Mathematics 30 June 1999 Grade 12 Diploma Exam

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Use the following information to answer the next question. A rectangular rug measuring 4 m × 3 m is stained in one corner. The rug is to be cut to elliptical shape to eliminate the stain. To mark the cutting line for the ellipse, a person tacks the ends of a piece of string to the rug in two places. When the string is pulled taut, it is 4 m long. The person traces the ellipse with a piece of chalk and finds that the chalk line does not fit on the rectangular rug, as shown in diagram 1. After changing her setup, she traced a new ellipse that fits perfectly inside the rug, as shown in diagram 2. Piece of chalk String Diagram 1 1 –2 –1 1 2 3 m Stain –1 Chalk line 4 m Diagram 2 1 –2 –1 1 2 3 m Stain –1 4 m 24. What change to the setup did the person make to ensure that the ellipse fits perfectly inside the rectangular rug? A. The string was shortened. B. The string was lengthened. C. The tacks were moved farther apart. D. The tacks were moved closer together. 16
25. The foci of a hyperbola are F 1 (–5, 0) and F 2 (5, 0). If point (–3, 0) lies on the graph of the hyperbola, then the value of PF 1 − PF 2 , where P is any point on the graph of the hyperbola, is A. 4 B. 6 C. 10 D. 16 Use the following information to answer the next question. A drawing of the cross section of the stadium roof is a semiellipse with foci at F 1 and F 2 , as shown below. The distance from F 2 to point P at the end of the longest axis is 8 m. F 1 F 2 P 8 m 26. If the ellipse has an eccentricity of 4 , then the distance from point P to the 5 nearest directrix, correct to the nearest metre, is A. 5 m B. 8 m C. 9 m D. 10 m 17
Page 1 and 2: athematics 30 Mathematics 30 Mathem
Page 3 and 4: Multiple Choice • Decide which of
Page 5 and 6: 1. The function f (x) = x 3 - 6 is
Page 7 and 8: Use the following information to an
Page 9 and 10: Numerical Response 1. The polynomia
Page 11 and 12: 13. If (π, -6) satisfies the equat
Page 13 and 14: 14. Given that log b 64 = 3 , the v
Page 17 and 18: Numerical Response 4. An exponentia
Page 19: Use the following information to an
Page 25 and 26: 32. If the sum of the first n terms
Page 27 and 28: 37. In the expansion of (x + 2y) 8
Page 31 and 32: • Write an expression for t n as
Page 33 and 34: • Assume that it becomes necessar
Page 35 and 36: • Identify the error that was mad
Page 37 and 38: Fold and tear along perforation. 0
Page 39 and 40: No marks will be given for work don
Page 41 and 42: Mathematics 30 Diploma Examination
Page 43 and 44: SAMPLE ANSWERS TO THE WRITTEN-RESPO
Page 45 and 46: • The store will lose money on th
Page 47 and 48: • Assume that it becomes necessar
Page 49 and 50: A POSSIBLE SOLUTION Student A Stude

Mathematics 30 June 1999 Grade 12 Diploma Exam

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