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

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1 Grade: IX Level: Extended Holidays(summer break)homework Topics: All topics covered in Grade 8 Session CALCULATOR IS PERMITTED/NOT PERMITTED All the answers must be given to 3 sf, angle to dp or the degree of accuracy specified in the question. Show a neat sketch of the graph wherever needed with ALL NECESSARY DETAILS ON IT. Q. n( ) = 2, n(a B) = 9, n(a B ) = 8 and n(a) = 2. Complete the Venn diagram to show this information. Answer A B [3] 2. The table gives the average surface temperature ( C) on the following planets. Planet Earth Mercury Neptune Pluto Saturn Uranus Average temperature (a) Calculate the range of these temperatures. [] (b) Which planet has a temperature 20 C lower than that of Uranus? [] 3. A house was built in 985 and cost $ It was sold in 2003 for $ (a) Work out the 985 price as a percentage of the 2003 price. [2] (b) Calculate the percentage increase in the price from 985 to [2] 4. (i) Hassan sells oranges for $0.35 per kilogram. He reduces this price by 40%. Calculate the new price per kilogram. [2] (ii) The price of $0.35 per kilogram of oranges is an increase of 25% on the previous day s price. Calculate the previous day s price. [2]

2 5. In 2004 Colin had a salary of $7200. (a) This was an increase of 20% on his salary in Calculate his salary in [2] (b) In 2006 his salary increased to $800. Calculate the percentage increase from 2004 to [2] 6. Each year a school organises a concert. (i) (ii) In 2004 the cost of organising the concert was $385. In 2005 the cost was 0% less than in Calculate the cost in [2] The cost of $385 in 2004 was 0% more than the cost in Calculate the cost in [2] 7. The points A(6, 2) and B(8, 5) lie on a straight line. (a) Work out the gradient of this line. [] (b) Work out the equation of the line, giving your answer in the form y = mx + c. [2] 8. y 5 l 0 0 x (a) Calculate the gradient of the line l. [2] (b) Write down the equation of the line l. [2]

3 9. y y = mx + c x One of the lines in the diagram is labelled y = mx + c. Find the values of m and c. [2] 0. y 2x + 3y = 7 4x y = 6 A C (4,3) x B (, 2)

4 In the diagram, the line AC has equation 2x + 3y = 7 and the line AB has equation 4x y =6. The lines BC and AB intersect at B (, 2). The lines AC and BC intersect at C (4, 3). (a) Use algebra to find the coordinates of the point A. [3] (b) Find the equation of the line BC. [3]. The equation of a straight line can be written in the form 3x + 2y 8 = 0. (a) Rearrange this equation to make y the subject. [2] (b) Write down the gradient of the line. [] (c) Write down the co-ordinates of the point where the line crosses the y axis. [] 2. A straight line passes through two points with co-ordinates (6, 8) and (0, 5). Work out the equation of the line. [3] 3. Find the co-ordinates of the mid-point of the line joining the points A(2, 5) and B(6, 9). [2] 4. Magazines cost $m each and newspapers cost $n each. One magazine costs $2.55 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. [2] (ii) Find the values of m and n. [3] 5. Angharad had an operation costing $500. She was in hospital for x days. The cost of nursing care was $70 for each day she was in hospital. (a) Write down, in terms of x, an expression for the total cost of her operation and nursing care. [] (b) The total cost of her operation and nursing care was $2370. Work out how many days Angharad was in hospital. [2] 6. Two quantities c and d are connected by the formula c = 2d Find c when d = 00. []

5 7. 7xcm 50 cm 24x cm The right-angled triangle in the diagram has sides of length 7x cm, 24x cm and 50 cm. (a) Show that x 2 = 36 [2] (b) Calculate the perimeter of the triangle. [] 8. ( x + 4) cm R 4x cm Q ( x + 2) cm ( x + 2) cm (a) (i) Write down an expression for the area of rectangle R. [] (ii) Show that the total area of rectangles R and Q is 5x x + 24 square centimetres. []

6 9. (i) On Monday a shop receives $60.30 by selling bottles of water at 45 cents each. How many bottles are sold? [] (ii) (iii) On Tuesday the shop receives x cents by selling bottles of water at 45 cents each. In terms of x, how many bottles are sold? [] On Wednesday the shop receives (x 75) cents by selling bottles of water at 48 cents each. In terms of x, how many bottles are sold? [] 20. Solve the simultaneous equations x 2y 6, 2 2x y 9. 2 [3] 2. Solve the inequality 4 5x < 2(x + 4). [3] 22. Solve the simultaneous equations 0.4x + 2y = 0, 0.3x + 5y = 8. [3] 23. Solve the equation x 2 2x 5, 4 3 [3] 24. Solve these simultaneous equations. x + 2y 8 = 0 3x 4y 4 = 0 [3]

7 25. entrance h m 3.7 m 5 pavement A shop has a wheelchair ramp to its entrance from the pavement. The ramp is 3.7 metres long and is inclined at 5 to the horizontal. Calculate the height, h metres, of the entrance above the pavement. Show all your working. [2] 26. l 0.7 cm h 6.5 cm.5 cm The diagram shows a pencil of length 8 cm. It is made from a cylinder and a cone. The cylinder has diameter 0.7 cm and length 6.5 cm. The cone has diameter 0.7 cm and length.5 cm. (a) Calculate the volume of the pencil. [The volume, V, of a cone of radius r and height h is given by V = r 2 h. [3] 3 (b) x cm 8 cm wcm

8 Twelve of these pencils just fit into a rectangular box of length 8 cm, width w cm and height x cm. The pencils are in 2 rows of 6 as shown in the diagram. (i) Write down the values of w and x. [2] (ii) Calculate the volume of the box. [2] (iii) Calculate the percentage of the volume of the box occupied by the pencils. [2] 27. A E B O D C A, B, C and D lie on a circle, centre O, radius 8 cm. AB and CD are tangents to a circle, centre O, radius 4 cm. ABCD is a rectangle. (a) Calculate the distance AE. [2] (b) Calculate the shaded area. [3] 28. The numbers 0,,,, 2, k, m, 6, 9, 9 are in order (k m). Their median is 2.5 and their mean is 3.6. (i) Write down the mode. [] (ii) Find the value of k. [] (iii) Find the value of m. [2]

9 29. The quiz scores of a class of n students are shown in the table. Quiz score Frequency (number of students) 9 3 a 5 The mean score is 7.2. Find (i) a, [3] (ii) n, [] (iii) the median score. [] 30. A block of cheese, of mass 8 kilograms, is cut by a machine into 500 equal slices. (a) Calculate the mass of one slice of cheese in kilograms. [] (b) Write your answer to part (a) in standard form. [] 3. The mass of the Earth is of the mass of the planet Saturn. 95 The mass of the Earth is kilograms. Calculate the mass of the planet Saturn, giving your answer in standard form, correct to 2 significant figures. [3] 2 V 32. Use the formula P to calculate the value of P when V = and R = [2] R 33. A spacecraft made orbits of the Earth and travelled a distance of kilometres. (a) Calculate the distance travelled in orbit correct to the nearest kilometre. [2] (b) The orbit of the spacecraft is a circle. Calculate the radius of the orbit. [2]

10 34. All 24 students in a class are asked whether they like football and whether they like basketball. Some of the results are shown in the Venn diagram below. F B = {students in the class}. F = {students who like football}. B = {students who like basketball}. (i) How many students like both sports? [] (ii) How many students do not like either sport? [] (iii) Write down the value of n(f B). [] (iv) Write down the value of n(f B). [] 35. = {,2,3,4,5,6,7,9,,6} P = {2,3,5,7,} S = {,4,9,6} M = {3,6,9} (a) Draw a Venn diagram to show this information. [2] (b) Write down the value of n(m P). [] 36. Yasmeen is setting up a business. She borrows $5000 from a loan company.the loan company charges 6% per year simple interest. How much interest will Yasmeen pay after 3 years? [2] 37. When x = 3 find the value of x 3 + 2x 2. [2] Alphonse spends $28 on food. This amount is of his allowance. Calculate 9 his allowance. [2]

11 mm 2 mm An old Greek coin is a cylinder with a diameter of 30 millimeters and a thickness of 2 millimeters. Calculate, in cubic millimeters, the volume of the coin. [The volume of a cylinder, radius r, height h, is πr 2 h.] [2] 40. (a) Expand the bracket and simplify the expression 7x + 5 3(x 4). [2] (b) Factorise 5x 2 7x. [] 4. Camilla has $5 to spend in the market. She buys kilograms of bananas priced at 80 cents per kilogram and 3 yams priced at 2 45 cents each. How much money does she have left? [3] 42. Country Area (km 2 ) Brazil Panama Guyana Colombia The table above gives the areas of four South American countries, correct to 3 significant figures. (a) List the countries in order of area, smallest to largest. Answer (a) < Guyana < < []

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