The City School. Prep Section. PAF Chapter. 2 nd Term Mathematics. Class 9. Worksheets for Intervention Classes

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1 The City School PAF Chapter Prep Section 2 nd Term Mathematics Class 9 Worksheets for Intervention Classes

2 (1) Express 17 as percentage. 40 EVERYDAY MATHEMATICS (2) When Peter went to Hong Kong, he changed 50 into $616. (3) Two varieties of tea, High Blend and Normal Blend, are made by mixing Grade A leaves and Grade B leaves. (i) In High Blend, the ratio of the masses of Grade A leaves to Grade B leaves is 3:2.Find the mass of Grade A leaves used in making 250g of High Blend. (ii) 1 Kg of Normal Blend is made by using 450g of Grade A leaves. Find, in its simplest form, the ratio of the masses of Grade A to Grade B leaves in Normal Blend. Give your answer in the form m: n, where m and n are integers. (iii) 250g of High Blend is mixed with 1Kg of Normal Blend. Calculate the percentage of the mass of this mixture that consists of Grade A leaves. (4) An amount of money is divided into two parts in the ratio 1:4. Find the smaller part as a percentage of the whole amount. (5) A bank exchanged Japanese yen and Singapore dollars ($) at a rate of 66 yen = $1 (i) Calculate, in yen, the amount received for $200. (ii) Calculate, in dollars, the amount received for 33,000 yen. (6) Express as a percentage. (7) The rate of exchange between pounds ( ) and dollars ($) was 1 = $2.80. (a) the number of dollars received in exchange for 120, (b) the number of pounds received in exchange for $224. (8) Calculate 5% of $280,000. (9) The rate of exchange between dollars and euros was $0.8 to 1 euro. Calculate the number of euros received in exchange for $300. (10) Find the simple interest on $450 for 18 months at 4% per year. (11) A jar contained 370g of jam. Usman ate 30% of the jam. What mass of jam remained in the jar? (12) In 2006 the population of a town was 30,000. This was 5000 more than the population in Calculate the percentage increase in population. (13) Sarah bought some soup, apples and mushrooms from her local shop. The table shows some of the amounts and prices. Items Price ($) p cans of soup at 90 cents per can nkilograms of apples at $q per kilogram 4.35 R kilograms of mushrooms at $6.40 per kilogram 1.60 The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 2 of 17

3 (i) Find the values of p, q and r. (ii) Sarah gives the shopkeeper $20.00 to pay for all these items. How much change does she receive? (14) A washing machine costs $980. The finance offer is to pay 20% deposit and 24 monthly payments of $36 each. Lavin decided to buy this washing machine. How much more would it cost Lavin if he paid for the washing machine using the finance offer instead of paying the $980 immediately? (15) The rate of exchange between pounds ( ) and dollars ($) is 1 = $1.87 The rate of exchange between pounds ( ) and euros ( ) is 1 = (i) Catherine changes 500 into dollars. Calculate how many pounds she receives. (16) Imran is paid $16 per hour. (i) One week he works 35 hours. Calculate the amount he is paid for the week. (ii) Imran is paid 20% extra per hour for working weekends. Work out the total amount Imran is paid for working 4 hours at the weekend. (17) The temperature in a freezer is 18 C. The outside temperature is 24 C. (a) (b) Find the difference between the outside temperature and the freezer temperature. The temperature in a fridge is 22 warmer than the freezer temperature. Find the temperature in the fridge. (18) A carton contains 2.5 litres of juice. Carlos drinks 650 ml of the juice. How much juice is left in the carton? Give your answers in litres. (19) The exchange rate between dollars and euros is $1 = Ben changes $275 into euros. Calculate the number of euros Ben receives. (20) A shopkeeper sells cartons of milk and bottles of water.each carton of milk costs $2.40, and each bottle of water costs $0.80. One day he sells x cartons of milk. On the same day he sells 20 more bottles of water then the carton of milk. (i) Write down an expression, in terms of x, for these cartons and bottles. Simplify your answers. (ii) (iii) The total amount he receives that day for the sales of these cartons and bottles is greater than $250 Hence write down the least number of cartons of milk that he sells that day. (21) A photo is 10 cm long.it is enlarged so that all dimensions are increased by 20% The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 3 of 17

4 (a) (b) Find the length of the enlarged photo. Find the ratio of the area of the enlarged photo to the area of the original photo. Give your answer in the form of k:1 (22) Exchange rate for 1 = $2.06, and 1 = 72 rupees (23) (i) Manraj changes 25,200 rupees into dollars ($). Calculate how many dollars he receives. (ii) Misja changes 380 euros into dollars ($). He receives $551. How many dollars does he receive for each euro? Account Simple Interest per Year Super Saver 3.4% Extra Saver 3.5% On 31 March 2011, Lydia and Simone each had $8000 in an account. Lydia s money is in a Super Saver Account. Simone s money is in the Extra Saver Account. (i) (ii) (iii) How much money did Lydia have in her account on 31 March 2012 after the interest had been added? On 31 March 2012, Lydia transferred this money to an Extra Saver Account How much money did she have in this account on 31 March 2013 after the interest had been added? Simone kept her money for the two years in the Extra Saver Account, which earned simple interest of 3.5% per year. After all interest had been added, who had more money in their account on 31 March 2013 and by how much? 24) A shop buys the posts from a manufacturer and sells them at a profit of 30%. The shop sells each post for $ (i) How much does each post cost from the manufacturer? (ii) Fence Panels for $50.7 each and Posts for $35.10 each Mr. Chan buys 4 fence panels and 5 posts. He hires a builder to put up the fence. The builder charges 220% of the total cost of the fence panels and posts to do the work. What is the total amount Mr. Chan pays for his fence? 25) Ami buys 3 drinks at $1.86 each and 1 drink for $2.04. She pays for 4 drinks with a $10 note. How much change should she receive? 26) The cost price of bicycle A is $620. The shopkeeper sells it and makes a profit of 45%. (i) Calculate the selling price. (ii) In a sale the price of bicycle B is reduced from dollar $2,400 to $1596. Calculate the percentage reduction given. (iii) Tax on the original price bicycle C is charged at 20% of the original price. After tax has been included, Matthew pays $1080 for this bicycle. Calculate the original price. The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 4 of 17

5 27) (a) Dwayne buys a camera for $90. He sells the camera for $126. Calculate his percentage profit. (b) The price of a computer is $375. In a sale the price was reduced by 15%. Calculate the reduction in the price of the computer. (c ) The exchange rate between euros and dollars is 1 = $1.25 (i) Convert 180 to dollars. (ii) Convert $500 to euros. 28) (i) Jack opens a bank account paying simple interest. He pays in $800 and leaves it in the account for 4 years. At the end of 4 years, he closes the account and receives $920. Calculate the percentage rate of simple interest paid per year. (ii) Jack uses some of the dollar $920 to pay for a holiday and a computer. He saves the remainder. The money is divided between the holiday, computer and savings in the ratio 4:5:7. Calculate the amount he saves. 29) Mavis went to a cafe to meet some friends. (a) She bought three drinks at $1.42 each and 1 cake for 85 cents. How much did she altogether? spend (b) She left home at 10:45 a.m and returned at 1:20 p.m. How long, in hours and minutes, was she away from home? 30) A car travels at 90 km per hour. How many metres does it travel in 1 second? 31) In 2013 Mary worked for Company A. Her salary for the year was $ (i) $5625 of her salary was not taxed. What percentage of her salary was not taxed? (ii) The remaining $13125 of Mary s salary was taxed. 22% of this amount was deducted for tax. Mary's take home pay was the amount remaining from $18750 after tax had been deducted. She received this in 52 equal amounts as a weekly wage. Calculate Mary's weekly wage. (iii) In 2012 Mary had worked for Company B. When she moved from Company B to Company A, her salary increased by 25% to $ Calculate her salary when she worked for Company B. 32) The rate of exchange between pounds ( ) and Indian rupees ( R) is 1 = R The rate of exchange between pounds ( ) and Swiss Francs (F) is 1 = F1.53. (i) Mavis changed 750 into Indian rupees. How many rupees did she received? (ii) David changed F450 into pounds. How many pounds did he receive? (iii) Brian changed R50000 into Swiss francs. How many Swiss francs did he receive? 33) Cookery book states that the time it takes to cook some meat is 13 minutes for every 500 grams of meat + 20 minutes. Calculate the number of minutes it takes to cook 1.5 kg of meat? It takes T minutes to cook M grams of meat. Find a formula for T. The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 5 of 17

6 Q1) Find all the integers which satisfy both: 2x + 7 < 3 and x > -4 Q2) (i) Find the smallest integer k which satisfies 7k > 36 (ii) Find the largest integer which satisfies 3n - 1 < 26. Q3) (a) Solve -7 <3x -4 < 2. (b) Write down all the integers which satisfy -7 < 3x - 4 < 2 LINEAR INEQUALITIES Q4) Given that y is an integer and -3 < 2y -6 < 4, List the possible values of y. Q5) (a) Solve the inequality 2(4-x) < x - 10 (b) FInd the smallest integer n such that 3n > -17. Q6) (a) Solve x (b) Write down all the integers that satisfy this inequality -1 <4y + 3 < 11 Q7) Find one value of x that satisfies both x > 4 and 17-4x > 2 x The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 6 of 17

7 Frequency Density The histogram and the table are both incomplete. They represent the same information about the ages of people living in a small village. (a) Use the information in the histogram to complete the frequency table. (b) Complete the histogram. [2 marks] [2 marks] The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 7 of 17

8 The table shows the distribution of ages in a health club. (a) Draw a histogram to illustrate this data. [3 marks] (b) Members over 65 pay a reduced subscription. Estimate how many members are over 65. [1 mark] The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 8 of 17

9 Mean, Median and Mode Q1. Find the mean, median and mode of the following set of numbers: (a) 12, 11, 13, 11, 15, 16 (b) 10.5, 9.6, 7, 11, 9.4, 8.1, 10.4, 11.7, 8.1, 9.4, 8.1 Q2. A factory manufactures strapping machines. Over a fifteen-day period, the number of machines produced each day was 35, 38, 40, 45, 47, 45, 39, 45, 39, 38, 36, 43, 45, 42, 38. Calculate the mean, median and modal number of machines produced per day over this period. Q3. The record of the number of potato chips sold each day in a store is as follows: Number of packets Number of days (a) Calculate the mean number of packets sold. (b) Find the difference between the mode and the median. Q4. A gardener sowed 5 seeds into each of 100 plant pots. The number of seeds germinating in each pot was recorded and the results are as given in the table below. Calculate the mean, median and mode of the distribution. Number of seeds germinating Number of pots Q5. The heights (in metres) of a group of players are 1.8, 1.9, 2.0, 1.7, 1.8, 1.9, 1.6, 2.0, 1.8, 1.9 and 1.8. (a) Find the mean, median and modal height of the group. (b) When the 12 th member joined the group, the mean height became 1.9 m. What was his height? Q6. The mass of a group of children are 9, 11, 13, 13, 15, 15, 15, a, 13, 20. Given that the median mass is 0.4 greater than the mean mass, find the value of a and state the modal mass. Q7. In a Mathematics test, the mean score of 30 students was Mary, one of the 30 students, scored 8 marks. It later transpired that her score was recorded wrongly. After correcting her score, the new mean score became What was Mary s actual score? Q8. The following table gives the frequency distribution of the marks obtained by students in an English test. Calculate the mean mark. Marks (x) Number of students 20 < x < x < x < x < x < x < x 90 2 Q9. The heights of a group of 30 children measured to the nearest centimetre are as follows: The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 9 of 17

10 (a) Copy and complete the table given. (b) Estimate the mean height of the 30 children using the table below. (c) Estimate the percentage of children whose heights are below 135 cm. Height (cm) Mid-value (x) Frequency (f) fx f = fx = Q10. The following grouped frequency table shows the times some boys and girls took to complete one lap around a race track. Frequency Time (minutes : seconds) Boys Girls 2:00 2: :15 2: :30 2: :45 3: :00 3: :15 3: :30 3: (a) What is the modal class for girls? (b) What is the modal class for boys? (c) What is the modal class for the participants irrespective of their gender? The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 10 of 17

11 Coordinate Geometry Q1. Calculate the distance and mid-point of the line joining the following pairs of points: (a) (1, -2) and (3.5, -5.5) (b) (1, 0) and (0, -1) (c) (6.5, -8) and (5, 5) Q2. A is a point (4.5, -4.5) and B is a point (6, k). Find the value of k if: (a) the distance of AB is 8 units (b) the mid-point of AB is (0, -3) Q3. Given the points A(2, 1), B(5, 4) and C (7, c), find the value of c if the gradient of AB is equal to the gradient of AC. Q4. Find the equation of the straight line joining each of the following pairs of points. (a) (6, 0) and (0, 7) (b) (5, 7) and (5, -2) (c) (0, 3) and (1, -5) Q5. Three of the vertices of a parallelogram ABCD are A(-2, 3), B(7, 12) and C(11, -5). Find: (a) the equations of AD and CD (b) the fourth vertex D (c) the length of the diagonal BD Q6. If the points (2, -5), (0, 3) and (-3, k) lie on a straight line, find the value of k. Q7. Find the equation of each straight line, given its gradient and the coordinates of a point that lies on the line. (a) 2, (5, 4) (b) 1, (-1, 3) 2 (c) -5, (7, 6) (d) - 1 3, (0,3) Q8. A straight line with equation 2y = k x + h passes through the points (-3, 6) and (1, 11). Find the value of k and h. Q9. The points A, B and C are (9, 8), (12, 4) and (4, -2) respectively. (a) Calculate: (i) the gradient of the line through A and B (ii) the equation of the line through C which is parallel to AB (iii) the length of AB and BC (b) Show that AB is perpendicular to BC (c) Calculate the area of the triangle ABC The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 11 of 17

12 Q10. The diagram shows the points A(1, 2), B(4, 6) and D(-5, 2). B(4, 6) D(-5, 2) A(1, 2) (a) Find the coordinates of the mid-point of AB. (b) Calculate the length of AB. (c) Calculate the gradient of the line AB. (d) Find the equation of the line AB. (e) The triangle ABC has line of symmetry x = 4. Find the coordinates of C. The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 12 of 17

13 Symmetry Q1. From the shapes given below, write down the letters of those which have: (a) exactly one line of symmetry (b) rotational symmetry of order 2 Q2. On the regular hexagon below, draw all the lines of symmetry. Q3 (a). In the diagram, two small triangles are shaded. Shade one more small triangle so that the diagram will then have one line of symmetry. Q3 (b). In the diagram, two small squares are shaded. Shade two more small squares so that the diagram will then have rotational symmetry of order 2. The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 13 of 17

14 Q4. From the following shapes: Square, Rectangle, Equilateral Triangle, Kite, Trapezium and Parallelogram, write down the name of the shape which always has: (a) rotational symmetry of order 3 (b) rotational symmetry of order 2 and exactly 2 lines of symmetry (c) one line of symmetry only Q5. For the following solids, state: (i) (ii) the number of planes of symmetry, and the number of axes of rotational symmetry Cube Cuboid Hemisphere Right pentagonal prism A right circular cone A right prism with an equilateral triangle as the base Regular tetrahedron Sphere Square pyramid The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 14 of 17

15 Congruent and Similar Triangles 1. Decide whether the following pairs of triangles are congruent or not. If they are, what condition do they satisfy? The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 15 of 17

16 1. A girl 160 cm tall, stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamp post? 160 cm 90 cm 360 cm 2. Calculate the values of all the unknown variables, given that the two shapes are similar c 5 cm 3 cm a e 9 cm cm 53 6 cm b d a =.. c =.. b =.. d =.. e =.. The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 16 of 17

17 3. Find the value of unknown sides in the following a) b) 9 c) The City School /PAF Chapter / Prep Section / Worksheet for Intervention Class / Math / Paper -1/Class 9 Page 17 of 17