Year 10 Mathematics Examination SEMESTER 2 2016

Year 10 Mathematics Examination

SEMESTER 2 2016

QUESTION AND ANSWER BOOKLET

STUDENT NAME:

TEACHER:

DATE:

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.

Kinross College Year 10 Mathematics Exam, Semester 2 2016 1


Do not turn this page over until you are asked to do so.



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


4. 6400 mm converted to metres is:

a) 0.0064 m b) 0.064 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 cm2 b) 27 cm2 c) 54 cm2 d) 42 cm2

7. Find the total surface area of the solid shape.

a) 104 mm2 b) 60 mm3 c) 1074.42 mm2 d) 120 mm3


8. The volume of the following triangular prism is:

a) 140 m3 b) 145 m3 c) 150 m3 d) 155 m3

9. What is the mode for this set of scores?

a) 6

b) 9

c) 7

d) 8

10. The intersection point of the graphs y = –3x and y = –9 is:

a) (2, 0)

b) (2, –9) c) (3, –9)

c) (2, –6)


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) 17

12.

The interquartile range of the data displayed in the boxplot above is:

a) 15 b) 20 c) 25 d) 35

13. Stem Leaf

0 4 9

1 0 2 3 5 8

2 1 3 6 7

3 2

The mean of the data displayed in the above stem-and-leaf plot is:

a) 15

b) 17.5 c) 17 d) 16.5


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


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) 0

18. The gradient of the following line is:

a) 4

b)

1

4

c) −4 d) zero


19. The gradient of the line joining the points (−2, 5) and (1, −4) is:

a) −3

b) −1

3

c) 3

d) 1

3

20. Which of the following points does not lie on the line 2 5y x ?

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


22. The solution to the simultaneous equations y = x+8and y = 2x+ 5 is:

a) (4, 11)

b) (11, 4)

c) (3, 11)

d) (11, 3)

23. The solution to the simultaneous equation 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

9 2 3 and 3 2 9x y x y


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


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.

Die 2

1 2 3 4

Die

1

1

2

3

4

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) _______________________________

4

2. Consider the following Venn diagram displaying the number of elements belonging to the events A and B. Find: a) Pr(B) b) Pr(A only) c) Pr(B only)

d) Pr(A B)

4


3. Consider the given data set: 9 6 17 8 4 13 10 12 24 8 11 5 13

a) List the data in order, from smallest to largest. ________________________________________________________________ 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 (Q2) ___________________________ vi the lower and upper quartiles ___________________________

(Q1 and Q3) vii the interquartile range (IQR) ___________________________ viii any outliers ___________________________

5

4. Consider the given data set: 9 6 17 8 4 13 10 12 24 8 11 5 13

Draw a boxplot to summarise the data, marking outliers if they exist.

5


5. Solve the following equations.

a) 4-5x =19 b) -2x - 2

4= -3

c) 2(4 - 3x) = x - 7

6

6. Find the gradient and -intercept of the following equations. Use these to sketch their graphs on the axes provided.

8

a)

b)


7. Graph each of the following linear equations using the given method. Clearly mark the two points you use to draw the graph.

a) 4

13

y x b) -4x+2y-10 = 0

Use gradient and y-intercept.

6

8. Find the equation of the straight lines shown. a) ____________________ b) ______________________

4


9. The following distance-time graph shows the distance travelled by a bushwalker over

a 6-hour period.

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?

_____________________________________________________________________

4

10. a) Find the perimeter of this shape if x = 6.2. b) Find x if the perimeter is 27.4 m.

4


11. Find the area of these shapes, rounding to two decimal places where necessary. a) b)

4

12. Find the Total Surface Area of these solids, rounding to two decimal places where necessary. a) b)

6

13. Find the volume of these solids, rounding to two decimal places where necessary. a) b)

6


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.

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 cm2. 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 cm3.

7


15. Decide whether the pairs of triangles are similar, giving reasons. a) b)

4

16. If the following pair of triangles is known to be similar, find the value of x.

3

17. Solve the following pairs of simultaneous equations using the elimination method. a)

b)

6

9 2 3 and 3 2 9x y x y

2 7 1 and 3 4 8x y x y


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.

4

19. Consider the variables x and y and the corresponding bivariate data.

x 1 2 3 4 5 6 7 8

y 7 6 1 4 5 3 3 2

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?

5


END OF EXAMINATION

20. A bag contains 3 red (R) and 4 white (W) marbles and two marbles are selected without

replacement.

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 __________________________

5

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Year 10 Mathematics Examination SEMESTER 2 2016