The diagram shows a path, ST, up a hill. The path is 1.2 kilometres long and slopes at an angle of 21 to the horizontal.

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Barnard Mitchell
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1 Grade: 9 th Holiday s HomeworkSession All the answers must be given to sf, angle to dp or the degree of accuracy specified in the question. Show a neat sketch of the graph wherever neededwith ALL NECESSARY DETAILS ON IT.. A boat sails due east 65 Km and then it sails north 0 Km, Calculate the distance of the boat from the starting position,giving your answer to the nearest 0. km... km T S The diagram shows a path, ST, up a hill. The path is. kilometres long and slopes at an angle of to the horizontal. Calculate the height of the hill, showing all your working. Give your answer in metres.. Factorise completely (a) 7ac + 4a, [] (b) a + 8a. [] 4. A square ABCD, of side 8 cm, has another square, PQRS, drawn inside it. P, Q, R and S are at the midpoints of each side of the square ABCD, as shown in the diagram. (a) Calculate the length of PQ. [] A S P B Q (b) Calculate the area of the square PQRS. [] D 5. Simplify R C 7 (a), [] 7 (b). [] 4

2 6. Simplify (a) a 0, [] (b) [] (c). [] 7. Joseph, Maria and Rebecca each win a prize. Their total prize money is $0. 7 Joseph wins of the $0. Maria wins 0% of the $0. Rebecca wins the rest of the $0. Calculate the amount each receives. [++] 8. Alphonse, his wife and child fly from Madrid to the Olympic Games in Beijing. The adult plane fare is 450 euros. The child fare is 68% of the adult fare. (a) Show that the total plane fare for the family is 06 euros. Show all your working clearly. (b) The ratio of the money spent on plane fares : accommodation : tickets = 6 : 5 :. 9. y = m 4n. Calculate the total cost. (i) Factorise m 4n. [] (ii) Find the value of y when m = 4.4 and n =.8. [] (iii) m = + and n =. Find y in terms of, in its simplest form. [] (iv) Make n the subject of the formula y = m 4n. 0. (a) The first four terms of a sequence are, 7,,. (i) Write down the net two terms of the sequence. [] (ii) State the rule for finding the net term of the sequence. [] (iii) Write down an epression for the nth term of this sequence. []

3 (b) The first four terms of another sequence are,, 7,. Write down an epression for the nth term of this sequence. [] (c) Add together the epressions for the nth terms of both sequences. Write your answer as simply as possible. []. In the diagram below ABD is a straight line. AB = 4 m and AC = 6 m. Angle BAC = 90. A 4 m B D 6 m C (a) (i) Use trigonometry to calculate angle ABC. [] (ii) Find angle CBD. [] (b) Calculate the length of BC. [] (c) Work out the perimeter and area of triangle ABC. Give the correct units for each.. The diagram below shows a sequence of patterns made from dots and lines. dot dots dots 4 dots (a) Draw the net pattern in the sequence in the space above. [] (b) Complete the table for the numbers of dots and lines. Dots Lines 4 7 0

4 (c) How many lines are in the pattern with 99 dots? [] (d) How many lines are in the pattern with n dots? [] [] (e) Complete the following statement. There are 85 lines in the pattern with dots. []. Maria, Carolina and Pedro receive $800 from their grandmother in the ratio Maria : Carolina : Pedro = 7 : 5 : 4. (a) Calculate how much money each receives. (b) Maria spends of her money and then invests the rest for two years at 5% per 7 year simple interest. How much money does Maria have at the end of the two years? (c) Carolina spends all of her money on a hi-fi set and two years later sells it at a loss of 0%. How much money does Carolina have at the end of the two years? [] (d) Pedro spends some of his money and at the end of the two years he has $00. Write down and simplify the ratio of the amounts of money Maria, Carolina and Pedro have at the end of the two years. [] 4. A candle, made from wa, is in the shape of a cylinder. The radius is.5 centimetres and the height is 0 centimetres. (a) (b) (c) Calculate, correct to the nearest cubic centimetre, the volume of wa in the candle. [The volume of a cylinder, radius r, height h, is πr h.] [] The candle burns 0.8 cm of wa every minute. How long, in hours and minutes, will it last? Write your answer correct to the nearest minute The candles are stored in boes which measure cm by 4 cm by 0 cm. Each bo contains 96 candles. Calculate the minimum value of. 4

5 [] (d) A shopkeeper pays $5 for one bo of 96 candles. He sells all the candles for 5 cents each. (i) How much profit does he make? [] (ii) Calculate his profit as a percentage of the cost price. 5. C A B The diagram above shows a cuboid and its net. 6 cm (a) Calculate the total surface area of the 4 cm cuboid. C (b) Calculate the volume of the cuboid. [] (c) An ant walks directly from A to C on the surface of the cuboid. (i) Draw a straight line on the net to show this route. [] B (ii) Calculate the length of the ant s journey. A (iii) Calculate the size of angle CAB on the net cm 5

6 5 m. m The diagram shows a swimming pool of length 5 m and width 4 m. A cross-section of the pool, ABCD, is a trapezium with AD =.5 m and BC =. m. (a) Calculate D.5 m 4 m B C (i) A the area of the trapezium ABCD, [] (ii) the volume of the pool, [] (iii) the number of litres of water in the pool, when it is full. [] (b) AB = 5.0 m correct to decimal places. The sloping rectangular floor of the pool is painted. It costs $.5 to paint one square metre. (i) Calculate the cost of painting the floor of the pool. [] (ii) Write your answer to part (b)(i) correct to the nearest hundred dollars. [] (c) (i) Calculate the volume of a cylinder, radius.5 cm and height 4 cm. [] (ii) When the pool is emptied, the water flows through a cylindrical pipe of radius.5 cm. The water flows along this pipe at a rate of 4 centimetres per second. Calculate the time taken to empty the pool. Give your answer in days and hours, correct to the nearest hour. [4] 7. Solve the simultaneous equations y y Simplify. Write your answer as a fraction in its simplest form. 6, 9. Solve (a) =., [] 6

7 (b) 0. Solve the inequality. Simplify (a), [] 7 (b). [] 4. Rearrange the formula to make y the subject. y 9. (a) Factorise a + b. (b) Make the subject of the formula [] 4. Amira takes 9 hours 5 minutes to complete a long walk. (i) Show that the time of 9 hours 5 minutes can be written as hours. [] (ii) She walks (y + ) kilometres at km/h and then a further (y + 4) kilometres at km/h. Show that the total time taken is 9y 6 6 hours [] (iii) Solve the equation 9y 6 =. 6 [] (iv) Calculate Amira s average speed, in kilometres per hour, for the whole walk. 5. Write c d c d cd as a single fraction in its simplest form. 6. (i) m 4 6n 4 can be written as (m kn )(m + kn ). Write down the value of k. (ii) Factorise completely m 4 n 6n Magazines cost $m each and newspapers cost $n each. One magazine costs $.55 more than one newspaper. The cost of two magazines is the same as the cost of five newspapers. (i) Write down two equations in m and n to show this information. (ii) Find the values of m and n. [] [] [] [] 7

8 8. Solve the simultaneous equations y = 0, y = Simplify 7. [] 0. Solve the equation. The length of time, T seconds, that the pendulum in the clock takes to swing is given by the formula 6 T. ( g ) Rearrange the formula to make g the subject.. (a) Simplify [] (b) 5 = p. Find p. 6 ( 7 ). 5, 4 [4] []. The surface area, A, of a cylinder, radius r and height h, is given by the formula A = πrh + πr. (i) Calculate the surface area of a cylinder of radius 5 cm and height 9 cm. [] (ii) Make h the subject of the formula. [] (iii) A cylinder has a radius of 6 cm and a surface area of 77 cm. Calculate the height of this cylinder. [] (iv) A cylinder has a surface area of 00 cm and its radius and height are equal. Calculate the radius. 4. 8

9 5. 6. [] [] 9

10 9. [4] 40.. Arestaurant offerstwo kinds of dishes for a function. Ifa group of 0 people attend the function and the bill comes to a total of $64, If number of people ordered fish dish and Y number of people ordered meat dish, i. Form two equations in and y using the information given above. ii. Find the number of guests who ordered each dish. [] [4] 0

PATHWAYS WORLD SCHOOL: Mathematics Department. Grade: IX Level: Extended Holidays(summer break)homework

PATHWAYS WORLD SCHOOL: Mathematics Department. Grade: IX Level: Extended Holidays(summer break)homework Grade: IX Level: Extended Holidays(summer break)homework Topics: All topics covered in Grade 8 Session-204-205 CALCULATOR IS PERMITTED/NOT PERMITTED All the answers must be given to 3 sf, angle to dp or