answer in hours and minutes, to the nearest minute). 4 If Lisa takes the Monday flight leaving London at 1345, what time will she arrive in Brisbane? 1 (c) Lisa s sister, who lives in London, plans to phone and chat to Lisa on Tuesday at 1900 UK time. Will this be a suitable time to phone? Justify your answer. 2 (d) Lisa will be at work from 0830 to 1700 Monday to Friday. She likes to be in bed by Give her sister advice on the best time to contact her on weekdays from her home in the UK. 1 Practice Assessment 2 October

3 2 A helicopter flies from Aberdeen to two oil rigs following the route below. Route From Aberdeen the helicopter flies: 350 km on a bearing of 045 to the Everest Platform Then 170 km on a bearing of 130 to the Elgin Platform Using a suitable scale, make a scale drawing of the helicopter s flight. 4 The helicopter returns directly to Aberdeen from the Elgin Platform. Calculate the distance of the return journey. 3 (c) If the helicopter flies at a steady speed of 130 km/h ±10% calculate the minimum and maximum time taken to complete the whole journey. 6 Practice Assessment 2 October

4 3 Peter makes wax candles. Each candle is in the shape of a cone, with diameter 10 cm and slant height 12 cm, as shown. V 1 2 r h 3 1 Peter buys wax in 7 litre tubs. How many candles can he make from one tub of wax? 5 Peter also wants to make candles in the shape of a cylinder. If each has height of 5 cm and the same volume as the cone-shaped candle, calculate the radius of the mould 7 for the new candle. 2 Practice Assessment 2 October

5 4 Jack is moving house. He has hired a removal van as shown below: A 3. Jack has a lot of boxes to go into the van. The size of each box is given below (not to scale): 5 0 c m T h 3 5 c m 4 5 c m What is the maximum number of boxes Jack can pack into the van? Justify your answer. 4 Practice Assessment 2 October

6 5 You are going to the cinema to watch a 3D movie. The following is a list of things you need to do: A B C D E F G H Meet with some friends Collect tickets Travel to cinema Watch movie Book tickets Get ready Buy popcorn Pick up 3D glasses Some of these activities might be done at the same time. Complete the precedence table below by putting the activities into a logical order and identify one occasion when two activities could be done at the same time. Put the second activity in the right-hand column. Order of activities Activities that could be done at the same time 2 Practice Assessment 2 October

7 6 Most avalanches occur on slopes with gradients which lie in the range 0 7 to 1 0. A ski company in Europe is looking at a hill to see if it safe to develop it as a ski run. a) The top part of the run starts at a height of 2170 m, is 210 m in length and drops to a height of 2060 m, as shown in the diagram m 210 m 2060 m Is the slope considered safe from avalanches? 5 The lower part of the run is considered safe as it has a gradient of 2 1. It starts from a height of 2060 m and drops to a height of 1830 m. What is the length of the slope? 3 Practice Assessment 2 October

8 7 Orla wants to paint her lounge walls. The room has the following dimensions (diagram not to scale): Orla wants to give the walls two coats of paint. How many 1 litre tins of paint must she buy to paint her lounge? 5 Paint is sold in either 1 litre or 2 5 litre tins. 1 litre tins cost 7 80 each 2 5 litre tins cost each What is the minimum cost of painting the lounge? 3 (c) Orla wants to lay decking in the shape of a quarter circle, as shown in the diagram. The cheapest quote is 50 per m². Orla has a budget of 1400 for the decking. Can she afford the decking? Justify your answer. 4 Practice Assessment 2 October

9 Question Number Points of strategy and process and of communication in assessment for candidates (Appendix 1) 1 Each illustrates one mark S: know to use formula P: calculate time Communication: convert to hours and minutes P: add stop-over time P: calculate UK and Australian time time = distance/speed = = hours 18 hours 22 mins + 3 hours 45 mins = 22 hours 3 mins 1345 add 22 hours 3 mins 1148 UK +9 hours = 2048 Brisbane (c) Communication: convert time 1900 Tues UK = 0400 Wed Brisbane This isn t a suitable time as she will probably be in bed d) 2 Communication: conclusion with justification Communication: conclusion with justification S: scale stated Process: construct angles Process: construct sides Communication: scale drawing complete and annotated Brisbane She should call anytime between UK weekdays. Accept any time between these limits. 1 cm : 50 km (or any suitable scale) Angles of 045º and 130º(±2º) 70mm and 34 mm (±2mm) Bearings and distances 350 km N Ev E Ab 0 (c) P: evidence of measuring final leg Communication: conversion to km Communication: bearing of return journey S: calculate max/min speed 8 2 cm (accept an error tolerance of ± 0 2 cm) = 410 km Bearing answer ±2º speeds 930 / 143 Practice Assessment 2 October

10 P: start to calculate max time P: Complete C: time in hours and mins P: complete for min time C: time in hours and mins 930/143 = 6 50 hours = 5 hours and 5 of 1 hour = 5 hours mins = 5 hours 30 mins minimum 930/117 = 7 95 hours = 7 hours + 95 of 1 hour = 7 hours mins = 7 hours and 57 mins maximum 3 S: know formulae P: calculate height of cone P: calculate volume h² = 12² 5² = = 119 cm h = 119 = cm V = 1/3πr 2 h = ² = cm³ S: convert litres to cm³ and know to divide Communication: calculate number of candles and round correctly 7 litres = cm³ so 24 candles S: equate to find radius P: calculate the radius V = πr 2 h = 3 14 r² = r² r² = r = 3 6 cm 4 S: knows boxes can be packed different ways P: calculates number of boxes to be packed using 35 cm facing Shows two ways of packing boxes Number of 35 cm boxes = = 360 boxes P: calculates number of boxes to be packed using 45 cm facing Number of 45 cm boxes = = 336 boxes Communication: maximum number with justification 360 boxes if packed 35 cm facing side A of van, 24 more than if 45 cm packed facing side A of van. 5 S: knows to order Uses letters or phrases Practice Assessment 2 October

11 6 Communication: orders appropriately for example Order of Activities E F C A B H G D Process: Calculate height Activities that could be done at the same time Strategy: Know and start to use Pythagoras Process: Calculate side Strategy: Calculate gradient Communication: Correct conclusion Accept any logical order and at least one activity that could be done at the same time as another. G and D should be last two, but a case could be made for many other approaches. N.B. Justification not required. 110 m = x m 110/ 179 = 0 61 Slope is safe from avalanches since 0 61 lies is outwith range 0 7 to 1 0 or 0 7. Strategy: Use gradient to find missing side Process: Know and start to use Pythagoras Process: Calculate length ½ = 230/ = r m 7 S: know and start to find area P: calculate area of walls P: calculate area of door and window S: start calculate number of tins to be bought Area = l b (11 2 5) + (6 2 5) + (6 2 5) + (6 2 5) + (5 2 5) + (12 2 5) = 115 m² = (4 2) + (1 1 5) = 9 5 m² = = m² 1 litre covers 15 m² Number of Tins = 211/15 = She must buy 15 tins Practice Assessment 2 October

12 (c) Communication: state number of tins Process: cost of one option Process: cost of remaining options Communication: state correct combination S: know and start to find area of circle P: calculate area of decking P: calculate cost of decking C: answer with justification using result One of: 2 5 litre = = 37 5 m² 4 tins cost = OR litre tins = = litre tin = = 7 80 = Remainder from above Minimum cost = A r = ² = m² Cost = = 1413 Orla can t afford to lay the decking as it costs more that her budget. Practice Assessment 2 October