YEAR 10 Mathematics (Enrichment)

Transcription

1 Hampton Park Secondary College Student s Name: Senior School Examinations November 010 Home Group: Student Number Figures Words YEAR 10 Mathematics (Enrichment) Number of questions Written Examination QUESTION AND ANSWER BOOK Structure of book Number of questions to be answered Number of Marks Section A Multiple Choice Questions Section B Worked Responses Section C Extended Responses 4 4 Reading Time: 10 minutes Completion Time: 80 minutes Students are permitted to bring into the examination room: pens, pencils, coloured pencils, templates, highlighters, erasers, set squares sharpeners and rulers Students are permitted to bring into the examination one CAS calculator and/or one scientific calculator Students are permitted to bring into the examination one bound reference or summary notes. Students are not permitted to bring into the examination room: blank sheets of paper and/or white out liquid/tape. Materials Supplied Question and answer book Additional writing paper should you need it. Instructions Write your name, your Home Group and your class teacher s name in the space provided on this page. Write your student number in numerals and words in the space provided above on this page. Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room.

2 Section A: Multiple Choice Questions(Each worth 1 mark) Q1. Which triangle is correctly labelled? A B C A H θ O H A θ O A θ O H D A O θ H E A θ O H Q. Which ratio is stated correctly? A B C D E Q3. The value of in degrees, minutes and seconds in the equation: A 6º31 11 B 6º18 40 C 0º59 59 D 0º7 33 E 0.459º

3 Q4. Find the height of the tree in the following diagram. A 6.50m B 8.99m C 10.08m D 11.58m E 7.16m Q5. Find the correct value of the pronumeral in the following diagram, to decimal places A 9.73m B 1.00m C 13.45m D 16.04m E 8.33m Q6. John is sitting on a 11 m tall cliff. The angle of depression of a boat km out to sea is: A 0º0 7 B 5º57 55 C 9º34 13 D 45º3 15 E 84º 5 In a survey of shoppers at a large mall, 00 people said that they preferred Unsafeway

4 Q7. supermarket, 50 preferred BiHi supermarket, 100 preferred Benjamin s supermarket and 50 were undecided. What is the probability that a single shopper prefers Unsafeway? A 1 B 1 3 C 1 4 D 1 5 E 1 7 Q8. In the figure below, the intersection of sets A and B contains how many members? A 5 B 4 C 8 D 16 E 0 Q9. The odds that it will rain tomorrow are quoted as 15. The exact probability that it will not rain tomorrow is: A 13 B 15 C 17 D E Q10. A bag contains 36 balls, 16 black, 8 red, 3 white and the rest blue. Pr(not black nor blue) is: A B 5 9 C 9 36 D 7 36 E 5 36

5 Q11. A coin is tossed and a die is rolled. The probability of a number greater than on the die and a Head on the coin is: A 3 B 1 3 C 9 D 5 1 E 5 9 Q1. The probability of a train arriving on time is What is the probability of it never being late for three days? A 0.75 B C 0.5 D E Q13. Choose the correct answer is approximately equal to: A 7.61 B C D E Q14. Choose the correct answer. 3 7 fully simplified is: A 1 4 B 1 44 C 4 11 D 4 6 E Q15. Choose the correct answer simplifies to: A -1 B C D 7 91 E Q16. Choose the correct answer. The area of a square of side length is: A 74 B C D 1 E

6 Q17. Choose the correct answer. 3 5 expressed with a rational denominator is: 3 A B C 3 15 D 3 5 E 15 Q expressed with a rational denominator is: A 6 B 6 1 C 6 + D E 6 1 Q19. The x-intercepts of y = x 5x 14 are: A (-7, 0) and (, 0) B (0, -7) and (0, ) C (7, 0) and (0, -) D (7, 0) and (-, 0) E (0, 7) and (0, ) Q0. Choose the correct answer. The graph of y = 3x +4x has: A no x-intercepts B no y-intercepts C one x-intercept D two x-intercepts E Not enough information given. Q1. The turning point form of y = 3x + 6x is: A y = 3(x + 1) 5 B y = 3(x 1) 5 C y = 3(x + 1) + 5 D y = 3(x + 1) 5 3 E y = 3(x 1) + 5

7 Q. To sketch y = (x + 3) 5 the transformations that need to be applied to y = x are: A make it narrower, move it 3 units left and 5 units down B move it 3 units left and 5 units down C make it wider, move it 3 units right and 5 units down D make it wider, move it 3 units left and 5 units down E make it narrower, move it 3 units right and 5 units down Q3. Compared with the graph y = x, the graph y = 1 (x-3) will be: A moved up 3 units and narrower B moved down 3 units and wider C moved 3 units to the left and narrower D moved 3 units to the right and wider E moved 3 units to the right and narrower Q4. This question refers to the following quadratic graph. The equation of the axis of symmetry is equal to: A y = 3 B x = 4 C x = 6 D x = 8 E y = 4 Q5. A cyclic quadrilateral has one angle measuring 97 and another angle measuring 10. Another angle in the quadrilateral is: A 80.5 B 97 C 161 D 83 E 10 Q6. The angle formed by an arc at the circumference of a circle is 76. Another angle on the same arc at the circumference is: A 8 B 38 C 104 D 76 E 15

8 Q7. The value of x in this diagram is: A 45 B 30 C 90 D 60 E 135 Q8. The value of x in this diagram is: A 110 B 70 C 0 D 10 E 5 Q9. The value of x in this diagram is: A 4 B 36 C 00 D 13 E 7 Q30 The value of x in this diagram is: A 180 B 10 C 60 D 45 E 30

9 Section B: Worked Responses. Q1. Provide a approximate scale diagram of the following: () An angle of depression of 30 An angle of elevation of 70 Q. Provide a diagram of the following bearings () N38 0 E 31 0 T S17 0 E Q3. Complete the table below by filling in the empty cells with positive (+) or negative (-) as appropriate, based on the unit circle in the Cartesian plane. (3) First Quadrant Second Quadrant Third Quadrant Fourth Quadrant Sin θ Cos θ Tan θ X coordinate Y- coordinate Q4. A helicopter lifts of from its helipad and flies 7 kilometres north and 0 kilometres west and then lands.. What is the bearing of its helipad from its landing place? (3)

10 \ Q5. The number of students at a school is recorded according to the following table: (3) Year level No. Of students A student is chosen at random to represent the school at a concert. Find the probability that: a)the student was in Year 9 b) the student was in either Year 9 or 10 c) the student was below Year 9. Q6. At the IQ Secondary College (IQSC) The probability of Mrs. Q arriving on time to class is 0.9. The probability of Mr I arriving on time to class is 0.7. (3) a) What is the probability of Mr I being late? b) What is the probability of both of them being late? c) What is the probability of one being late, but not the other? Q7. The Probability of it being windy on a week day is 0.4. The probability of it being windy and raining on a week day is 0.. The probability of it being neither rainy nor windy is 0.5. Produce and complete a Karnaugh Map of this information in the space below. (4) a) State whether the events of Rainy and Windy are independent of each other, providing evidence from your table.

11 Q8. Write the following expressions as entire surds. () (a) 5 (b) 3 Q9. Expand and simplify the following expressions: () (a) ( 5+ 3 )( 4 5 5) (b) Q10. Express the following fraction in simplest form with a rational denominator. (3)

12 Q11. The area of a triangle is 35 cm. If its base length is 5 cm, find its height as an exact value. (3) (Express your answer with a rational denominator.) Q1. A standard parabola (y = x ) is transformed by inverting it, moving it horizontally left by one unit and up by two units. a) What is the turning point/ vertex form equation of the transformed parabola? (4) b) What is the discriminant of the transformed parabola? c) What are the x-intercepts (if any)? Q13. For the function: y = x + 3x + 1, answer the following questions: (6) a) Re-arrange to Turning Point/ Vertex Form: b) What is the coordinate of the Turning Point? c) Sketch the graph of the above function, clearly labelling all critical points. Show all working. c) What is the value of the discriminant of the above function? What does it show?

13 Section C: Extended Responses (Each worth 6 marks). Q1. Calculate the area of the triangle XYZ. Show all working and label all necessary sections. Z 100m X 45 o 60 o Y Q. In the Year 9 elective program there are 50 students. If they can choose art, drama and music classes and: There are 4 students who chose all 3 subjects. There are 7 students who chose music and drama. There are 11 students who chose art and drama. There are 5 students who chose art and music. There were 1 students in total who chose art, 19 in total who chose music and 5 in total who chose drama. Complete a Venn diagram of this situation, and use it to calculate the probability that a student does not study any of Art, Music or Drama.

14 Q3. A rectangular swimming pool has an area of 180m. If its length is twice its width, Find: a) The exact dimensions (width and length) of the pool b) The approximate perimeter of the pool. c) A one metre wide path is to be made around the perimeter of the pool. On the outside of the path, a patterned border of bricks will be built. Find the exact length of the (internal) border of bricks. Q4. The height(h) of a model rocket above the ground as a function of time(t) is given by the following equation: h(t) = 4t(50 t) for 0 t 50 Sketch a graph of the rocket s height (on the y-axis) against time (on the x-axis) below. a) Determine the height of the model at launch (i.e t = 0) b) What is the maximum height the rocket reaches during it s flight? c) What is the total flight time of the rocket?

15 Name: Hampton Park Secondary College Mathematics Domain End of Semester Examination Class: Section A Q1 Q11 Q1 Q Q1 Q Q3 Q13 Q3 Q4 Q14 Q4 Q5 Q15 Q5 Q6 Q16 Q6 Q7 Q17 Q7 Q8 Q18 Q8 Q9 Q19 Q9 Q10 Q0 Q30 Early Finisher Activities