Hampton Park Secondary College Year 10 Mathematics Semester 1, 2009 Reading time: Completion time: Section A: Section B: Section C: Section D: 10 minutes 80 minutes 15 Questions 40 Questions 17 Questions 6 Questions (OPTIONAL) Students may bring the following into the exam: 1 scientific and/or graphic calculator 1 bound book for reference 1 Ruler (optional) 1 Compass and protractor (optional) Instructions Answer Sections A&B on the answer sheet provided at the back of this test Section C questions are to be answered in the space provided In Section B no credit will be given for a question if two or more letters are selected for that question. Answer all questions in Section A, Section B and Section C. Section D is optional and earns no marks. DO NOT REMOVE ANY PAGES FROM THIS EXAM PAPER.
Section A: Numeracy ANSWER ALL QUESTIONS IN SECTION A ON THE ANSWER SHEET 1. Forty-nine and twenty five hundredths plus three and sixty-two thousandths? 2. Write 99999 in words. 3. How many seconds are there in two days and three hours? 4. 111 - (-1 1) - 200 = 5. 49 + 3 2 = 6. Place the following distances in ascending order: 1.01 km, 1001 m, 10000 cm. 7. How much change will a student receive if bought a packet of chips costing $1.95 and a can of coke costing $1.65 if he paid with a $20 note? 8. A student has five $2 coins, five $1 coins, five fifty cents coins, five twenty cents coins, five ten cents coins and five five cents coins. What is the total amount of money he has? 9. A year 10 student working part-time in a super market works 19 hours per week and is paid $10.90 per hour. How much will he receive if he paid no tax? 10. If you took the morning train from Hallam station at 7.56 am and got off at Richmond station at 8.49 am, how much time did you spend on the train? 11. In a supermarket, 3 litres of milk costs $3.70 where as 1 litre milk costs $1.62.Which container of milk is better value for money? 12. This year Hampton Park Secondary College has 1340 students. If the student numbers increase by 5% next year, what will be the student numbers in 2010? 13. A family living in Hampton Park pays $235 a week in rent. How much money will the family pay in one year? (hint: how much per day?) 14. The 6.00 am temperatures in Melbourne and in Canberra were 3 0 C and - 4 0 C respectively. What was the temperature difference between the two cities at 6.00 am? 15. How many 150 ml glasses of water can be poured out from a 3 L container of water?
Section B: Multiple Choice Questions ANSWER ALL QUESTIONS IN SECTION B ON THE ANSWER SHEET Use the map of Melbourne CBD below to answer questions 1-4 SCALE 3cm = 400m Q1. Approximately how far is it from Flinders Street Station (J12) to Spencer Street Station/ Southern Cross Station (B12) in a direct line? A. 400 metres B. 800 metres C. 1200 metres D. 1600 metres
Q2. Approximately which direction is it from Flinders Street Station (J12) to Spencer Street Station/ Southern Cross Station (B12)? A. North B. East C. South D. West Q3. What is found at map coordinates D8? A. Flagstaff Station B. Flagstaff Gardens C. Queen Victoria Markets (South) D. Southbank Q4. If you start at the northeast corner of Federation Square (M11) and travel 500 metres directly northeast, you are at: A. Alexandra Gardens B. Carlton Gardens C. Melbourne Central D. Parliament Station A B Q5. In the diagram above, A. B has been translated from A B. B has been rotated from A C. B has been translated and rotated from A D. B and A are the same.
Q6. In the diagram below, What is the size of the angle labelled x? A. 67 B. 48 C. 65 D. 115 Q7. In the diagram below, What is the size of the angle labelled x? A. 45 B. 56 C. 79 D. 124 Q8. In the diagram below, which angles are the same sizes? A. a & b B. a & c C. b & c D. a & b & c
Q9. The best definition of a chord is A. a straight line that joins two points in a circle B. straight line joining two points on the circumference of a circle C. a straight line joining two points on the circumference of a circle that passes through the centre of the circle D. a straight line from the centre of a circle to the circumference E. a straight line that touches the outside of a circle once and then continues Q10. The value of x in this diagram is: A. 35 B. 125 C. 90 D. 180 E. 55 Q11. Choose the correct answer. A cyclic quadrilateral has one angle measuring 97 and another angle measuring 102. Another angle in the quadrilateral is: A. 80.5 B. 97 C. 161 D. 83 E. 102 Q12. Choose the correct answer. The angle formed by an arc at the centre of a circle is 68. The angle formed by the same arc at the circumference is: A. 136 B. 112 C. 34 D. 68 E. 292 Q13. Choose the correct answer. 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. 82 B. 38 C. 104 D. 76 E. 152
Q14: What is the approximate size of the angle to the right? A. 25 degrees B. 75 degrees C. 100 degrees D. 125 degrees E. 150 degrees Q15. What would be the appropriate unit to use to approximate the area of your home group room? A. Square millimetres B. Square centimetres C. Square metres D. Square kilometres Q16. Which is the greater amount six hundred and fifty millilitres (650 ml) or one half litre(0.5 l)? A. 650 ml B. 0.5 litres C. You can t compare millilitres and litres D. They are the same amount Q17. A time of 1.5 hours is the same as: A. 1 hour and 3 minutes B. 1 hour and 5 minutes C. 1 hours and 30 minutes D. 1 hours and 50 minutes E. 15 hours Q18. If I am buying timber, and I want to buy a length accurate to the millimetre, which of the following do I have to order? A. 2.1 m B. 2.10 m C. 2.100 m D. 2.1000m E. 2.10000m Q19. The following measurements are all given with either a relative or percentage error. Which one could be the largest? A. 100m ± 20m B. 80m ± 40% C. Both could be equally large D. You can t compare relative and percentage error Q20. What is the approximate area of the circle to the right? A. 14 m 2 B. 88 m 2 C. 138 m 2 D. 616 m 2
Q21. Which of the following is the net of a cube? A. B. C. D. E. Q22. Which of these sequences of numbers are created by adding a constant amount to the previous term? A. 1, 2, 4, 8, 16 B. 1, 3, 5, 7, 9 C. 1, 4, 9, 16, 25 D. 1, 1, 2, 3, 5 Q23. What would be the first step in solving the equation below? A. Subtract 7 B. Add 1 C. Multiply by 3 D. Divide by 2
Q24. What is the next number in this sequence? 1, 4, 10, 22,... A. 46 B. 42 C. 40 D. 38 Q25. What is the rule that links this sequence of numbers: 3, 7, 15, 31, 63 A. Next term = previous term + 4 B. Next term = (3 *previous term) -2 C. Next term = 10 - previous term D. Next term = (2 * previous term) + 1 Q26. On which axis of the Cartesian plane (X Y plane) do you plot the independent variable? A. The X-axis B. The Y-axis C. Both Axes D. Neither X or Y. Q27. What inequality is shown on the number line below? A. x > 1 B. x < 1 C. x = 1 D. x 1
Q28. Which number line represents the inequality below: x -2 A. B. C. D. Q29. Solve the following equation for x. 3x - 3 = 6 A. x = 9 B. x = 6 C. x = 3 D. x = 0 Q30. What is the definition of a common factor? A A number which multiplies to a product B A term which is multiplied by all terms in an expression C A term which is in common to all terms in an expression D A term which is common 2 2 b b Q31. x + bx + + c is an example of: 2 2 A Perfect Squares B Difference of Perfect Squares C A Trinomial D Completing the Square. 2
2 2 Q32. ( a + b)( a + b) = a + 2ab + b is an example of: A B C D Perfect Squares Difference of Perfect Squares A Trinomial Completing the Square. Q33. To make x 2 + 8x a perfect square you must add A 16 B 4 C 8 D 64 E 1 2 Q34. The factors of x 5x 24 are: A (x 12)(x + 2) B (x 8)(x + 3) C (x 4)(x + 6) D (x 3)(x + 8) E (x 5)(x + 1) Q35. Which of the following is a perfect square? A B C D E Q36. The factors of 4x 2 + 7x 15 are: A (4x+ 5)(x 3) B (4x +3)(x 5) C (4x 5)(x 3) D (4x 5)(x + 3) E (4x 3)(x + 5) Q37. (x + 6) 2 expands to: A x 2 + 6x + 36 B x 2 + 36 C x 2 + 12x + 36 D x 2 + 6x + 6 E x 2 + 2x + 36 Q38. The expanded form of 3x 2 (x 3y + 1) is: A 3x 3 9x 2 y + 3x 2 B 3x 3 + 9x 2 y 3x 2 C 3x 3 + 9x 2 y D 3x 3 + 9x 2 y + 3x 2 Q39. When expanded and simplified, 6(2a 1) (5a + 3) is equal to A. 7a - 9 B. 7a + 2 C. 7a -3 D. 7a - 2 Q40. Expanding and simplifying the expression (a 2)(a + 1)(a 3) gives A. B. C. D. a 3 + 4a 2 + 2a + 6 a 2 4a 2 + a + 6 a 3 4a 2 + a + 6 a 3 4a 2 + a 6
Section C: Worked Responses ANSWER ALL QUESTIONS IN SECTION C IN THE SPACES PROVIDED Q1. Find the value of x in this diagram: Q2. Find the value of x in this diagram: Q3. Find the value of x in this diagram: Q4. Find the size of the smallest angle in a quadrilateral if all the angles form a pattern with each new angle being 10 larger than the previous angle.
Q5. In the diagram below, the circle has a radius of 10 metres. What is the term for the dashed line? What is the length of the dashed line? Q6. For the triangle below: What is the length of the base? 8 m 10 m What is the area of the triangle? Q7. What is the longest straw that can be placed entirely within a cylindrical glass of radius 4 cm and height 15 cm? 4 cm 15 cm Q8. For the shape below, calculate: What is the perimeter of the shape? 10 cm 40 cm What is the total area of the shape?
Q9 Find the area of the shape shown below 20 cm 40 cm 8 cm Q10. Find the volume of the shape shown below 20 cm 40 cm 10cm 8 cm Q11. What is the surface area of the following shape? 4 cm 15 cm
Q12. Find the highest common factor of: a) 15 and 25 b) 24 and 60 Q13. Factorise, if possible, the following expressions by removing the highest common factor: a) 2g + 16 b) 30q + 25pq c) 5x + 15x 2 Q14. When the left hand side of the following expressions are expanded, are the right hand side of the expression True (T) or false (F)? 3(a + b) = 3a + 3b 2(x - 5) = 2x - 7 4(2a - 3) = 8a - 12 3( x - 2) = - 3x - 6-3 (x -3) = -3x - 9 Q15. Factorise the following expressions a 2 + 4a 3 + 2a 2 + a 3 14z 2 + 2z + 21z + 3
Q16. Expand the following expressions a) (x-3) 2 b) (x+3) (x+5) c) (x-2) (x+4) d) (2x+1) (3x+5) Q17. Factorise the following expressions x 2 + 7x + 12 y 2 11y 12 4x 2 + 8x + 12 4x 2 11x + 6 x 4 2x 2 8
Section D: Timefiller KEN KEN puzzle rules: 1. use numbers 1 6 only 2. each area must combine to target number, using +,1,x or 3. Numbers cannot be repeated in a row or column
NAME: Hampton Park Secondary College Mathematics Domain Year 10 Examination Answer Sheet Homegroup SECTION A: NUMERACY 1 6 11 2 7 12 3 8 13 4 9 14 5 10 15 SECTION B: MULTIPLE CHOICE 1 14 27 2 15 28 3 16 29 4 17 30 5 18 31 6 19 32 7 20 33 8 21 34 9 22 35 10 23 36 11 24 37 12 25 38 13 26 39 40