*1 (a), leaving the answer in recurring decimal.

Transcription

1 *1 (a) Calculate , leaving the answer in recurring decimal. (7 3)3.3 Answer (a) [1] (b) Write your answer to part (a) correct to 2 significant figures. Answer (b) [1] *2 If find the value of Answer [1] *3 (a) Express 90 as the product of its prime factors. Answer (a) [1] (b) Find the greatest integer that is a factor of 90 and 12. Answer (b) [1] (c) A bell rings once every 12 minutes. Another bell rings once every 90 minutes. If the two bells first rang together at 6 am, when will they next ring together? Answer (c) [1]

2 9 *4 (a) metres can be written as k terametres. Find the value of k. (b) A bacteria grows one nanometre in one second. Answer (a) k = [1] Find the length of the bacteria in one hour giving your answer, in standard form. (b) m [1] 5 The volume of air, V cm 3, inside a bicycle pump is inversely proportional to the cube root of the air pressure, P units. (a) If the air pressure is 343 units when 30 cm 3 of air is pumped, find an equation for V in terms of P. (b) Find the volume of air when the air pressure is 999 units. Answer (a) [2] Answer (b) cm 3 [1]

3 6 Factorise the following completely (a) 3tx 2sx 3t 2s, Answer (a) [2] (b) 50x 2 2. Answer (b) [2] *7 (a) Solve 5 2x 1 9. Answer (a) [2] (b) Write down all integers which satisfy 5 2x 1 9. Answer (b) [1]

4 *8 In the diagram, AB = 6.3 cm, AC = 6.5 cm and BC = 1.6 cm. BCD is a straight line. B 1.6 cm C 9 cm 6.3 cm 6.5 cm D A (a) Prove that triangle ABC is a right-angled triangle. Answer [2] (b) Express the following as a fraction in its simplest form. (i) tanbca, (ii) cosacd. Answer (i) [1] Answer (ii) [1] (c) Wayne claims that he can draw a triangle ACD with sides AC = 6.5 cm, CD = 5 cm and AD = 12 cm. Justify whether you agree with his claim. Answer [1]

5 *9 {x : x is an integer and 1 x < 10} A = {prime numbers} B = {factors of 6} (a) List the elements in A B'. Answer (a) [1] (b) List the elements in ( A B)'. Answer (b) [1] (c) Is {2, 3} A? Justify your answer. Answer [1] (d) Draw a Venn diagram to represent the sets, A and B. Answer (d) [2]

6 10 Cylinder A is geometrically similar to cylinder B. Cylinder A has a radius 30% greater than cylinder B. Write down the ratio of the mass of cylinder A to the mass of cylinder B. Answer : [2] *11 The first four terms of a sequence are 123, 117, 111 and 105. (a) Write down the next two terms in the sequence. (b) Find an expression for the nth term of the sequence. Answer (a) [1] Answer (b) [1] (c) The kth term of the sequence is Find the value of k Answer (c) k = [2]

7 *12 (a) 2 Express 6x 7 in the form x a b. x 2 Answer (a) [2] (b) Sketch the graph of 2 y x 6x 7, indicating clearly the turning points. Answer y 0 x [2] (c) 2 Write down the equation of the line of symmetry of y x 6x 7. Answer (c) [1]

8 *13 ABO is a triangle. If A is on a bearing of 320 o from O and the bearing of B from A is 245 o, find the bearing of (a) O from A, A N O B (b) A from B. Answer (a) [1] Answer (b) [2]

9 *14 The graph shows the average sales of the cars for an ABC company over a number of years. Average sales Huge Improvement in Average Sales Year Explain two ways in which the graph is misleading. Answer [2] *15 The dot diagram shows the Maths marks of 20 students scored in class A and class B. Class A Marks Class B (a) Write down the range of the Maths marks in class A. (b) Write down the median of the Maths marks in class B. Answer (a) [1] Answer (b) [1] (c) State, with a reason, which class performed better in maths. Answer (c) [1]

10 *16 A map is drawn to a scale of 1: (a) A road is 5.4 cm long on the map. Calculate the actual length of the road in kilometres. (b) 2 The actual area of a river is 10.2km river on the map. Answer (a) km [1]. Find, in square centimetres, the area of the 2 Answer (b) cm [2] 17 Solve these simultaneous equations. 0.4x 0.5y 6 0.6x 0.7y 4 Answer x = y = [3]

11 *18 A stall sells two different types of food. They are apple pie and banana cake. The total number of each item sold on three different days is given in the table below. apple pie banana cake Monday Tuesday Wednesday The information can be represented by the matrix S = (a) Given that K = ( ), calculate KS. Answer (a) [2] (b) Explain what each element in KS represents. Answer (b) [1]

12 19 The diagram shows a regular hexagon with sides of length 4 cm. 4 cm Calculate the area of the hexagon. Answer 2 cm [2] *20 The rate of exchange between British pounds ( ) and Australian dollars (AUD$) was 1 = AUD$ On the same day, the rate of exchange between Australian dollars (AUD$) and Singapore dollar ($SGD) was SGD$1 = AUD$0.98. Rohani spent 80% of in London. She changed the remaining amount into Singapore dollars. Calculate the amount of Singapore dollars she received. Answer SGD$ [2]

13 *21 3,5 3,2 The triangle with vertices A, B and C is 0, 1 is shown in the diagram. (a) 2 ABCD is a trapezium with AB parallel to DC. The area of trapezium is 12 units. Find the coordinates of D. Answer (a) D = [1] (b) Find the coordinates of the point E such that ABCE is a parallelogram Answer (b) E = [1] (c) Calculate the area of the parallelogram ABCE Answer (c) units 2 [1] (d) Find the length of BC Answer (d) units [2] (e) Find tan CAB Answer (e) units [1]

14 *22 The diagram shows the speed-time graph for a car journey. Speed (m/s) Time (t seconds) (a) Calculate the acceleration of the car when t 19. 1seconds. Answer (a) 2 m/s [1] (b) Find the speed of the car when t 6 seconds. Answer (b) m/s [1] (c) Calculate the total distance travelled on the journey. Answer (c) m [2]

15 *23 The diagram shows a window made up of a large semicircle and a rectangle. The large semicircle has four identical sections A, B, C, D and a small semicircle E. The rectangle has three identical square sections F, G and H. The side of each square is 10 cm. 10 cm Find an expression, in the form a b, for (a) the area of the whole window, (b) the perimeter of section C. Answer (a) cm 2 [2] Answer (b) cm [3]

16 24 In the quadrilateral ABCD, the diagonals AC and BD intersect at X. AB is parallel to CD and DX = 4 cm and BX = 3 cm. A B 3 cm X 4 cm D C (a) Show that triangles CXD and AXB are similar. Answer [2] (b) Find AX (i) AC, Answer (b) (i) [1], (ii) Area of triangle CBD Area of triange CXD Answer (ii) [1] (iii) Area of triangle ABX Area of quadrilateral ABCD Answer (iii) [1]

17 Answer 1a b a b 6 3c 9am 4a b a 210 V 3 P b a 6b 7a 7b ( 3t 2s)( x 1) 2(5x 1)( x 1) 3 x 4 3, 2, 1, 0,1, 2,3 8(a) AC 2 = = AB 2 + BC 2 = = Since AC AB BC, thus by converse of Pythagoras theorem, ABC is a rightangled triangle. (b)(i) tan BCA (b)(ii) cosacd (c) From triangle equality theorem, AD = 12 cm AC + CD = = 11.5 < 12 The sum of any 2 sides should be more than the third side. Thus, I disagree with him. 9(a) 5, 7 (b) 4, 8, 9 (c) No. {2, 3} A {2, 3} is a set. It should be a subset of set A.

18 (d) : (a) 99,93 (b) 129 6n (c) 57 12(a) x (b) 12(c) x 3 13(a) (b) (1) Not all years are shown (2) Inconsistent scale as vertical axis exaggerates the difference between the years (3) Vertical axis should be % sales as no. of cars likely to be different each year 15(a) 17 (b) 51.5 (c) 16(a) median mark for class A is higher than class B. Therefore class A performed better in maths km (b) cm

19 17 x 110, y (a) a = 5, b = 2 (b) (c) Each element represents the total number of apple pies and banana cakes sold respectively in all the 3 days. OR Each element represents the total number of each type of food sold in all the 3 days (a) 21(b) 0,4 0,2 21(c) 9 21(d) 21(e) 22(a) 4.24 units (b) 9 22(c) (a) 23(b) 24(a) ABX BAX CDX DCX AXB CXD alt angles alt angles vert opp angles By AAA (b)(i) 3 7

20 (ii) (iii)