ESSENTIAL MATHEMATICS 2 WEEK 8/9 NOTES AND EXERCISES

Transcription

1 ESSENTIAL MATHEMATICS 2 WEEK 8/9 NOTES AND EXERCISES Street maps use letters and numbers to locate positions. Letters are across the top and numbers are down the side. Example (i) What park is located at F4 (ii) What are the position coordinates of Willowburn Oval? Solution (i) Find the position where the vertical line through F and the horizontal line through 4 meet. The park is Hillview Avenue Park. (ii) Willowburn Oval is between J and K on the horizontal scale and between 5 and 6 on the vertical scale. The position coordinates of Willowburn Oval could be J5, J6, K5 or K6. A lot of local information is provided in street directories. Roundabouts, traffic lights, railways stations, train lines, one-way streets, street numbers, police stations and post offices are just a few of the features included on the maps. To assist map users, the meaning of abbreviations and symbols used in the street directory can be found in the legend. The legend and a map of Townsville are shown on the next two pages.

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4 Exercise Set 1 Q1. Use the legend to find the meaning of these symbols. a ) b) c) d) e) f) Q2. What features are at the following locations on the Townsville map? a) K6 b) E12 c) E7 d) C17 e) N12 f) G6 g) H9 h) J6 Q3. Give the grid references for these places. a) The roundabout where Fryer Street and The Strand meet. b) St Josephs School c) Townsville South Primary School d) Lowths Bridge Q4. What is the name of the TAFE and what are its position coordinates? Q5. How many sets of traffic lights are shown on Sturt Street? Q6. What is the significance of the red line going up the middle of Ross Creek? Q7. In what suburb is the vehicular ferry terminal at P9?

5 Q8. Why can t you drive along Wickham Street from The Strand to Flinders Street? Q9. On the map there are three bridges across Ross Creek. Describe how the bridges are different. The four major directions of a compass are north (N), south (S), east (E) and west (W). North is usually at the top. Four other major points on a compass lie exactly halfway between these directions. North-east (NE) is halfway between north and east. South-east (SE) is halfway between south and east. South-west (SW) is halfway between south and west. North-west (NW) is halfway between north and west. The arrow on a wind vane always points to the direction the wind is coming from. When a weather forecast predicts a southerly wind, it means a wind that comes from the south.

6 Example The diagram shows the arrow on a wind vane. What type of wind is blowing? Solution The arrow is pointing in the middle of north and east. The direction is north-east. The arrow points to the direction the wind is coming from. This wind is coming from the north-east. This wind is called a north-easterly wind. Exercise Set 2 Q1. Match the wind vane diagrams in a to e to the wind directions in A to E a) b) c) d) e) A south-westerly B westerly C south-easterly D southerly E north-westerly Q2. A westerly wind is bringing smoke from a bushfire to Emerald.

7 a) Near which town on this map could the bushfire be? b) If the wind keeps blowing in the same direction, which other town will have smoke blown into it? Q3. Winds from over the ocean carry moisture and are likely to bring rain. Winds from overland are likely to be dry. The temperature of the land over which a wind has blown will determine whether the wind will be warm or cold. In winter, winds from over the snowfields will be cold while summer winds from over the centre of Australia are likely to be dry and hot. Are the following winds likely to be hot or cold and bring rain or dry weather? a) A westerly wind in Mt Isa in February b) A westerly wind in Perth c) A north-easterly wind in Hervey Bay in June d) A southerly wind in Canberra in winter e) A north-westerly wind in Broome in May f) A southerly wind in Darwin in December g) A south-westerly wind in Adelaide in winter.

8 Exercise Set 3 Use the Townsville map to answer the questions in this set. Q1. Bill drives his car along Oxley Street from E8 to the intersection of Oxley Street and The Strand (E5). In which compass direction is he driving? Q2. Julie is driving north-west along The Strand at J8. Where might she be going? Q3. A fishing charter boat is travelling along Ross Creek from the small boat moorings at K12 towards the Western Breakwater at Q4. In what direction is the boat travelling? Q4. In what direction, as the crow flies, is it from St James Cathedral (E9) to the following locations? a) St Patricks College (E6) b) Arcades Theatre (E14) c) Breakwater Marina (J6) d) George Roberts Bridge (H12) e) Strand Central (C7) f) Perfumed Garden (E11) f) Barrier Reef Institute of TAFE (B13) g) Magnetic Island Ferry Terminal (N9) Q5. Sanjay is riding his bike along The Strand from the Channel 10 Heritage Building to the Cliff Gardens Waterfall. In what direction is he riding? Q6. Katrina works at Customs House (K9). She is going to meet a friend for lunch. Katrina walks south-east along The Strand and turns left into the first street on the left. She walks to the Y-intersection and follows the left section of the Y. She is meeting her friend at a hotel on the left. What is the name of the hotel? Q7. Paula and Tony live in Upper Clifton Street (C8) on the corner of Leichhardt Street. They leave home to go fishing. They walk north-east along Leichhardt Street, turn left into Eyre Street, then turn right at the second set of traffic lights. Then they walk in a north-easterly direction until they get to the beach. From their position on the beach, in what direction do they need to walk to reach the nearest public phone? Q8. Scott catches a taxi outside his work at the State Government Office (C12) to go to his sporting practice. He tells the taxi driver to go north-east on Walker Road up to the traffic lights and then turn left. He then tells the driver to turn right into the second street on the right and then right again at the roundabout. The place where Scott trains is about 200 m after the rounbabout on the left. For which sport is Scott training?

9 Q9. Write instructions for Francesca to walk from the train station at C17 to the Art Gallery at F11. Maps in a street directory can have different scales. The Townsville map has a scale where 10 cm represents 1 km, or 1 cm represents 100 m. This scale can be shown as: Example How long is the Flinders Mall? (F12 on the Townsville map.) The Mall (measured with a ruler) is approximately 4.5 cm long, thus it is 0.45 km or 450 m long. Exercise Set 4 Q1. How far is it, as the crow flies, from Cliff Gardens Waterfall (H8) to: a) the roundabout at The Strand and Oxley Street? b) the Quarter Deck Tavern (N6)? c) the railway station (C16)? d) the Soundshell in Dean Park (J17)? Q2. Kim walks from the YMCA (E10) along Denham Street and Dean Street to the Soundshell in Dean Park (J17). How far does she walk? Q3. Darryl rides his bike from the telephone box in Allen Street (P16) along Allen Street. He turns right into Tully Street, left into Archer Street and then left into Palmer Street to go to the Maritime Museum (L12). How far does he ride?

10 Q4. The football team trains in Dean Park (H17). At the beginning of each training session they run from the roundabout at Morehead and Morey streets, north-west to Dean Street and then north along Dean Street to Victoria Bridge. They run across the bridge and down Stokes Street to Walker Street. They then turn left into Walker Street, left again into Stanley Street and run across Lowths Bridge to the traffic lights. Finally, they run across Dean Park back to the starting position. How far is their training run? Q5. Aleisha walks 450 m from her work to the Perfumed Garden (E11) during her lunch break. Where might Aleisha work? When you need to solve problems involving distance (D), speed (S) and time (T), you ll find this road sign will help you remember how to do the calculations. Always put the letters D, S, T in the road sign in alphabetical order. To calculate speed, cover S with a finger. This leaves D T. This means S D T. In the same way, these formulas can be found. Example Alex is hiking at 5 km/h. How far will he hike in 3 hours? Check the units first. The speed is in km/h and the time is in hours. The units are correct. The question gives the information S = 5 and T = 3. It asks for the value of D. To work out the formula, cover D on the road sign. S and T are together, so the formula is: D = S T D = 5 3 D = 15 km Alex will hike 15 km.

11 Example Erin is paddling her canoe at an average speed of 8 km/h. How long will it take her to paddle 20 km? First check the units. The speed is in km/h and the distance is in kilometres. The time will be in hours. In the question, S = 8, D = 20 and the value of T is required. Cover the T in the road sign and you can see. The formula is T = D S T = 20 8 T = 2 5 hours or 2 hours 30 minutes Exercise Set 5 Q1. a) Use the formula D = S T to find the value of D when S = 50 and T = 2. b) In the formula S = D, what is the value of S when D = 48 and T = 3? T c) Convert 3.6 hours into hours and minutes. Q2. Chantelle walks at a pace of 5 km/h. How far can she walk in: a) 1 hour? b) 6 hours? c) 1 2 hour? Q3. Calculate the speed of these trips in km/h. a) Santo walks 12 km in 3 hours. b) Rina rides her bike for 4 hours and she travels 64 km. c) Chris drives his truck 200 km in 5 hours. Q4. Nicole runs at a speed of 8 km/h. How long will it take her to run these distances? a) 8 km b) 32 km c) 4 km d) 28 km e) 34 km f) 14 km Q5. Kristina flies her light plane 650 km from Brisbane to Rockhampton at an average speed of 200 km/h. How long does the flight take?

12 Q6. Adam drove his car for 4 hours and 15 minutes at an average speed of 50 km/h. How far did he drive? Q7. It takes Cameron 3 hours and 20 minutes to ride 200 km. Calculate his average speed. Q8. When Justin was on holidays on Fraser Island, he rode his bike from Happy Valley to Moon Point, which is a distance of 27 km, at an average speed of 12 km/h. How long did the ride take him? Give your answer in hours and minutes. Q9. At 11:45 am Thurza put her canoe in the river at Fitzroy Bridge. She paddled her canoe at 2 km/h up Moores Creek to Juds Park, which is a distance of 5 6 km. At what time did she arrive at Juds Park?