Mathematics Exam 21 Year 10 Semester 2, 2010
Mathematics Exam 21 Year 10 Semester 2, 2010
EXAM 2: APPLICATIONS SECTION
Mathematics Exam 21 Year 10 Semester 2, 2010
(Answer in the spaces provided) TOTAL: /42
Use of a calculator is allowed in this exam.
Mathematics Exam 21 Year 10 Semester 2, 2010
- A diver uses a springboard to dive into a pool, and her height, in metres (m), above the water after t seconds is given by:
a)Find the height of the springboard.
[1]
b)Factorise the above equation
[2]
c)At what time does sheenter the water?
[1]
d)What is the maximum height reached by the diver?
[1]
e)How far above the water is she after 3 seconds?
[1]
f)Sketch the graph labelling the axes with the correct variables. Show all intercepts and the coordinates of the turning point.
[5]
g)The diver continues on her path after hitting the water. What depth will she reach after her dive has been going 4 secs?
[1]
- The number, y, of bacteria present in two meat pies when it is not refrigerated can be modelled by the following equations:
Pie A
Pie B
where t is the number of minutes unrefrigerated.
a)How many bacteria are initially in each pie?
[2]
b)For pie A, find when the number of bacteria exceed 50
[1]
c)How many bacteria would be present in pie B after 20 minutes?
[1]
d)Find when the number of bacteria is the same in both pies. (give your answer correct to 1 decimal place)
[1]
e)Using an appropriate scale, draw the graphs of the two equations. Label axes,y intercepts, the graphs, and indicate the coordinates of the point of intersection of the two graphs.
[7]
f)The meat pie will make a person ill when the number of bacteria exceeds half a million. How long before pie A becomes inedible? (give your answer to the nearest minute)
[2]
g)If you were unsure of how long the pies had been unrefrigerated, which pie would be safer to eat? Give a reason.
[2]
- A meteorologist is trying to determine the height of a weather balloon which is above a lake, 1.5km away. The angle of elevation of the balloon from where he is standing at point P is 430.
a)Draw a diagram of the situation.
[1]
b)Determine the height of the balloon.
[2]
c)Find the angle of elevation of the balloon for another observer who is 2km from the lake at point Q.
[2]
d)The bearing of the balloon from P is 300 True and the bearing of the balloon from Q is N600W.
(i)Draw a clear diagram of the situation.
[2]
(ii)Find the distance between P and Q
[2]
- A chord, AB,long forms an angle of 600 at the centre of a circle, as shown in the diagram.
a)Find angle
[1]
b)Find the diameter of the circle and leave your answer in simplified surd form
[2]
c)Calculate the area of the circle and leave your answer in terms of .
()
[2]
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Mathematics Exam 2 Year 10 Semester 2, 2010
Exam 2: Multiple Choice Name:______Mark: /18
(Answer by circling the appropriate letter on the Answer Sheet)
1
Mathematics Exam 2 Year 10 Semester 2, 2010
1.Expand -(2x - 3)2
A -4x2-12x – 9 B -4x2 – 12x + 9
C (2x+3)2 D -4x2 + 12x - 9
2.The solution to -x2 = 49 is:
A x = –7 only
B x = -7,7
C x = 7 only
D x = no solution possible
3.The discriminant (∆ = b2 – 4ac)
of -2x2 + 7x – 5 = 0 is:
A 89
B -33
C 9
D 69
4. written in simplest form is:
A
B
C
D
5. The X-intercepts of y = x2 – 3x – 10 are:
A (–5, 0) and (2, 0)
B (0, –5) and (0, 2)
C (5, 0) and (0, –2)
D (5, 0) and (–2, 0)
6. in simplest form is equivalent to:
A
B
C
D
7.When expressed in index form
becomes:
A
B
C
D
8. The exact value of (2.2)-2
A 4.4B
C 0.21D
9. For the triangle shown, which of the following statements is true?
b
A
A C
BD
10.An equation of the graph shown could be:
A y = x2 + 1
B y = (x - 1)2 - 1
C y = (x+1)2 - 1
D y = x 2 + 1
11.The turning point of the graph shown could be:
A (1, 2)B (2, 1)
C (-1, 2)D (-2, -1)
12. If cosa = , the value of a is:
A 600B 300C 0.9999D undefined
13. Which of the following cannot be factorised by the ‘difference of two squares’ rule?
A y2 - 49
B x2 +16
C 36 ─ z2y2
D5g2 – 12
14. Simplifies to:
A B
C D
15. simplified and expressed with positive indices is:
AB
CD
16. simplifies to
A
B
C
D
17. For the diagram shown, points A and B are equidistant from O and point B is at a true bearing of 1200 from O and A is due west of O. The true bearing of point A from B is:
A 750 TC 2850 T
B 1500 T D 3000 T
18. If the angle of depression of a point on the ground,(X) from a helicopter is 32º, which of the following is true?
A The angle of elevation of the helicopter from X is 32º
B The angle of elevation of the helicopterfrom X is 58º
C The angle of depression of the helicopter from X is 32º
D The helicopter is directly above point X.
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Mathematics Exam 2 Year 10 Semester 2, 2010
Multiple Choice Answer Sheet Name:______
Q1 / A / B / C / DQ2 / A / B / C / D
Q3 / A / B / C / D
Q4 / A / B / C / D
Q5 / A / B / C / D
Q6 / A / B / C / D
Q7 / A / B / C / D
Q8 / A / B / C / D
Q9 / A / B / C / D
Q10 / A / B / C / D
Q11 / A / B / C / D
Q12 / A / B / C / D
Q13 / A / B / C / D
Q14 / A / B / C / D
Q15 / A / B / C / D
Q16 / A / B / C / D
Q17 / A / B / C / D
Q18 / A / B / C / D