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WOODMILL HIGH MATHEMATICS INTERMEDIATE 2 END OF COURSE REVISION (Units 1 & 2) Intermediate 2 Maths Exam Revision (Week 1) 1. The population of Dunfermline is increasing at 2∙5% per year. Currently it is 55420. What will it be in 3 years time? 2. Find the volume of this shape. 7∙9 cm Give your answer to 2 significant figures. 3. 9∙6 cm y Find the equation of this straight line. (4,5) 3 x 4. A line has equation 3x + 4y = 12. Find the gradient of this line. 5. Expand and simplify (a) 6. 7. (p – 3)(p + 4) + 2p2 + 6p Factorise (a) (c) 2πrh + 2πr2 y2 – 9y + 14 (b) (x – 7)(x2 + 3x – 6) (b) 36 – 25a2 Find the area of this triangle. Give your answer to 3 significant figures. 170 m 42° 152 m 8. Find the length x, giving your answer to 2 significant figures. 9. Solve the system of equations. 3x + 2y = 13 and 4x – 3y = 6. 10. Draw a box plot for the following data 0, 2, 5, 8, 3, 9, 14, 16, 21, 6, 12, 1, 18 11. Calculate the mean and standard deviation of the following set of numbers 104 110 113 120 128 133 x Intermediate 2 Maths Exam Revision (Week 2) 1. The population of Mathsville decreased by 3% in 2010 but with a new factory and housing development is expected to increase by 1∙5% in each of 2011 and 2012. If it was 22000 at the start of 2010, what might it expect to be at the end of 2012? 2. Find the volume of this shape. It is a half sphere sitting on a cylinder. Give your answer to 3 significant figures. 3. 9∙6 cm y Find the equation of this line. 4 8 4. A line has equation 5x 2y 8 = 0. Find the coordinates of the point where it cuts the y axis. 5. Solve the following simultaneous equations (a) 4x + 6y = 16 x + 2y = 5 (b) 3y – 8x = 24 3y + 2x = 9 (c) 3x + 4y = 19 4x – 3y = 8 6. Two customers enter a shop to buy milk and cornflakes. Mrs Smith buys 5 pints of milk and 2 boxes of cornflakes for £688. Mr Brown buys 4 pints of milk and 3 boxes of cornflakes and receives £206 change from a £10 note. Form a pair of equations to work out the cost of a pint of milk and a box of cornflakes. 7. Multiply out and simplify ( x 3)( x 4) ( x 4) 2 x Intermediate 2 Maths 1. Exam Revision (Week 3) y y= 1 3 x+2 Part of the graph of 1 y x2 3 is shown. Find the coordinates of the point B B 2. x Expand and simplify (a) 3. (x + 7)(x2 + 3x + 5) (b) (2x + 3)2 The shape of material used for a lampshade is a sector of a circle. 280° The circle has radius 25 cm and the angle of the sector is 280°. Find the area of material in the lampshade. 4. 5. In question 3, the lampshade is to have a decorative trim round its rim. How much of the trim will be needed if a 1 cm overlap is necessary? B Find the length of BC in the triangle. 53° A 6. Factorise (a) 7. 130 m x2 3x + 2 (b) 4p2 49q2 (c) 6x2y + 15xy2 Find the mean and standard deviation of: 235, 252, 214, 222, 248, 236 68° C Intermediate 2 Maths 1. 2. Exam Revision (Week 4) A local shopkeeper kept a record of the number of people who bought different numbers of newspapers one Sunday. Number of newspapers Frequency 0 1 2 3 4 25 43 52 24 16 (a) Make a cumulative frequency table from the above data. (b) Find the median, lower quartile and upper quartile for this distribution. The boxplot shows the number of hours of TV watched in a week by a group of students. 5 11 21 28 35 Calculate the semi-interquartile range. 3. (a) The average price of a house in thousands of pounds in different areas of the UK in 2008 is shown below. 111 113 104 117 159 107 Use appropriate formulae to calculate the mean and standard deviation. Show all your working clearly. (b) In 1988 the mean was £98000 and the standard deviation was £10200. Comment on the change in house prices. 4. Multiply out and simplify 5. Factorise 6. (x 3)(x2 + 3x – 6) (a) 9x2 – 16y2 (b) x2 – 8x + 15 (c) p2 – 3p – 10 (d) 12a2 - 7a – 10 Solve the pair of equations: 2x + 5y = 8 and 3x 4y = 12 Intermediate 2 Maths 1. Exam Revision (Week 5) A strawberry jelly is in the shape of a hemisphere. The diameter is 18 centimetres. As the jelly sits in a warm room it begins to melt and loses 5% of its solid volume every hour. What would be the solid volume of the jelly left after 3 hours? 2. 18 cm Find the equation of this relationship connecting P and t P (4,8) 5 t 3. By accident, 5 tonnes of a chemical are released into a sea loch. If the tides remove 40% of the chemical in the loch each week, how many tonnes of chemical will be expected to remain after 3 weeks? Give your answer to one decimal place. 4. The diagram shows a glass bowl with two chopsticks resting on the rim at A and B. The lengths of the parts of the chopsticks inside the bowl are 10 cm and 12 cm respectively and the angle between them is 120. B A Find the length of AB to 2 significant figures. (a) 2 36p 1 (b) 2 a 7a 30 120 5. Factorise 6. What is the probability that a student chosen at random from this list of marks scored less than 8? 9 5 6 8 6 9 7 8 6 5 Intermediate 2 Maths 1. 2. Exam Revision (Week 6) (a) Calculate the area of this triangle (b) Calculate the length of AB B 62 cm A Calculate the length BP in the diagram. 58 cm B 36 C 67 P 25 km 32 A 3. Solve algebraically the system of equations x + 3y = 10 4. 3x y = 10 Nairn Savings Bank offers 6% compound interest per annum. How much interest would be received after two years on a deposit of £380 in this bank? 5. A new car cost £12,300. The value of the car depreciated by 16% after the first year and by 9% after the second year. Calculate the value of the car after the second year. 6. Multiply out and simplify: (a) (p 8)(p + 3) (c) (x + 5)2 (x 5)2 (b) (2m 7)2 Intermediate 2 Maths 1. Exam Revision (Week 7) A family wants to fence off a triangular part of their garden for their pet rabbits. They have a long straight wall available and two straight pieces of fencing 6 metres and 7 metres in length. They erect the fencing as shown. 120 6m 7m Find the area of garden enclosed by the wall and the two pieces of fencing. 2. Solve the simultaneous equations 2x + 3y = 5 x – 4y = 8 3. 800 The graph on the page shows the annual cost, £C, of running a car, plotted against the annual mileage, M miles. 600 Annual Cost, £C 400 Write down a formula connecting C and M. 4. (a) The following data (arranged in order) shows the number of people visiting a public swimming pool on Monday mornings throughout the first half of 2011. 12 18 22 26 30 72 13 19 23 27 30 15 20 25 27 31 16 21 26 28 32 200 18 21 26 29 63 0 4000 6000 8000 2000 Annual Mileage, M miles Draw a box plot to illustrate this data. (b) The box plot below represents the attendance at the swimming pool on Saturday mornings throughout the first half of 2011. 60 62 71 77 80 Compare the box plots in parts (a) and (b) and suggest two reasons for any differences. Intermediate 2 Maths 1. Exam Revision (Week 8) A ship is first spotted at position R, which is on a bearing of 315 from a lighthouse L. The distance between R and L is 10 kilometres. After the ship has travelled due West to position T, its bearing from the lighthouse is 300. T N R 10 km W How far has the ship travelled from R to T? 2. 3. 4. Factorise (a) p2 + 6p (b) 4x2 25y2 (c) x2 5x + 6 (d) 10x2 11x 6 Multiply out the brackets and collect like terms (a) (2x + 1)(x2 5x 4) (b) (2x 5)2 L ( L ig S h t h o u s e ) Seats on flights from London to Edinburgh are sold at two prices, £30 and £50. Let x be the number of £30 seats and y be the number of £50 seats on the flight. On one flight a total of 130 seats were sold (a) Write down an equation in x and y which satisfy this condition. The total cost of the seats on this flight is £6000. 5. E (b) Write down a second equation in x and y which satisfies this condition. (c) Solve the equations to find how many seats were sold at each price. Solve algebraically the system of equations 2a + 4b = 7 3a 5b = 17 ANSWERS (Week 1) 59681 5. 6. (a) 3p2 + 7p 12 (a) 2πr(h + r) (b) (c) (y 7)(y 2) 8650 m2 7. 2. 1 x+3 2 (b) x3 4x2 27x + 42 36 25d2 (d) (6 + 5a)(6 5a) 8. 120 m 9. 800 cm3 1. 3. y= 4. m= 3 4 x = 3, y = 2 10. 0 11. 8 2∙5 mean = 118 15 21 standard deviation = 11∙1 (Week 2) 2. 1120 cm3 1. 21985 5. 6. (a) x = 1, y = 2 (b) milk = 68p, cornflakes £1∙74 1 x+4 4. 2 y = 4, x = 1∙5 (c) 7. 7x 28 3. y= (0, 4) x = 1, y = 4 (Week 3) 1. 3. 6. 7. (6, 0) 2. (a) x3 + 10x2 + 26x + 35 (b) 2 1527 cm 4. 123 cm 5. 121 m (a) (x 1)(x 2) (b) (2p + 7q)(2p 7q) (c) mean = 234∙5 standard deviation = 14∙6 4x2 + 12x + 9 3xy(2x + 5y) (Week 4) 1. 2. 4. 5. Number of newspapers Frequency Cumulative Frequency 0 25 25 1 2 43 52 68 120 3 4 24 16 144 160 median = 2, Q1 = 1, Q3 = 2∙5 8∙5 hours 3. mean = £118500, standard deviation £20350 3 x 15x + 18 (a) (3x + 4y)(3x 5y) (b) (x 5)(x 3) (c) (p 5)(p + 2) (d) (3a + 2)(4a 5) 6. x = 4, y = 0 (Week 5) 1. 1039 cm3 2. 4. 19 cm 3 5 5. 6. 3 t+5 3. 4 (a) (6p + 1)(6p 1) 1∙1 tonnes 14∙4 km 3. £9402(∙12) (b) 4m2 28m + 49 x = 4, y = 2 y = 1, x = 4 C = 0∙1 M + 100 P= (b) (a 10)(a + 3) (Week 6) 1. 4. 6. 1057 cm2 2. £46∙97 5. 2 (a) p 5p 24 (c) 20x (Week 7) 1. 4. 18∙2 m2 (a) 12 (b) 2. 19 25∙5 19 3. 72 Much higher attendances on Saturdays, much less spread out number of attendances on Saturdays. Much higher attendances on 2 Mondays than other Mondays. Reasons More people can go on a Saturday, eg. work, school 2 busy Mondays could be bank holidays (Week 8) 1. 2. 3. 4. 5. 5∙18 km (a) p(p + 6) (c) (x – 3)(x – 2) (a) 2x3 9x2 13x 4 25 seats at £30 and 105 seats a = 1∙5, b = 2∙5 (b) (2x + 5y)(2x – 5y) (d) (5x + 2)(5x – 3) (b) 4x2 20x + 25 at £50