Gozo College Secondary School Victoria HALF-YEARLY EXAMINATIONS FEBRUARY 2018

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1 Gozo College Secondary School Victoria Track 3 HALF-YEARLY EXAMINATIONS FEBRUARY 2018 YEAR 10 MATHEMATICS TIME: 1 hr 40 mins Main Paper Question Total Main Non Calc Global Mark Mark DO NOT WRITE ABOVE THIS LINE NAME: CLASS: INSTRUCTIONS TO CANDIDATES: Answer all questions. This paper carries 80 marks. Calculators and mathematical instruments are allowed but all necessary working must be shown. 1. The diagram shows a compound prism. a. Find the area of the cross-section ABCDE. 12 cm Ans: cm 2 b. Hence, find the volume of the prism. Ans: cm 3 (5 marks) Mathematics Main Paper HY 2018 Page 1 of 10 Year 10 (Track 3)

2 2. a. Express 60 and 108 as a product of their prime factors. Ans: 60 = 108 = b. The rectangular floor of a doll s house has dimensions 60 cm by 108 cm. Identical square tiles are used to cover the floor of the doll s house. Given that only complete tiles can be used, find the largest possible tile size. 3. A motorbike depreciates by 8% each year. a. In January 2013, Andrea bought a motor bike for Calculate the value of the motor bike after five years. Give your answer correct to the nearest Euro. Ans: cm (3 marks) Ans: b. Calculate the percentage decrease in value of the motor bike after these 5 years. % (5 marks) Mathematics Main Paper HY 2018 Page 2 of 10 Year 10 (Track 3)

3 Name: Class: 4. WXYZ is a trapezium. WX is parallel to YZ and WZ is the perpendicular height, y, of the trapezium. All lengths are in centimetres. x y Diagram not drawn to scale z a. Express the area of triangle WXZ in terms of x and y. Ans: b. Express the area of triangle ZXY in terms of z and y. c. Hence, show that the area A of trapezium WXYZ is given by: A = Ans: y(x + z) 2 d. Find the area of trapezium WXYZ when x = 20 cm, z = 12 cm and y = 6 cm. Ans: (5 marks) Mathematics Main Paper HY 2018 Page 3 of 10 Year 10 (Track 3)

4 5. The equation of line L1 is y = 2x + 5. a. L1 intersects the x-axis at point A and the y-axis at point B. Find the co-ordinates of point A and point B. (Hint: draw a sketch.) b. The equation of another line L2 is y = 5x + 4. Write down the gradient of line L2. Ans: A = (, ) and B = (, ) c. A third line L3 is parallel to line L2 and passes through the point (2, 9). Write down the equation of line L3. Ans: 6. a. Factorise completely the following expressions: i. 4xy + 20x 2 ii. x 2 + 5x 14 (8 marks) iii. x iv. 2x 2 + x 3 b. Expand and simplify: i. 5 2(3 x) ii. (2x + 1)(2x 1) iii. 4(3x + 1) 2(x + 5) (12 marks) Mathematics Main Paper HY 2018 Page 4 of 10 Year 10 (Track 3)

5 Name: Class: 7. The diagram shows a wooden frame 3 cm wide all around. The outer border of the frame is 5y cm long and 4y cm wide. a. Show that the expression for the perimeter of the inner border is 18y 24. b. The inner border has a perimeter of 66 cm. Find the value of y. c. Hence, find the dimensions of the outer border. cm by cm (6 marks) Mathematics Main Paper HY 2018 Page 5 of 10 Year 10 (Track 3)

6 8. a) A sequence starts with the following four terms: 5, 8, 11, 14,... i. Write down the next two terms of the sequence. ii. Find the n th term of the sequence. iii. Is 124 a term in this sequence? Explain. b) Look at the following pattern: Shape 1 Shape 2 Shape 3 Shape 4 i. Complete the table below: Shape number Number of grey squares Number of white squares Total number of squares ii. What is the n th term for the number of grey squares? iii. What is the total number of squares in shape 25? (11 marks) Mathematics Main Paper HY 2018 Page 6 of 10 Year 10 (Track 3)

7 9. The table below shows the weight, w, in kg, of a group of children a. Use the information to fill in the table below. Weight, w, in kg Tally Frequency 20 w w w w w 70 b. Draw a barchart to illustrate the above data. (5 marks) Mathematics Main Paper HY 2018 Page 7 of 10 Year 10 (Track 3)

8 TOTAL COST ( ) 10. The total cost of a holiday in Spain consists of the cost of the flight and the cost of the hotel according to the number nights spent. The graph shows how the total cost changes with the number of nights NUMBER OF NIGHTS a. Work out the gradient of the line. b. Underline the correct answer. The gradient of the line represents: i. The cost of the flight ii. The cost of one night at the hotel iii. The total cost of the flight and accommodation. iv. The total cost of the hotel. c. What does the y-intercept represent? d. Work out the total cost T of this holiday for n nights. Ans: T = (5 marks) Mathematics Main Paper HY 2018 Page 8 of 10 Year 10 (Track 3)

9 11. The diagram shows two vertical flagpoles AB and PQ on a horizontal ground QBX. The angle of elevation of A from Q is 65 o and the angle of depression of X from A is 34 o. The distance between the two flagpoles BQ is 2.4 m. P A Q B X Find, giving your answers correct to 1 decimal place: a) The height of the flagpole AB. m b) The distance AX. m c) Given that the difference in height of the two flagpoles AB and PQ is 1 m, find the angle of elevation of A from P. (9 marks) Mathematics Main Paper HY 2018 Page 9 of 10 Year 10 (Track 3)

10 12. Make x the subject of the formula: a. ax b = c Ans: x = b. w = z + 2x y Ans: x = (6 marks) END OF PAPER Mathematics Main Paper HY 2018 Page 10 of 10 Year 10 (Track 3)