WASSCE CORE MATHEMATICS TRIALS Question 1 (a) Two children shared an amount of money in the ratio 3/4 : 2/5. If the smaller share was GH¢25.00, how much was shared between them? https://whatsapp.com/channel/0029VaEW2JPEawdvPSdOBG1m (b) A box contains 5 red, 3 green and 4 blue balls of the same size. If a boy picks two balls from the box one after the other without replacement, what is the probability that both balls are red? Question 2 (a) (i) Solve the inequality: 1/2x - 5/6( ex + 2) ≤ 1 + x. (ii) Illustrate the solution on a number line. (b) When the price of an apple increased by N 5.00f18 apples cost N 60.00 more than 20 apples cost before the increase. Find the new price of an apple. https://whatsapp.com/channel/0029VaEW2JPEawdvPSdOBG1m Question 3 (a) In a right angled triangle, sin x = 3/5. Evaluate 5(cos x)³ - 3. (b) The angle of elevation of the top of a vertical pole from a point 63m east of the base of the pole is 30°. From another point due west of the pole, the angle of elevation of the top is 60° 0542743763 (i)Draw a sketch diagram to illustrate the information. (ii)Calculate, correct to three significant figures, the distance of the second point from the base of the pole. Question 4 (a) The diagonals of a rhombus are 14cm and gcm. Calculate, correct to the nearest centimetre, the perimeter of the rhombus. (b) The cross section of a rectangular tank measures l.2m by 0.9m. It contains water to a depth of O.4m. If a cubical block of side 50cm is lowered into the tank, calculate, correct to 2 significant figures, the rise in the water level (in metres). _542743763 Question 5 (a) In a class of 50 students, 30 offered History, 15 offered History and Geography while 3 did not offer any of the two subjects. (i)Represent the information on a Venn diagram. (ii)Find the number of candidates that offered: (A) History only; (B) Geography only. (b) A trader sold an article at a discount of 8% for N 828.00. If the article was initially marked to gain 25%, find the (i)cost price of the article; (ii)discount allowed. https://whatsapp.com/channel/0029VaEW2JPEawdvPSdOBG1m Question 6 Using ruler and a pair of compasses only: (a) construct a triangle PQRwith /PQ/ = lOcm, ∠QPR = 90° and ∠PQR = 30°; (b) (i) construct I, the locus of all points equidistant from PR and QR; (ii) locate M, the point where / intersects with po, (c) (i) with M as centre and radius MP, draw a circle; (ii) calculate the area of the circler correct to one decimal place. [Take Π= 22/7]. Question 7 The table gives the distribution of marks for 360 candidates who sat for an examination. Marks (%) 0-9 10 - 19 20 - 29 30 -39 40 - 49 50 - 59 60 - 69 70 -79 80 -89 Number of candidate 20 48 60 72 80 40 25 10 5 (a) Draw a cumulative frequency curve for the distribution. (b) Use your graph to estimate the semi-interquartile range. (c) If the minimum mark for distinction is 75%, how many candidates passed with distinction? Question 8 (a) A ship Pis 3km due east of a harbour. Another ship Q is also 3 km from the harbour but on a bearing of 042° from the harbour. (i)Find the distance between the two ships. (ilFind the bearing of ship Q from ship P. (b) A motorist travelled 300 km at an average speed of 75 km/h and returned at an average speed of v km/b. If his average speed for the whole journey is 60 km/h, find v.