2014成都国际学校初升高数学试题

ENTRY EXAMINATIONFOR THE YEAR OF 2011 The International Curriculum Program Entry Exam (Mathematics, Grade 10), 2011 Candidate Name 6Candidate Number : PAPER CODE 11/2011 READ THESE INSTRUCTIONS FIRST 1. There are 30 questions. Each question is followed by 5 options marked A, B, C, D, E. Only one of these is correct. Enter the letter A-E corresponding to the correct answer in the corresponding box on the Answer Sheet. 2. Time allowed:60 minutes. 3. Calculators are forbidden. 4. Scoring rules: 0 marks are awarded for each question left unanswered; 2.5 marks are awarded for each correct answer; 0.5 marks is deducted for each incorrect answer. 1. ?30?K, K 2. m60 UO; 3. zKZY: ?2 0.5 ?0; 4. Y?3Y? (?k?iP“; 1ALL RIGHTS RESERVED ENTRY EXAMINATIONFOR THE YEAR OF 2011 5. 3=K U?e;c. midpoint:line segmentgradient? evaluateOpositive?constant valueequal root?expandm inequality?percentzgraph” side(/)?set8number minimum?functionintervalm point:vertex:sum angle?right angle?distinct? quadrilateralo/integer?area lengthintersect?equation trianglen?/planereal number slope? gradientaltitude(n?/)p linejoin?vertices (pl.): prime numbermaximum?perfect square? square?/cubeNremainder trapeziumF/diagonal?inscribeS? circle?prismcplane surface areaLrhombus!/shadedK? hexagon8/median regular hexagon?8/ positive?semicircle?centre%! ?% two-digit number probabilityVmean random?diameteroverlap-U pentagon/even numberodd number polygon/hypotenuse?perimeter There are 8 printed pages ?8 2ALL RIGHTS RESERVED ENTRY EXAMINATIONFOR THE YEAR OF 2011 1. The midpoint of the line segment joining (?4;?5) to (8;?5) is A (2;4) B (?1;?4) C (2;?5) D (1;5) E none of the above 2. The gradient of the line joining (3, -4) and (-1, 8) is A 3B ?3C 1 3 D ?1 3 E 1 3. The two lines x + y = 0 and 2x ? y + 6 = 0 intersect at the point A ?1; ?1 2 ? B (?1;1)C (3;4)D (?2;1)E (?2;2) 4. Evaluate 1 2 ? sin ? 3 ? ? ? ? p2 2 ? (?1)3 ? ? ? 0 ? sin90? A 1 4 B p2 3 C p3 4 D p3 8 E None of these 5. The length of the line segment joining (1;?4) to (?7;2) is A 6B 7C 8D 9E 10 6. The values of x for which (2x + 1)(x ? 3) 3 B x 3 or x ?1 2 D ?1 2 x 3x + 3 x?1 3 ? x?4 2 2 , gives A. ?2 x ?1 B. 1 x 2 C x ?2 D x ?2 14. In a magazine, 10 pages of the 80 pages are devoted to sports. What percent of the magazine is NOT devoted to sports? A.27%B.37.5%C.47.5%D.62.5%E. 87.5% 15. The minimum value of the function y = x2+ 2x + 3 over the interval ?2;1 is A -2B -3C 0D 2E 3 16. Which of the following number is a perfect square? A. 445566B. 446665.C. 455466.D. 465465E. 465564. 17. What is the value of q 1 26 + 1 62? A. 1 10 B. 1 9 C. 1 3 D. 5 24 E. 7 24 4ALL RIGHTS RESERVED ENTRY EXAMINATIONFOR THE YEAR OF 2011 18. 200 T-shirts have been bought for a Fun Run at a cost of $400 plus tax at 171 2%. The cost of entry for the run is $5 per person. What is the minimum number of entries needed in order to cover the total cost of the T-shirts? A. 40B. 47C. 80D. 84E. 94 19. In the gure shown, AB=AF and ABC, AFD, BFE, and CDE are all straight lines. Which of the following expressions gives z in terms of x and y? A. y?x 2 B. y ? x 2 C. y?x 3 D. y ? x 3 E. y ? x 20. The symbol r is dened by xry = xy? 2xy. What is the value of (1r0)r4? A. -9B. ?7C. 5D. 0.E. 3: 21. In the xy-plane, point R(2;3) and point S(5;6) are two vertices of triangle RST. If the sum of the slopes of the sides of the triangle is 1, which of the following angles could be a right angle? I RII SIII T A NoneB I onlyC III only D II and III only E I, II and III 22. There are 10 girls in a mixed class. If two pupils from the class are selected at random to represent the class on the School Council, then the probability that both are girls is 0.15. How many boys are in the class? A. 10B. 12.C. 15D. 18E. none of these 23. Which one of the following rational numbers can not be expressed as 1 m + 1 n, where m;n are dierent positive integers? A. 3 4 B. 3 5 C. 3 6 D. 3 7 E. 3 8 5ALL RIGHTS RESERVED ENTRY EXAMINATIONFOR THE YEAR OF 2011 24. The diagram shows an equilateral triangle touching two straight lines. What is the sum of the four marked angles? A. 120?.B. 180?.C. 240?.D. 300?.E. 360? 25. Dean runs up a mountain road at 8km per hour. It takes him one hour to get to the top. He runs down the same road at 12 km per hour. How many minutes does it take him to run down the mountain? A. 30B. 40C. 45D. 50E. 90 26. Which of the following is equivalent to (x + y + z)(x ? y ? z)? A. x2? y2? z2.B. x2? y2+ z2.C. x2? xy ? xz ? z2. D. x2? (y + z)2.E. x2? (y ? z)2. 27. The numbers x;y and z satisfy the equations x + y + 2z = 850;x + 2y + z = 950;2x + y + z = 1200 what is their mean? A. 250B. 1000 3 C. 750D. 1000E more information is needed. 28. Expanding ?3 +p2?3 gives A 15 + 26p3 B 29p2 + 45 C 45p2 + 29 D 26 + 15p3 E none of the above 6ALL RIGHTS RESERVED ENTRY EXAMINATIONFOR THE YEAR OF 2011 29. The distance between two neighboring dots in the dot lattice is 1 unit. What, in square units, is the area of the region where the two rectangles overlap? A. 6B. 61 4 C. 61 2 D. 7E. 71 2 30. Five touching circles each have radius 1 and their centers are at the verti