[PDF] Australian Mathematics Competition AMC Warm-Up Paper 8 Intermediate.pdf | Plain Text

AUSTRALIAN MATHEMATICS COMPETITION WA R M - U P PA P E R INTERMEDIATE 8 c 2009 Australian Mathematics Trust Questions 1 - 4, 3 marks each 1.(0.01) 2equals (A) 0.1 (B) 0.01 (C) 0.001 (D) 0.0001 (E) 0.0002 2.The value of0.75 15is (A) 5 (B) 0.5 (C) 0.05 (D) 0.005 (E) 0.0005 3.In the diagramPQ=PR=QSand QP R=20 ◦. Thesizeof RQS, in degrees, is (A) 20 (B) 40 (C) 60 (D) 80 (E) 100 PSQ R..................................................................................................... ............................................. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20◦ 4.My children are aged six, eight and ten years. Between them they receive $12 pocket money each week, proportional to their ages. How much does the eldest receive per week? (A) $3 (B) $4 (C) $5 (D) $6 (E) $10 Questions 5 - 8, 4 marks each 5.Two fractions are equally spaced between 14and 23. The smaller of the two fractions is (A)13 24(B)7 18(C)29 36(D)5 12(E)1 3

Intermediate 8 Page 2 6.TrianglePQRis right angled atQand trianglesPST andRT Uare isosceles as shown. If ST Umeasuresx ◦ then the value ofxis (A) 30 (B) 45 (C) 50 (D) 55 (E) 60 QR P S . . . .. . .. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . . . . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. . . . ....................... ........................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . UT x◦ 7.The diagram shows a 5 by 5 table. PQRST PQR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The top row contains the symbolsP,Q,R,SandT. The fourth row contains the symbolsP,QandRat the centre. The remaining squares can be filled withPs, Qs,Rs,SsandTs such that no row, column or diagonal contains the same symbol more than once. The symbol that must go into the shaded square is (A)P(B)Q(C)R(D)S(E)T 8.Ifa 2=a+2, thena 3equals (A)a+4 (B) 2a+8 (C) 3a+2 (D) 4a+8 (E) 27a+8 Questions 9 - 10, 5 marks each 9.Here is the plan of a building which has a courtyard with two entrance gates. Passers-by can look through the gates but may not enter. Dimensions of the building are given in metres, and all corners are right angles. What is the area, in square metres, of that part of the courtyard which cannot be seen by passers-by? Gate 10 Gate 30 40 40 3010 10 40 20 2030 15 10 10 10 .......... .......... (A) 250 (B) 200 (C) 300 (D) 400 (E) 325

Intermediate 8 Page 3 10.Each face of a solid cube is divided into four as indicated in the diagram. P • • .................... ........................................... ...... ................................. .............................. ......................................................... .............. ................................................. ..................................................................... Q Starting from vertexP, paths can be travelled to vertexQalong connected line segments. If each movement along the path takes one closer toQ,thenumberof possible paths fromPtoQis (A) 46 (B) 90 (C) 36 (D) 54 (E) 60