8/9/2019 MathematicsPaperI http://slidepdf.com/reader/full/mathematicspaperi 1/13 I PAPER DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED. STUDENT’S NAME: Read the instructions on the ANSWER SHEET and fill in your NAME, SCHOOL and OTHER INFORMATION. Use a 2B or B pencil. Do NOT use a pen. Rub out any mistakes completely. You MUST record your answers on the ANSWER SHEET. MM Mark only ONE answer for each question. Your score will be the number of correct answers. Marks are NOT deducted for incorrect answers. MULTIPLE-CHOICE QUESTIONS: Use the information provided to choose the BEST answer from the four possible options. On your ANSWER SHEET fill in the oval that matches your answer. FREE-RESPONSE QUESTIONS: Write your answer in the boxes provided on the ANSWER SHEETand fill in the oval that matches your answer You may use a ruler and spare paper. A CALCULATOR is required. P r a c t i c e Q uestio n s nternational ompetitions and ssessmentsfor chools
Read the instructions on the ANSWER SHEET and fill in yourNAME, SCHOOL and OTHER INFORMATION.Use a 2B or B pencil.Do NOT use a pen.Rub out any mistakes completely.
You MUST record your answers on the ANSWER SHEET.
MMMark only ONE answer for each question.Your score will be the number of correct answers.Marks are NOT deducted for incorrect answers.
MULTIPLE-CHOICE QUESTIONS:
Use the information provided to choose the BEST answer fromthe four possible options.On your ANSWER SHEET fill in the oval that matches your answer.
FREE-RESPONSE QUESTIONS:
Write your answer in the boxes provided on the ANSWER SHEET
and fill in the oval that matches your answer
You may use a ruler and spare paper.A CALCULATOR is required.
3. During 2001, Australia exported goods toa total value of $123 000 million.The graph shows the percentage of thesegoods exported to different parts of theworld.
41%
12%
10%
19%Japan
Key
USA
ASEAN
EU
China
Other 12% 6%
What was the value, in millions of dollars,of the goods exported to China?
8. Anna forgot the code of a 3-digit lock onher case. The code was made of 3 digitsranging from 0 to 9. She remembered thatthe first digit was less than 5, the seconddigit was an odd number, and the thirdone was either 7 or 8. There were noidentical digits in the code.
How many different combinations couldpossibly open her lock?
(A) 25(B) 36(C) 41(D) 50
9. The diagram represents a regular octagon
of area 500 cm2.
How long, to the nearest centimetre,is one side of the octagon?
10. In the diagram H represents the positionof a hawk hovering above the ground, andM the position of a mouse on the ground.
M
H
50
0
050100
100150150200 200
250
250
200
150
100
50
ALL MEASUREMENTS IN CENTIMETRES
The mouse moves to a new position N ,which is 50 cm from position M .
What is the maximum possible distance,
in cm, from H to the new position N correct to the nearest whole number?
The perimeter of the shaded shape is made of 11 bases of the given triangle + 2 heights +2 sides. You need to calculate the height and the sideof the triangle first.Calculating the height: the area is given(60 square units), therefore you can find theheight using the formula: Area = ½ × height
× base, h × 10
260 = which gives
h = 12 unitsCalculating the side by cutting the triangledown the middle, a right-angled triangle isformed with base = 5 cm and height = 12 cm.
The unknown side is called s. Using Pythagoras’
Theorem, h2 + 52 = s2. Substitute h = 12 and
find s:
s = 122 + 52
. Therefore, s = 13 units.Now add all the values in the originalcalculation: 11 bases of the given triangle +2 heights + 2 sides.11 × 10 + 2 × 12 + 2 × 13 = 160 units.
Space andGeometry
Hard
8 C
The first two digits filled 5 × 5 ways, the lastdigit 2 ways BUT must delete117, 118, 337,338, 077,177,277,377 and 477.5 × 5 × 2 – 9 = 41.
Chance andData
Hard
9 10
This item requires a lot of work and someknowledge of Pythagoras’ Theorem and theinternal angles of an octagon.
There are several approaches, but they all workby finding the area of triangles, rectanglesor trapeziums. From there, an equation thatrelates the area of the octagon to the length of the side can be written.One method is to think of the octagon as arectangle between two trapeziums. A different way is to think of it as a square with trianglescut off.
Apart from reading 3D coordinates the mainmathematics in this question is Pythagoras’Theorem.If we look at the mouse and the hawk fromabove we would see this:
M
H
The line shows the hawk’s path. The distancealong the ground of this path (the horizontal
component) is 1002 + 502
. This is about111.8 cm. The mouse runs 50 cm away fromthe hawk to a new position ‘N’. The mouse canrun in any direction but wants to maximise thedistance from the hawk. This means he should
run in the same direction as the line NH in thediagram below.
N
H
Measurement Hard
Along the ground this gives a distance of 111.8+50=161.8 cm
This is just the horizontal distance. Fortunately
for the mouse, the hawk is further away thanthat because it is hovering above the ground ata height of 100 cm. We can show this on a new diagram from adifferent point of view.
N
H
161.8 cm
100 cm
We can now use Pythagoras’ Theorem again tofind the distance from the hawk to the mouse.
161.82 + 1002
This gives an answer of 190.2 cm. To thenearest whole number this is 190.Comment The underlying mathematics in this problem isnot very difficult and boils down to two instancesof Pythagoras’ Theorem. As a problem, though,the question is more difficult. Students haveto realise that Pythagoras’ Theorem is theappropriate piece of mathematics to use and haveto extract information presented in an unusual way. Also some insight is required to understandin what direction the mouse should run.
