2005SD - if""QUESTIONS — SENIOR DIVISION Questions 1 to 10 3 marks each 1 The value of(4 x 5 —I—(2 x 10 is(M4(B i(C 2(D(E 1 2 In the

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Unformatted text preview: if" - "QUESTIONS — SENIOR DIVISION Questions 1 to 10, 3 marks each 1. The value of (4 x 5) —I— (2 x 10) is (M4 (B) i (C) 2 (D) (E) 1 2. In the diagram, the value of x is (M20 (3)90 (0)30 (0)80 (EH30 70° 130° 1 3! 1 — 1 +3+ equas 9 5 (A) (B) (c):— (D) — (E) 4. The straight line 1; = m + 9 passes throught the point (2.3). The value of g is (A) 0 (B) 1 (G) 2 (DJ 3 (E) —1 25 5. A twordigit number has tens digit 1: and its units digit is. If the digit 8 is placed between these digits, the value of the three-digit number is (A) £+u4 8 (D) 100t+ 10u+8 (D) 105+80+ u to; 10: i u I e (E) 100: + 80 + u . APXQ is a right angled triangle with sides of length 3 and 7 as shown. At P, PR is drawn so that [RPQ = 90° and PR = PQ. The area of APRQ is a 2 (B) 29 (C) V557: (n) 58 (E) 100 (A) . In our school the average mark in Year 11 for a test was 70 and in Year 12 it was 80 for the same test. There were 20 students in Year 11 and 30 students in Year 12 who set the test. The average mark for the two groups was (A) 1’2 (B) 75 (C) 76 (D) 78 ' (E) 74 . Difl‘erent tyres were fitted to a car, increasing the circumference of the wheels from 200 cm to 225cm. On a journey of 1800 km, the number of revolutions of each wheel was reduced by (A) 50 000 (B) 1000 (C) 2000 (D) 100000 (E) 7200 000 26 9. The sum of all but one of the internal angles of a pentagon is 400‘? The number of degrees in the remaining angle is (A) 40 {by in; L'Ci Mn |_Dl {HO {1:} AW) 10. The value of {V5 x w 32x45 is (A) 8 [13} 4 (C) 406 (D) 44’? (E) 16% Questions 11 to 2D, 4 marks each 11. The difference between a positive fraction and its reciprocal is 3 The sum of the fraction and its reciprocal is 20 20 41 25 {A} 3 (B) E6 (C) 1—6 (D) 5 (E) not uniquely determined 12. At time t = 0 a split forms in a balloon and the quantity Q of gas left in the balloon at time t is given by 100 “m- Tbe time taken for half the gas to escape is g_ (A) $21 (Bi; (0)12“E (D) V? [E 27 13. Two dice are thrown at random. The probability that the two numbers obtained are the two digits of a perfect square is 7 ,D1 1 (A) 35' ‘ l 4 <5? 9; 1 2 g (B) g (c) 14. A square piece of paper has area 12 cm2. It is Coloured white on one side and shaded on the other. One corner of the paper has been folded over so that the sides of the triangle formed are parallel to the sides of the square as shown. The total visible area of the paper is half shaded and half white. What is the length, in centimetres, of the fold line U V? (A) 4 (B) m (c) 3 (D) 6 (E) »/8‘ P Q 28 15. In the triangle PQR shown, 5' and U are points on QR and T is a point on PQ such that TS n PR and UT [| SP. If Q3 = 4cm and SR 2 2.4cm, then the length of QU. in (teatime- t; -a‘ so (A) 2.4 (B) 2.5 (c; 3 (D) 3.2 (E) 4 16. A train leaves Canberra for Sydney at 12 noon, and another train leaves Sydney for Canberra forty minutes later. Both trains follow . l the same route and travel at the same uniform speed, taking 37 2 hours to complete the journey. At what time will they pass? (A) 1:45pm (B) 2:00pm (G) 2:05 pm (D) 2:15 pm (E) 2:25 pm 29 17. A spiral is formed by starting with an isosceles right-angled triangle 0X 1 X 2, where 0X1 is of length 1, then using the hypotenuse 0X3 as a shorter side of another isosceles rightvangled triangle, and SO on. The first few steps are shown in the diagram. Eventually we will reach for the first time a situation where a. side OXk of a triangle everiaps OX1. What is the length of XIXk? (A) s (e) sv’i—i (C) We (D) 15 (E) 14 X4, X3 X? X5 0 X1 18. The number of 5-digit numbers in which every two neighbouring digits differ by 3 is (A) 40 (B) 41 (C) 43 (o) 45 (E) 50 19. A ladder resting against a wall makes an angle of 60° with the ground. When the base of the ladder is moved 1m further from the wall it makes an angle of 45” with the ground. The length of the ladder, in metres, is I (A) 2 {Bl Eli/5+1) ‘5“ \ (0) Va 1 (D) v’5 I m 2 (E) V5+1 30 20. A quarter circle is folded to form a cone. D If 3° is the angle between the axis of symmetry and the slant height of the cone, then sin 9° equals 1 1 1 vs 1 A — B —-- 0" ~ "— ——— Questions 21 to 30, 5 marks each 21. The number of real solutions of a: + V 1‘2 + v.15 + 1 = 1 is (A) U {B} 1 (C) ‘2 (DJ 3 {E} 4 22. The area of the shaded rectangle is (A) between i and % (B) between % and g [C] between S— and 1% l (D) between {6 and (E) more than 31 23. 24. When (1 — 2:3)30 -+- its? is expanded, two values in and kg of It give the coefficient of x2 as 40. The value of k1 + kg is (A) F1 (B) 8 {Cl 10 (ll) 1‘) [ill 11 What is the area, in square units, enclosed by the figure whose boundary points satisfy Isl + Jyl = 4'? (A) 2 (B) 4 (C) s (D) 16 (s) 32 25. 26. The number of digits in the decimal expansion of 22005 is closest to (A) 400 (s) 500 (C) 600 (o) 700 (E1) 800 For questions 26 to 30, shade the answer as an integer from D to 999 in the space provided on the answer sheet. My name is Louisiand my father has cooked me an L-shaped cake for my birthday. He says that I must cut it into three pieces with a single CutI so that my brother and sister can have a piece too. So, I have to cut it like this 10cm or this but not like this. 300m \Jocm 10cm 20cm He says that I have to be polite and let them have the first choice of the pieces. but I just know they'll be greedy and leave the smallest possible piece for me. So I want to cut the cake so that my little piece will be as big as possible. If I do this, how big, in square centimetres, will my piece be? I 32 . The function y : fix] is a functiori such that J’L'ft'a'lj z 62,- ~ 2005 for every real number 2:. An integer it satisfies the equation fit) = 6t — 2005. What is this value of t? . A regular octahedron has eight triangular faces and all sides the same length. A portion of a regular octahedron of volume 120 cm3 consists of that part of it which is closer to the top vertex than to any other one. In the diagram, the outside part of this volume is shown shaded, and it extends down to the centre of the octahedron. What is the volume, in cubic centimetres, of this unusually shaped portion? . If :r, y and z satisfy the system of equations s+y+z = 5 $2 + yz + 32 = 15 my = 22‘ . 1 1 1 determine the value of — + — + — . 9: y z . A positive integer is equal to the sum of the squares of its four smallest positive divisors. What is the largest prime that divides this positive integer? 33 ...
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This note was uploaded on 09/27/2010 for the course 456 9852 taught by Professor Chaohue during the Spring '10 term at Mackenzie.

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2005SD - if""QUESTIONS — SENIOR DIVISION Questions 1 to 10 3 marks each 1 The value of(4 x 5 —I—(2 x 10 is(M4(B i(C 2(D(E 1 2 In the

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