1、1 of 10GRADE 10 PRINCIPLES OF MATHEMATICS (ACADEMIC)MPM 2DTotal Marks:INSTRUCTIONS:1. Calculators may be used.2. Read all instructions carefully in order to maximize your mark.A/CK Part A Multiple Choice 25 Marks (25 questions * 1 mark each)For each of the following questions in this section, circle
2、 the letter representing the correct answer.1. A linear system of two equations that has one solution represents two lines that are:a) parallel b) coincident c) intersecting d) none of these2. The midpoint of RS is M(8, -1). If point S has coordinates (11, 4) what are the coordinates of point R?a) (
3、3, -6) b) (15, -6) c) (5, -6) d) (3, 9)3. The midpoint of the line segment with end points A(-8, 8) and B(6, 4) is:a) (0, 10) b) (1, 2) c) (7, 2) d) (-1, 6)4. The equation of a horizontal line passing through the point (4, 2) is:a) b) c) d)2x4y2y4x5. The equation of a line with a slope of and a y in
4、tercept of 8 is:5ma) b) c) d)85xy8xyx5xyFeel free to use any of the material in this document. Marks are only guidelines.We have categorized each question into one of the 4 achievement chart (A/C) categories: Knowledge/Understanding (K), Thinking and Inquiry (T), Application (A) and Communication (C
5、). You can change or modify the categories as you see fit.2 of 106. The slopes of 2 lines are -7 and . These lines are said to be:71a) parallel b) perpendicular c) coincident d) none of these7. The slope of a line segment passing through 2 points (10,- 4) and (-2, -16) is:a) 1 b) 2 c) -1 d) -28. The
6、 length of a line segment with end points (-6, 7) and (-1, -5) is:a) 12 b) 5 c) 13 d) 1699. The diameter of a circle whose equation is is:2892yxa) 15 b) 16 c)17 d) none of these10. The equation of a circle with a centre of (0, 0) that also passes through the point (-8, -6) is:a) b) c) d)102yx102yx14
7、2yx 482yx11. The y-intercept of the line is:5a) 2 b) -2 c) 10 d) 512. The slope of the line is:0124yxa) 2 b) -2 c) 1 d) 013. If (-3, y) is a solution to the equation , what is the value of y?32yxa) 3 b) 6 c) 5 d) 814. The product is equal to: zyxz32324a) b) c) d)261zxy61261zxy0412zyx15. A simplified
8、 expression for is:nm52a) b) c) d)m7n73nm73 of 1016. A simplified expression for is:2497abca) b) c) d)ac3323ac23ca17. The slope of the line, which is perpendicular to the line, is:084yxa) -4 b) 4 c) 1 d) -118. The shortest distance from the point (2, -3) to the line is:xa) 5 b) 3 c) 2 d) 619. The va
9、lue of the polynomial when is:8542a3a) 59 b) 44 c) 13 d) 2920. Which of the following is not a function:a) b) c) d)7,654,322xy2yx3,87,2621. The range of the relation whose equation is is:5a) b) c) d)y5yy5y22. The vertex of the parabola is:642xa) b) c) d)6,4,4,4,623. The equation of the axis of symme
10、try of the parabola is:52xya) b) c) d)5x5x2x2x24. A parabola with a vertex of and a stretch factor of (relative to ) would 3,241yhave an equation of:a) b) c) d)412xy3412xy23xy2341xy25 The parabola passes through the point . The value of is:k2 ,2k4 of 10a) -19 b) 11 c) 13 d) 19A/C Part B Short Answer
11、sFor each of the questions in this section, write your answers in the spaces provided. Use the foolscap provided for any rough work. Show details of calculations wherever requested.1. In the accompanying diagram, state each of the following: (4 Marks)K a) domain: _ (1 Mark)K b) range: _ (1 Mark)C c)
12、 Is the relation a function? Justify your answer. (2 marks)A 2. The x-intercepts of the parabola are: _ and _.289xy(Show your work) (2 Marks)A 3. The roots of the quadratic equation are: _ and _.01732x(Show your work) (3 Marks)A 4. Write the equation of the parabola with a vertex of (4, 23) if it pa
13、sses through the point (-1, -2): (Show your work) (3 Marks)2 4-2-45 of 10x_T 5. A line passes through 2 points (1, 4) and (2,-4). Calculate the slope of the line. Also show the equation of the line in the form . (Show your work) (4 Marks)0CByAx_ _Slope Equation K 6. The Tangent of is: _ (1 Mark)45A
14、7. a) In the accompanying diagram, the two triangles are similar. What is the value of ?x(Show your work) (2 Marks)_xT b) If the area of the smaller triangle is 8 cm2, what is the area of the larger triangle?(Show your work) ( 2 Marks)Area = _K 8 Given that sin A = , find (to the nearest degree) _ (
15、1 Mark)21AA 9. In the accompanying right triangle, find the value of x to one decimal place.(Show your work) (2 Marks)1218276 of 10_xA 10. Use the SINE LAW to find the value of side x to one decimal place.(Show your work) (2 Marks)x = _A 11. Use the COSINE LAW to find the value of side x to one deci
16、mal place.(Show your work) (2 Marks)x = _T 12. Factor each of the following to the fullest extent possible: (4 Questions * 2 marks each)a) _yxm2b) _3142xc) _2469yx3028x5642 x30562030x7 of 10d) _225309srA/C Part C Full Solutions RequiredFor each of the questions in this section, full solutions are re
17、quired. Record your answers in the spaces provided. Use the foolscap provided for any rough work.A 1. Solve the linear system using the elimination method. Remember to find values for both x and y. (5 Marks)25y13C Explain what the solution above represents geometrically. How do you know that the sol
18、ution you arrived at is the correct answer? (2 Marks)A 2. Expand and simplify the polynomial . (4 Marks)21432xxT 3. Find the equation of the line perpendicular to the line and passing 08yxthrough the point (-4, 1). (4 Marks)8 of 10T 4. From the window of one building, a man finds that the angle of e
19、levation to the top of a second building is 47 and the angle of depression to the bottom of the same building is 58. The buildings are 60 m apart. Find the height of the 2nd building to the nearest metre. A diagram is required. (6 Marks)T 5. ABC has vertices A(1, 7), B(-5, 3) and C(3, -1). Determine
20、 the equation for AE, the altitude from vertex A to the opposite side BC. (5 Marks)9 of 106. The hypotenuse of a right triangle is 26 cm. The sum of the other two sides is 34 cm. (9 Marks)T a) Find the length of the other two sides of the triangle. (3 Marks)T b) Find the measure of the other two ang
21、les. Round to the nearest degree. (3 Marks)C c) Describe a situation where you would be able to use knowledge of the Pythagorean theorem in a practical, real life situation. (3 Marks)T 7. A rectangular skating rink measures 20m by 20m. It has been decided to increase the area of the rink by a factor
22、 of 4. Determine how much each side should be extended. Assume that each side is extended by the same amount. (6 Marks)10 of 10C What is the significance of keeping the skating rink in the shape of a square? Justify your answer. (3 Marks)A 8. a) Solve using the quadratic formula. (2 Marks)3512dA b) Solve by factoring. Check your solutions. (2 Marks)0312x
