[PDF] Australian Mathematics Competition AMC Warm-Up Paper 7 Intermediate.pdf | Plain Text

AUSTRALIAN MATHEMATICS COMPETITION WA R M - U P PA P E R INTERMEDIATE 7 c 2009 Australian Mathematics Trust Questions 1 - 4, 3 marks each 1.In the diagram, the value ofxis (A) 50 (B) 55 (C) 60 (D) 65 (E) 70     115 ◦ x◦ 125 ◦ 2.If 5n+7>100 andnis an integer, the minimum possible value ofnis (A) 18 (B) 19 (C) 20 (D) 21 (E) 22 3.A kilogram of a certain sweet contains from 24 to 30 sweets. The minimum weight, in kilograms, of 240 of these sweets is (A) 7 (B) 7.5 (C) 8 (D) 8.5 (E) 10 4.Ann and Barbara share a $250 prize in the ratio of 3 : 2. Barbara’s share is (A) $50 (B) $100 (C) $125 (D) $150 (E) $200 Questions 5 - 8, 4 marks each 5.Which is the greatest of the following numbers? (A)4 0.4(B)4 0.44(C)4 (0.4) 2 (D)4 √0.44(E)4 (0.44) 2 6.The trianglePRSis equilateral and its area is half that of the trianglePQR. What is the size, in degrees, of the anglePRQ? (A) 75 (B) 80 (C) 90 (D) 100 (E) 120 ..................................................................................................... ............................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . QSP R

Intermediate 7 Page 2 7.OX, OYare radii of a circular quadrant. A semi-circle is drawn onXYas shown.T,SandCdenote the resulting triangle, segment and crescent. The ratio areaT areaC equals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      ....................... ..... .... ... .. ... .. .. .. . .. .. . .. . . .. . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TSC O Y X (A)3 π(B) 1 (C)13 4π(D)7 2π(E)15 4π 8.A large watermelon weighs 20 kg, with 98% of its weight being water. It is left to stand in the sun, and some of the water evaporates so that now only 95% of its weight is water. What does it now weigh? (A) 17kg (B) 19.4kg (C) 10kg (D) 19kg (E) 8kg Questions 9 - 10, 5 marks each 9.In the 5×5 square the numbers 1, 2, 3, 4, 5 are arranged in such a way that every number occurs precisely once in each row and precisely once in each column. 12 1 x 4 25 54 In the 5×5 square shown, the entry in the position marked with anxis (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 10.In a soccer tournament eight teams play each other once, with two points awarded for a win, one point for a draw and zero for a loss. How many points must a team score to ensure that it is in the top four (ie has more points than at least four other teams)? (A) 8 (B) 9 (C) 10 (D) 11 (E) 12