# Year 10 Mathematics, 2007

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1 Student s Name: Teacher s Name: 10 Year 10 athematics, 2007 lgebra Use straightforward algebraic methods and sketch and interpret features of linear graphs Time: 20 minutes. Check that you have entered your name and your teacher s name in the top left hand corner of this paper. You should answer LL the questions in this paper. You should show LL working. Check that this paper has pages 2 4 in the correct order and none of these pages is blank. YOU UST HND THIS PPER TO THE SUPERVISOR T THE END OF THE EXINTION. For ssessor s Plot and interpret simple graphs. Solve linear equations. Describe simple patterns. with erit Interpret linear graphs. Find terms in patterns. Carry out more complex algebraic manipulations. Solve equations. with Excellence Solve algebra problems using graphs and manipulation. Overall Level of Performance (all criteria within a column met)

2 lgebra 2 ake sure you show LL relevant working for each question. obile Phones ssessor s QUESTION Simplify the following. 2x 3 + 5x + 4 4pq 2 x 2p 2 q 3 4x 2 y 12x (d) If h a 2 + b 2 and a 6 and b 8, find the value of h. QUESTION Natasha sells mobile phones. The table below represents how much Natasha can earn per week depending on the number of phones she sells. N represents the number of phones sold per week and the amount in dollars she could earn. No. of phones (N) Earnings () If Natasha sold 10 phones in a week, how much would she earn? What rule could Natasha use to work out her pay () in terms of the number of phones she sells per week (N)? On the grid provided on the right draw the rule Simon, who also sells phones, but for another company, uses to work out the amount he gets paid each week. Simon s rule is 20N (\$) No. of phones (N)

3 lgebra 3 QUESTION THREE Solve the equation 4x ssessor s Four times a number subtracted from 20 is 12. Form an equation to represent this, but do NOT solve it. The graph on the right represents the price of a particular model of mobile phone over a 12 month period. Give the gradient of the line drawn. Price (\$) QUESTION FOUR Expand 2x(x 5) No. of months (n) Factorise x 2 7x 18 Solve the equation 4 x (d) 4(x + 3) 3x (e) Simplify (2n 3 ) 3

4 lgebra 4 QUESTION FOUR cont.. ssessor s (e) The graph below represents the sales of a particular model of mobile phone for a period of 20 days after its official release. Write the equation of the graph drawn. Sales (S) QUESTION FIVE No. of days (n) Natasha has been working in the telecommunications industry 10 more years than Simon. Eight years ago Natasha would have been working in the telecommunications industry for twice as long as Simon. Form a linear equation and solve it to work out how long Natasha and Simon have been working in the telecommunications industry. Begin by letting x Simon s age and x + 10 Natasha s age. Show LL working. n answer alone is not sufficient.

5 SSESSENT SCHEDULE lgebra athematics: Use straightforward algebraic methods to solve problems and sketch and interpret features of linear graphs. CHIEVEENT Plot and interpret simple graphs. Solve linear equations. Describe simple patterns. Carry out simple algebraic manipulations. (d) 7x + 1 8p 3 q 5 xy 3 10 \$465 30N CO okay. CO okay. CO okay. CO okay. CO okay. CO okay. : Two or three of code 1 plus two or three of code 2 plus two or three of code 3. THREE Linear graph through (0, 100) and (20, 500). x CO okay. THREE THREE 20 4x 12 Gradient CO okay. Graph correctly drawn. CO okay. athematics lgebra ssessment Schedule Y Page 1

6 CHIEVEENT WITH ERIT Find terms in patterns. Interpret linear graphs. Carry out more complex algebraic manipulations. Solve equations. FOUR FOUR FOUR FOUR (d) FOUR (e) FOUR (f) 2x 2 10x (x 9)(x + 2) x 20 x 12 8n 9 S 20n CO okay. CO okay. CO okay. CO okay. CO okay. CO okay. erit: plus Four, five or six of Code. CHIEVEENT WITH EXCELLENCE Solve algebra problems using graphs and manipulation. EIGHT Let x Simon so Natasha x + 10 Twice Simon s length of service eight years ago equals Natasha s service 8 years ago. 2(x 8) (x + 10) 8 2x 16 x + 2 x 18 So Simon 18 years service and Natasha 28 years service. 1 3 E ust use algebra to form and solve an equation. Excellence: erit plus Code E. athematics lgebra ssessment Schedule Y Page 2

7 Student s Name: Teacher s Name: 10 Year 10 athematics, 2007 easurement Solve problems involving measurement of everyday objects Time: 20 minutes. Check that you have entered your name and your teacher s name in the top left hand corner of this paper. You should answer LL the questions in this paper. You should show LL working. Check that this paper has pages 2 5 in the correct order and none of these pages is blank. YOU UST HND THIS PPER TO THE SUPERVISOR T THE END OF THE EXINTION. For ssessor s Solve simple measurement problems. Use measurements in calculations and conversions. with erit Solve measurement problems. with Excellence Plan, carry out and evaluate a measuring task. Overall Level of Performance (all criteria within a column met)

8 easurement 2 ake sure you show LL relevant working for each question. The Sports Coach ssessor s QUESTION school has to purchase special tape for marking out their netball courts. You need to help Don the coach accurately calculate the length of the lines. The court is 30.5 metres long and half as wide as it is long. Calculate the length of all the straight lines m 0.9 m 4.9 m Length lines Width lines Total of straight lines 0.9 metre diameter centre circle is located in the centre of the court and there are two 4.9 metre radius semi-circles on each base line (called the goal circle). Calculate the circumference of both these semi-circles and the centre circle. (C 2πr) Centre circle Goal circles Total circles llowing 5% for wastage, what is the total length of special tape you recommend the coach purchase? Round your answer to the nearest 10 centimetres. QUESTION Tape required Don the school sports coach is a marathon runner. His fastest marathon is 2 hours minutes for the 42.2 kilometres. What is 2 hours minutes (2 h 38 min 15 sec) as a decimal fraction of an hour? Time (hours) What speed in kilometres per hour was Don running when he completed the 42.2 kilometres in 2 hours minutes? Speed (km/h)

9 easurement 3 QUESTION cont... Next week there is to be a marathon near the school. The visiting runners will run along city streets on a course in the shape of a parallelogram. The parallelogram has a base of 4.5 km and perpendicular height of 5.8 km but the runners run on a diagonal of 6.05 km. The course is 21.1 km long so the runners need to complete it twice ( 42.2 km). ssessor s 4.5 km Hamilton Road 5.8 km 6.05 km Oamaru Street Napier Road Wellington Road Nelson Street Christchurch Street 6.05 km 4.5 km Calculate the area of the town that the course will enclose. The area of a parallelogram is given by rea base x perpendicular height. QUESTION THREE rea s a result of time zone changes, a direct flight from Christchurch to Brisbane can take off at 6 am local time and arrive at 7 am local time in Brisbane, ustralia. The same aircraft returning to New Zealand can take off at 5 pm local time from Brisbane and arrive in Christchurch at 12 midnight, local time. Using these figures what is the time zone difference between Brisbane and Christchurch and what is the flying time? Time difference Flying time

10 easurement 4 QUESTION FOUR ssessor s Don has found a full can of paint used for marking lines, but it has lost its label indicating the quantity. The can is 45.5 cm tall and 22 cm in diameter. Volume cylinder πr 2 h 45.5 cm Find the volume of the can in cm cm Volume (cm 3 ) Calculate the maximum number of whole litres of paint the can could hold. QUESTION FIVE Don needs a large gymnastic ball which must have a volume of 1 m 3. What radius ball must he find? Capacity (litres) Use the formula. Volume 4 3 r r. 3 Ball s radius

11 easurement 5 QUESTION SIX ssessor s Don also has to mark out the athletics track. The straights are 100 metres long. The two semi-circular ends form a circle of radius R. R 100 m Calculate R so the total length of the track is 400 metres. The lanes on an athletics track are 1.2 metres wide. ll the straights remain 100 metres and only the radius of the curve changes. Radius R Don has to arrange for the first 2 of the lanes to be marked on the school track. The line marker draws a line 80 mm wide with a special paint. The paint covers 12.1 m 2 per litre. What is the length of line needed to mark out the first 2 lines of the track and how much paint is needed just for these 2 lines? Round your answer appropriately. Total lines length Paint needed

12 SSESSENT SCHEDULE easurement athematics: Solve measurement problems CHIEVEENT Use measurements in calculations and conversions to solve simple problems. Calculation and applications of perimeter and area of simple composite shapes in context. Time calculations and applications. rea and circumference of circles. Calculation of speed. Conversion of time measurements into decimals. THREE Straight lines 122 m Circles m Length m (must be 1dp) Time h Speed 16 km/h rea 26.1 km 2 Time difference 3 h Flying time 4 h CO okay for achievement. ust be to 10 cm so cm is correct. : Four or more of the seven code. CHIEVEENT WITH ERIT CHIEVEENT WITH EXCELLENCE Solve measurement problems. pplications of harder composite shapes. pplications of surface area of prisms, pyramids. pplications of volumes of cylinders, cones, and pyramids. Conversion between units of area and volume. pplications of speed. Plan, carry out and evaluate a measuring task. FOUR FOUR FIVE Volume cm 3 Capacity 17 litres (must be 0dp) Radius 0.62 m / / / ccept any appropriate rounding. ERIT: plus Two Code or ll three Code. SIX R m P P π x m Total m rea m 2 Paint 5.34 litres 6 litres (round up) for Total E Ignore 1 minor error that still leads to an acceptable answer. ccept correct number of litres or the quantity rounded up. nswer of 5 litres is wrong. Excellence: erit plus Code E. athematics easurement ssessment Schedule Y Page 1

13 Student s Name: Teacher s Name: 10 Year 10 athematics, 2007 Number Solve number problems Time: 20 minutes. Check that you have entered your name and your teacher s name in the top left hand corner of this paper. You should answer LL the questions in this paper. You should show LL working. Check that this paper has pages 2 3 in the correct order and none of these pages is blank. YOU UST HND THIS PPER TO THE SUPERVISOR T THE END OF THE EXINTION. For ssessor s Solve number problems. with erit Solve number problems in context. with Excellence Solve number problems in context involving several steps or reversing processes. Overall Level of Performance (all criteria within a column met)

14 Number 2 ake sure you show LL relevant working for each question. QUESTION New ipod ssessor s Round off to 4 significant figures (4 sig. figures) Write the number in standard form What is 48 out of 60 as a percentage? 48 out of 60 % (d) Calculate 75% of \$88. 75% of \$80 \$ (e) Share \$24 in the ratio of 3:1 3:1 of \$24 \$ to \$ (f) Decrease \$35 by 20%. 20% off \$35 \$ (g) Jody s job was to look after the bank s money in a board game. In one complete turn Peter paid the bank forty dollars, Clare was paid fifty dollars from the bank while aron paid the bank one hundred dollars. In this turn, how much money is the bank up (+) or down ( )? QUESTION Bank up or down (+ or ) \$ n ipod P3 music player needs 1 x 10 6 bytes of memory to store 1 minute of music. Joy s ipod player can hold 2000 songs, each 4 minutes long. How much memory does 2000 songs require? nswer in standard form. Total memory The 4GB ipod Nano sold in the US for \$249 in In 2007 the price of the latest 4GB ipod Nano is \$149. What percentage decrease is it from \$249 to \$149? Percent decrease % Joy uses her ipod to listen to music 5 2 of the time. She listens to audio books 8 3 of the time and the rest of the time she uses it to watch videos. What fraction of the time does Joy watch videos on her ipod? Fraction watching videos

15 Number 3 QUESTION cont... ssessor s (d) In million ipods were sold. In 2006 sales increased by 35%. What were the sales in 2006? Total sales in 2006 million (e) The number of transistors used on a single processor such as a P3 player has increased yearly. From 2000 the number of transistors on a single processor was predicted to b n Transistors (25 million) x 2 where n is the years since How many transistors were predicted for 2005 (n 5)? Transistors (25 million) x 2 n QUESTION THREE Joy would like to get a new ipod Nano 8GB. She could buy it locally for \$324 including GST. On the internet she can purchase it in US for US\$199 with freight to New Zealand of US\$15. When an item is imported into New Zealand, GST of 12.5% is added to the total cost. The exchange rate between US and New Zealand is US\$0.76 NZ\$1. Calculate the cost in New Zealand dollars of importing the ipod Nano 8GB. Explain what you are doing and any calculations you make. Which ipod should Joy purchase?

16 SSESSENT SCHEDULE Number athematics: Solve number problems. CHIEVEENT Solve number problems. Numbers into standard form. Rounding of numbers. Percentage problems. Sharing a quantity in a given ratio. Solving word problems involving integers and decimals. (d) (e) (f) (f) x Percentage 80% 75% of 88 \$66 \$18 : \$6 \$28 +\$90 (up \$90) Only answer ust be in std form. CO okay for all parts. Ignore units. Needs + or up. : Five or more of the seven code. CHIEVEENT WITH ERIT Solve number problems in context. Standard form. Increasing or decreasing by a given percentage. Calculation of percentage change. Ratio. Fractions. (d) (e) emory 8.0 x 10 9 (bytes) Decrease 40.2% (accept 40%) Videos 9 40 Sales \$24.3 million 800 million / / / / / ust be in std form. CO okay. ERIT: plus Three or four Code or ll five Code. CHIEVEENT WITH EXCELLENCE Solve number problems in context involving several steps or reversing processes. THREE THREE Cost + freight US\$214 Convert to NZ\$ 214 / 0.76 \$ dd GST of 12.5% Cost NZ \$ So should purchase from US as it is cheaper OR Needs minimum of two steps with at least a heading or explanation. Order of GST and conversion not important. ny supported conclusion is acceptable. Excellence: erit plus Code E. Purchase from NZ because it is not that much more expensive and it may be easier to get service etc. E athematics Number Y10 ssessment Schedule 2007 Page 1

17 Student s Name: Teacher s Name: 10 Year 10 athematics, 2007 Trigonometry Solve right-angled triangle problems Time: 20 minutes. Check that you have entered your name and your teacher s name in the top left hand corner of this paper. You should answer LL the questions in this paper. You should show LL working. Check that this paper has pages 2 4 in the correct order and none of these pages is blank. YOU UST HND THIS PPER TO THE SUPERVISOR T THE END OF THE EXINTION. For ssessor s Find simple unknown lengths of right-angled triangles using trig ratios and Pythagoras. with erit Find unknowns of rightangled triangles from words and diagrams using trig ratios and Pythagoras. with Excellence odel 2-D situations to find unknowns of a right-angled triangle using trig ratios or Pythagoras. Overall Level of Performance (all criteria within a column met)

18 Trigonometry 2 ake sure you show LL relevant working for each question. Rugby ssessor s QUESTION rugby field is a rectangular shape measuring 140 m by 70 m. x 70 m 140 m Calculate the length (marked x in the diagram above) from one corner of the dead ball line to the opposite corner at the other end. 35 m fullback has a penalty attempt 35 metres from the goal post. If the crossbar is 3 metres high, what angle of elevation (labelled in the diagram) will the fullback have to kick the ball, so it clears the crossbar. 3 m flyhalf punts the ball a total of 65 metres at an angle of elevation of 42. Calculate the horizontal distance parallel to the ground (labelled x in the diagram) the ball has travelled. 65 m x 42

19 Trigonometry 3 QUESTION Two players in the backline chase a high kick. If Player 1 runs 22.0 m and Player 2, 15.5 m to where the ball lands, calculate the distance (x) between the two players at the start. ssume the two players and where the ball lands form a right-angled triangle. See the diagram below. ssessor s Player 1 x Player m 15.5 m Calculate the distance (x) a player is standing from the base of one of the goal posts given the height of the goal posts are 4.2 m high and the angle of elevation from the player to the top of the goal post is 27. See the diagram below. Player 27 x 4.2 m rugby coach gets half his squad to run the route around the rugby field marked in the diagram below and the other half of the squad to run around the perimeter of the entire field (140 m by 70 m). Which run is longer and by how much? Show LL working. Halfway line 70 m 140 m

20 Trigonometry 4 QUESTION THREE On top of the goal posts are flags. player is standing 20.4 metres from the base of one goal post. The angle of elevation, from the player, to the top of the goal post is 11.9 and to the top of the flag is Find the height of the flag attached to the top of the goal posts. Show LL working and explain each step of your calculation. See the diagram below. ssessor s m

21 SSESSENT SCHEDULE Trigonometry athematics: Solve right-angled triangle problems CHIEVEENT Find simple unknown lengths of rightangled triangles using trig ratios and Pythagoras. Lgth Lgth m (1 dp) tan (1 dp). Kick over 4.9 cos 42 x 65 x 48.3 m (1 dp) Ignore units. Ignore units. ccept 4.9. Ignore units. : Two or three of code. CHIEVEENT WITH ERIT Find unknowns of right-angled triangles from words and diagrams using trig ratios and Pythagoras. Dist Dist 15.6 m (1 dp) tan x x 8.25 m (1 dp) Entire field 420 m lt. Route metres Entire field longer by 41 m. Ignore units. Ignore units. Ignore units. Conclusion drawn. erit: plus Two of Code or ll three Code. CHIEVEENT WITH EXCELLENCE odel 2-D situations to find unknowns of a rightangled triangle using trig ratios or Pythagoras. THREE Height of goal posts: tan 11.9 x 20.4 x 4.3 m (1 dp) Height to top of flag: tan 14.8 x 20.4 x 5.4 m (1 dp) Distance apart: m (1 dp) E ust have appropriate statements and clear layout. Working required. Excellence: erit plus Code E. athematics Trigonometry ssessment Schedule Y Page 1

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