Year 10 Mathematics Examination SEMESTER

Transcription

1 STUDENT NAME: TEACHER: DATE: Year 10 Mathematics Examination SEMESTER QUESTION AND ANSWER BOOKLET TIME ALLOWED FOR THIS PAPER Reading time before commencing work: 10 minutes Working time for this paper: 105 minutes MATERIAL TO BE PROVIDED BY THE SUPERVISOR This Question/Answer Booklet MATERIAL TO BE PROVIDED BY THE CANDIDATE Pen/pencil for answering questions Erasing stationery Up to two scientific calculators Written notes on one unfolded A4 sized paper; can be double-sided TOTAL QUESTIONS: 45 TOTAL MARKS: 125 Section 1: Multiple choice 25 marks Attempt questions 1-25 Section 2: Written answer 100 marks Attempt questions 1-20 AT THE END OF THE EXAMINATION Attach any extra sheets used to this Question/Answer booklet. IMPORTANT NOTE TO CANDIDATES No other items may be taken into the examination room. It is your responsibility to ensure that you do not have any unauthorised notes or other items of a non-personal nature in the examination room. If you have any unauthorised material with you, hand it to the supervisor BEFORE reading any further.

2 Kinross College Year 10 Mathematics Exam, Semester

3 Do not turn this page over until you are asked to do so. Kinross College Year 10 Mathematics Exam, Semester

4 Kinross College Year 10 Mathematics Exam, Semester

5 Section 1: Multiple choice (Total 25 marks, one mark per question) 1. A jar contains 9 red lollies, 6 yellow lollies and 5 green lollies. What is the probability that a lolly chosen at random from the jar is not green? a) b) c) d) 2. The probability of choosing, by random selection, a brown ball from a bag containing 3 red balls, 2 white balls and 4 brown balls is: a) b) c) d) 3. The tree diagram shows the probabilities associated with tossing a biased coin twice. The probability of obtaining exactly one head is: a) 0.48 b) 0.4 c) 0.6 d) 0.64 Kinross College Year 10 Mathematics Exam, Semester

6 mm converted to metres is: a) m b) m c) 0.64 m d) 6.4 m 5. The circumference of a circle with diameter 7 m, correct to the nearest metre, is: a) 14 m b) 22 m c) 28 m d) 36 m 6. The total surface area of a cube with sides of length 3 cm is: a) 18 cm 2 b) 27 cm 2 c) 54 cm 2 d) 42 cm 2 7. Find the total surface area of the solid shape. a) 104 mm 2 b) 60 mm 3 c) mm 2 d) 120 mm 3 Kinross College Year 10 Mathematics Exam, Semester

7 8. The volume of the following triangular prism is: a) 140 m 3 b) 145 m 3 c) 150 m 3 d) 155 m 3 9. What is the mode for this set of scores? a) 6 b) 9 c) 7 d) The intersection point of the graphs y = 3x and y = 9 is: a) (2, 0) b) (2, 9) c) (3, 9) c) (2, 6) Kinross College Year 10 Mathematics Exam, Semester

8 11. The median of the set of data is: (10,13,14,16,16,17,19,21,25,28) a) 15 b) 16 c) 16.5 d) The interquartile range of the data displayed in the boxplot above is: a) 15 b) 20 c) 25 d) Stem Leaf The mean of the data displayed in the above stem-and-leaf plot is: a) 15 b) 17.5 c) 17 d) 16.5 Kinross College Year 10 Mathematics Exam, Semester

9 14. Which similarity test proves that the given pair of triangles is similar? a) SSS b) SAS c) AAS d) RHS 15. The scale factor of the pair of similar triangles above is: a) 5 2 b) 4 3 c) 5 3 d) 3 2 Kinross College Year 10 Mathematics Exam, Semester

10 16. Which congruence test proves that the given pair of triangles is similar? a) SSS b) SAS c) AAS d) AAA 17. The y-intercept of the graph of the rule y = 3x 6 is: a) 2 b) 6 c) 3 d) The gradient of the following line is: a) 4 b) 1 4 c) 4 d) zero Kinross College Year 10 Mathematics Exam, Semester

11 19. The gradient of the line joining the points ( 2, 5) and (1, 4) is: a) 3 b) 1 3 c) 3 d) Which of the following points does not lie on the line y 2x 5? a) (4, 3) b) ( 2, 9) c) (3, 1) d) ( 1, 7) 21. The solution to the equation 5x -12 = 6 - x is: a) x = 3 b) x = 1 c) x = 6 d) x = 3 Kinross College Year 10 Mathematics Exam, Semester

12 22. The solution to the simultaneous equations y = x +8and y = 2x + 5is: a) (4, 11) b) (11, 4) c) (3, 11) d) (11, 3) 23. The solution to the simultaneous equation 9x 2y 3 and 3x 2y 9 is: a) (1, 3) b) (3, 2) c) (1, 2) d) (3, 1) 24. How many scores are represented in this stem-and-leaf plot? a) 25 b) 30 c) 34 d) 15 Kinross College Year 10 Mathematics Exam, Semester

13 25. At the start of a fun run, 15 runners had their blood pressure and pulse rate tested. The results were plotted on a scatter plot. The results suggest that as people exercise, their: a) pulse rate and blood pressure are unaffected b) pulse rate and blood pressure both decrease c) pulse rate and blood pressure both increase d) only the pulse rate decreases Kinross College Year 10 Mathematics Exam, Semester

14 Die 1 Section 2: Written answer (Total 100 marks) 1. Two four-sided dice, numbered 1 to 4, are rolled. a) List the sample space using the following table. 4 1 Die b) Find: i Pr(a 4 is rolled at least once) ii Pr(sum is equal to 4) iii Pr(sum is not equal to 4) iv Pr(sum is at most 4) 2. Consider the following Venn diagram displaying the number of elements belonging to the events A and B. 4 Find: a) Pr(B) b) Pr(A only) c) Pr(B only) d) Pr(A B) Kinross College Year 10 Mathematics Exam, Semester

15 3. Consider the given data set: a) List the data in order, from smallest to largest. 5 b) For the data, find: i the minimum and maximum values ii the range iii the mode iv the mean, correct to one decimal place v the median (Q 2 ) vi the lower and upper quartiles (Q 1 and Q 3 ) vii the interquartile range (IQR) viii any outliers 4. Consider the given data set: Draw a boxplot to summarise the data, marking outliers if they exist. 5 Kinross College Year 10 Mathematics Exam, Semester

16 5. Solve the following equations. a) 4-5x =19 b) -2x = -3 6 c) 2(4-3x) = x Find the gradient and -intercept of the following equations. Use these to sketch their graphs on the axes provided. a) 8 b) Kinross College Year 10 Mathematics Exam, Semester

17 7. Graph each of the following linear equations using the given method. Clearly mark the two points you use to draw the graph. 4 a) y x 1 b) -4x +2y -10 = 0 3 Use gradient and y-intercept Find the equation of the straight lines shown. a) b) 4 Kinross College Year 10 Mathematics Exam, Semester

18 9. The following distance-time graph shows the distance travelled by a bushwalker over a 6-hour period. 4 a) What was the total distance travelled? b) At one point, the bushwalker stopped for lunch. When did this occur and for how long did they rest? c) What was the total distance travelled after 3 hours? d) How fast was the bushwalker travelling during the first 2 hours? 10. a) Find the perimeter of this shape if x = b) Find x if the perimeter is 27.4 m. Kinross College Year 10 Mathematics Exam, Semester

19 11. Find the area of these shapes, rounding to two decimal places where necessary. a) b) Find the Total Surface Area of these solids, rounding to two decimal places where necessary. a) b) Find the volume of these solids, rounding to two decimal places where necessary. a) b) 6 Kinross College Year 10 Mathematics Exam, Semester

20 14. Adam is building a fish tank in the shape of a rectangular prism. The fish tank is 40 cm tall, 80 cm wide and 100 cm long. It is to be fully enclosed; that is, have a base, four sides and a lid, as shown in the following diagram. 7 a) The fish tank is to be made from flat glass panels. Find how much glass is required to build the fish tank by finding its total surface area in cm 2. b) Determine the total cost of the glass if it costs $62.50 per square metre. c) Find the volume of the fish tank in cm 3. Kinross College Year 10 Mathematics Exam, Semester

21 15. Decide whether the pairs of triangles are similar, giving reasons. a) b) If the following pair of triangles is known to be similar, find the value of x Solve the following pairs of simultaneous equations using the elimination method. 6 a) 9x 2y 3 and 3x 2y 9 b) 2x 7y 1 and 3x 4y 8 Kinross College Year 10 Mathematics Exam, Semester

22 18. Jason buys two highlighters and five pens and pays $16. Eddy buys four highlighters and three pens and pays $18. Determine the cost of a highlighter and the cost of a pen Consider the variables x and y and the corresponding bivariate data. x y a Draw a scatter plot for the data. b Is there positive, negative or no correlation between x and y? c Is the correlation between x and y strong or weak? Kinross College Year 10 Mathematics Exam, Semester

23 20. A bag contains 3 red (R) and 4 white (W) marbles and two marbles are selected without replacement. 5 a Draw a tree diagram showing all outcomes and probabilities. b Find the probability of selecting: i a red marble and then a white marble ii 2 red marbles iii exactly 1 red marble END OF EXAMINATION Kinross College Year 10 Mathematics Exam, Semester