Monfort Sec Sch P2 2020

1 3 Section A (52 marks) Answer all the questions in this section. (a) 64.5 Workout----0.0584x18.2 (b) y is directly proportional to the square of x. Given that y = 81 when x = 3, find y when x = 2. Answer ............................. [l] Answer y = ............. .......... [2]

4 2 The frequency table below shows the number of goals scored by a soccer team Colo-Colo in 25 matches. Number of ~oals 0 2 3 4 5 Number of matches 4 5 6 5 3 2 (a) Find the mode. Answer ...... ........ ........ ....... [!] (b) Find the mean. Answer ................. ...... ..... . [2] (c) One of the matches was selected at random. Find the probability that. on that day, the number of goals scored was 2 Answer ........................ .... . [!] 3 (a) Simplify q 4 xq5 J q Answer ... ..... .-... ........ ... ..... (2] 3 (b) Simplify (; y Answer ........ ...... . ............. [2]

5 4 (a) C B A D E ABC is an isosceles triangle. AB= AC and BADE is a straight line. AngleACB = 69° and angle CDE= 148°. Find angle x. Answer x = ................ .... .. [2] (b) The interior angle of a regular polygon is 135 ° . Find the number of sides of the polygon. Answer ............................ [2]

6 S The diagram shows a sketch of a field. (a) 90m Make an accurate scale drawing of the field. Use a scale of 1 cm to represent 10 m. (b) A pole, M, is placed in the field. It is on the perpendicular bisector of BC and also on the bisector of angle BAD. Construct and label the position of the pole on your scale drawing. [3] [2]

6 7 A mountain bike is marked · h . In a sale the p . . ed wit a pnce of$550 at a sports shop , nee 1s r uced to $440. · (a) Calculate the reduction as a percentage of the marked price. Answer ......................... %[3] (b) $440 is 300/o more than the amount the owner of the shop paid for the mountain bike. Calculate the amount the owner of the shop paid for the mountain bike. Answer $ .......................... (2]

8 7 The diagram shows the speed-time graph of a particle over a period of time. Speed (mis) 20 -----------------:x-------... .---------22c..__5 _____ 4!.....8 ---~66 _ __,. Time (s) (a) Describe the motion between t = 25 and t = 48. Answer ............................... . [l] . . ................................................. . (b) Calculate the retardation. Answer .......................... mis 2 [2] (c) The area under the graph represents the total distance travelled. Calculate the total distance travelled. Answer .......................... m [2]

8 (a) 9 Expand and simplify (3x-2y)(x+ 4y). (b) Factorise 8 y 2 - l 8x2 completely. (c) Rearrange this formula to make p the subject. 3u q=4(p-r) Answer ................ ......... .. . [2] Answer ........................ .... [2] Answer p = .................... ... [3]

10 [2] 9 (a) Complete the table of values for y = 3x. I X 2 1.5 I I -0.5 I 0 0.5 1 y 0.1 0.3 1 1.7 3 (b) On the grid, plot the graph of y = 3x for -2 X l . . [3] I l I t' I I I L

11 (c) On the grid, plot the graph of y =-x+ 1. [2] (d) Use the graphs to find the coordinates of the point where the two graphs intersect. Answer ( ..... ........ , ..... . ... .. . ) [l] 10 Gabriel and ten of his friends are spending the weekend at a chalet. He has been given $75 to spend on food. As they will be having their dinner at a nearby restaurant on both days , Gabriel will only need to plan for 3 meals - lunch for both days and breakfast for one day. The items the group need for breakfast and lunch are shown below. Items Quantity (per person) Bread 2 slices Breakfast Egg 1 egg Milo 1 packet Cup noodles 1 cup Lunch Lemon tea 1 packet Table 1 (a) Calculate the number of packets of lemon tea Gabriel needs to buy for both days . Answer ...... ................... ... [l] (b) Lemon tea is sold in three types of packaging as shown below. Item Description Unit cost Individual pack $0.80 Lemon Tea Packof6 $4.80 Packof20 $15.00 Table2 Gabriel wants to minimise the amount of money spent on each item. Based on your answer in part (a), how many of each type of packaging should he choose and how niuch will it cost in all? Answer ........... ...... .... ... ... ................ ...... . . $ ... ... .......... .......... .. (2]

(c) 12 . hi s He estimates that the In addition to the 3 meals, Gabriel wants to buy some potato c P · chips will cost $10. Item Description Unit cost Individual pack $0.70 Milo Packof6 $4.00 Individual pack $1.80 Cup Noodles Packof 10 $15 Eggs Tray of 12 $2.00 Trayof30 $5.00 Bread Loaf of 10 slices $1.80 Table3 Using information from Table 2 and 3, determine whether Gabriel will be able to buy chips after purchasing all the necessary items as shown in Table 1. Show your calculations clearly. Answer [5]