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 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 5 350 220 240 80 200 (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 $62 000. It was sold in 2003 for $30 000. (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 2003. [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]
5. In 2004 Colin had a salary of $7200. (a) This was an increase of 20% on his salary in 2002. Calculate his salary in 2002. [2] (b) In 2006 his salary increased to $800. Calculate the percentage increase from 2004 to 2006. [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 2004. Calculate the cost in 2005. [2] The cost of $385 in 2004 was 0% more than the cost in 2003. Calculate the cost in 2003. [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]
9. y 8 7 6 5 4 3 y = mx + c 2 0 2 3 4 5 6 7 8 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)
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 + 30. Find c when d = 00. []
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 2 + 30x + 24 square centimetres. []
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]
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
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]
29. The quiz scores of a class of n students are shown in the table. Quiz score 6 7 8 9 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 5.97 0 24 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 = 6 0 6 and R = 7.2 0 8. [2] R 33. A spacecraft made 58 376 orbits of the Earth and travelled a distance of 2.656 0 9 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]
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 7 2 2 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] 4 38. Alphonse spends $28 on food. This amount is of his allowance. Calculate 9 his allowance. [2]
39. 30 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 8.5 0 6 Panama 7.7 0 4 Guyana 2.5 0 5 Colombia.4 0 6 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 < < []