Gozo College Secondary Schools Victoria

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1 Gozo College Secondary Schools Victoria Track 2 HALF YEARLY EXAMINATION 2017 Year 10 (Form 4) MATHEMATICS TIME: 1 hr 40 mins Main Paper Ques Main NC Global Mark Mark DO NOT WRITE ABOVE THIS LINE Name: Class: INSTRUCTIONS TO CANDIDATES: Read all the questions carefully before you start answering. Answer all questions. This paper carries 80 marks. Calculators and mathematical instruments are allowed but all necessary working must be shown. 1. a) How many faces does a cube have? b) Work out the total surface area of this cube? Ans: faces Ans: cm 2 (4 marks) Gozo College Year 10 (Form 4) Mathematics (Track 2) Main Paper 2017 Page 1 of 10

2 2. a) Simplify: i) p q 0 ii) 2 3 (a 7 ) 3 Ans: Ans: b) Using product of prime factors, find the values of x and w in 2 x 7 w = 392. Ans: x = and w = (7 marks) 3. a = and b = a) Calculate the value of a b. Give your answer in standard form. Ans: b) Calculate the value of a + b. Give your answer as an ordinary number. c) Using your answers to parts (a) and (b), work out: to 2 d.p. Ans: a b.give your answer correct a + b Ans: (7 marks) Page 2 of 10 Year 10 (Form 4) Mathematics (Track 2) Main Paper 2017 Gozo College

3 4. A ladder PQ is 5.6 m long. It stands on a horizontal ground and leans against a vertical wall. The foot of the ladder, Q, is 1.5 m away from the foot of the wall X. a) On the diagram mark point P, point Q and the two measurements. b) Calculate the angle that the ladder makes with the ground ( PQX). wall X Ans: 5. In a store, employees work from 7:30 a.m. to 4:15 p.m. Lunch break is 45 minutes long. Each of the two coffee breaks is 15 minutes long. (4 marks) a) Calculate in minutes, the total time employees spend at work (including breaks). b) Calculate the total break time in minutes. Ans: minutes Ans: minutes c) Write down the following ratio in the form k : 1. total time employees spend at work (including breaks) : total break time Ans: : 1 (7 marks) Gozo College Year 10 (Form 4) Mathematics (Track 2) Main Paper 2017 Page 3 of 10

4 6. a) On her phone, Jenny can text 32 words per minute. She sends 8 SMSs with an average of 80 words each. How long does it take her? minutes b) The two piles (seen in the diagram below) consist of paper cm thick. The taller pile is 10.5 cm high cm Diagram NOT drawnto scale i) Work out ii) How many sheets of paper are there in the taller pile? Ans: iii) The ratio height of taller pile : height of shorter pile is 3 : 2. Work out the number of sheets of paper in the shorter pile. Ans: Ans: (8 marks) Page 4 of 10 Year 10 (Form 4) Mathematics (Track 2) Main Paper 2017 Gozo College

5 7. In the table below, p and q can be several numbers. To get the value of q, p is first multiplied by a number and then another number is added. p q a) Use the table above to complete the formula for p and q. b) What is the value of p when q = 52? q = Ans: p = 8. a) Make d subject of the formula: k = 4d 1 (4 marks) b) Expand: 3(4x 5) Ans: d = Ans: c) Simplify: 6x x Ans: (6 marks) Gozo College Year 10 (Form 4) Mathematics (Track 2) Main Paper 2017 Page 5 of 10

6 9. King Arthur is looking from his window. His eyes E are 8.5 m vertically above the ground. A horse H and a knight K stand on a horizontal ground. FH = 9.2 m and EK = 15.4 m. E 8.5 m 15.4 m F 9.2 m H K a) Use Pythagoras Theorem in triangle EFH to calculate the distance EH. Give your answer correct to 1 decimal place. Ans: m b) Use triangle EFK to calculate the distance FK. Give your answer correct to 1 decimal place. c) What is the distance between the knight K and the horse H? Give your answer correct to 1 decimal place. Ans: m Ans: m (8 marks) Page 6 of 10 Year 10 (Form 4) Mathematics (Track 2) Main Paper 2017 Gozo College

7 10. In a playschool the teachers set the tables and stools as shown in this diagram. 1 Table 2 Tables 3 Tables a) Draw a diagram when 4 Tables are set up. b) Complete the table. Number of Tables Number of Stools 5 8 c) Write an expression for the number of stools when n tables are used. d) Find the number of stools needed when 10 tables are put together. Ans: Ans: stools (8 marks) Gozo College Year 10 (Form 4) Mathematics (Track 2) Main Paper 2017 Page 7 of 10

8 11. a) Work out the area of the following shapes. (i) A square of side 12 cm. 12 cm Area = cm 2 (ii) A right-angled isosceles triangle. Area = cm 2 (iii) A circle of radius 3 cm. 3 cm Area = cm 2 Page 8 of 10 Year 10 (Form 4) Mathematics (Track 2) Main Paper 2017 Gozo College

9 b) The cross-section of a nut consists of a regular octagon with a circular hollow inside. Its dimensions are as in the diagram below. 5 cm 5 cm 5 cm 5 cm 6 cm 5 cm 5 cm 5 cm Diagram not drawn to scale 5 cm Use your results in part (a) to find the area of cross-section of the nut (shaded part). Give your answer correct to 1 decimal place. Area = cm 2 c) The nut is cast in solid metal. Its thickness is 4.2 cm as shown in the diagram. What is the volume of metal used? Volume = cm 3 (10 marks) Gozo College Year 10 (Form 4) Mathematics (Track 2) Main Paper 2017 Page 9 of 10

10 12. Teenagers are playing a game in Mdina. There are puppy pictures hidden in the streets. The job of each teenager is to find as many puppy pictures as possible. This frequency table shows the results. Puppy pictures collected (p) Frequency 0 < p < < p < < p < < p < < p < 25 2 a) How many teenagers participated in the game? Ans: b) How many teenagers collected 10 puppy pictures or less? Ans: c) Complete the histogram below displaying the data found in the above frequency table. Frequency Puppy pictures (7 marks) END OF EXAM PAPER Page 10 of 10 Year 10 (Form 4) Mathematics (Track 2) Main Paper 2017 Gozo College