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Mathematics PA PE R J Read the instructions on the ANSWER SHEET and fill in your NAME , SCHOOL and OTHER INFORMATION . Use a pencil. Do NOT use a coloured pencil or a pen. Rub out any mistakes completely. You MUST record your answers on the ANSWER SHEET . Mark only ONE answer for each question. Your score will be the number of correct answers. Marks are NOT deducted for incorrect answers. There are 5 MULTIPLE-CHOICE QUESTIONS (1 –5). 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. You may use a ruler and spare paper. You are NOT allowed to use a calculator . DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED. PRACTICE QUESTIONS

x x 3x x 3x x x x x 3x 10 cm 10 cm 30 cm 3 300 3000 41% 12% 10% 19% Japan Key USA ASEAN EU China Other 12% 6% 300 Β© UNSW Global Pty Limited 2

4. Jane was tossing a coin, but one side ofthe coin was weighted more heavily than the other. Here are the results she obtained. Based on her results, which of these is the best estimate of t he probabi lity of gett ing a head in a single toss of Jane’s coin? (A) 0.4 (B) 0.5 (C) 0.6 (D) 0.7 5.* In the diagram H represents the position of a hawk hovering above the ground, and M the position of a mouse on the ground. M H 50 0 0 50 100 100 150 150 200 200 250 250 200 150 100 50 ALL MEASUREMENTS IN METRES The mouse moves to a new position N, which is 50 m from position M. What is the maximum possible distance, in m, from H to the new position N correct to the nearest whole number? END OF PAPER QUESTION 5 IS FREE RESPONSE. Write your answer in the boxes provided on the ANSWER SHEET and fill in the ovals that match your answer. 3 Β© UNSW Global Pty Limited * Free response questions are only applicable to some assessments.

4. Jane was tossing a coin, but one side ofthe coin was weighted more heavily than the other. Here are the results she obtained. Based on her results, which of these is the best estimate of t he probabi lity of gett ing a head in a single toss of Jane’s coin? (A) 0.4 (B) 0.5 (C) 0.6 (D) 0.7 5.* In the diagram H represents the position of a hawk hovering above the ground, and M the position of a mouse on the ground. M H 50 0 0 50 100 100 150 150 200 200 250 250 200 150 100 50 ALL MEASUREMENTS IN METRES The mouse moves to a new position N, which is 50 m from position M. What is the maximum possible distance, in m, from H to the new position N correct to the nearest whole number? Β© UNSW Global Pty Limited 4 THIS PAGE MAY BE USED FOR WORKING.

Print your details clearly in the boxes provided. Make sure you fill in only one oval in each column. Rub out all mistakes completely. Do not use a coloured pencil or pen. HOW TO FILL OUT THIS SHEET: USE A PENCIL A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C a a a a a a a a a a a a a a a a a a a E E E E E E E E E E E E E E E E E E E c c c c c c c c c c c c c c c c c c c d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e e e e e e I I I I I I I I I I I I I I I I I I I J J J J J J J J J J J J J J J J J J J h h h h h h h h h h h h h h h h h h h i i i i i i i i i i i i i i i i i i i M M M M M M M M M M M M M M M M M M M k k k k k k k k k k k k k k k k k k k l l l l l l l l l l l l l l l l l l l P P P P P P P P P P P P P P P P P P P Q n n n n n n n n n n n n n n n n n n R o o o o o o o o o o o o o o o o o o S S S S S S S S S S S S S S S S S S S T T T T T T T T T T T T T T T T T T T r r r r r r r r r r r r r r r r r r r s s s s s s s s s s s s s s s s s s s t t t t t t t t t t t t t t t t t t t u u u u u u u u u u u u u u u u u u u v v v v v v v v v v v v v v v v v v v Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ – – – – – – – – – – – – – – – – – – – / / / / / / / / / / / / / / / / / / / DATE OF BIRTH STUDENT ID CLASS Day Month Year (optional) (optional) 0 M M M M M M M M M M M M M M A h 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 B i 2 2 2 2 2 2 2 2 2 2 2 2 2 2 C M 3 3 3 3 3 3 3 3 3 3 3 3 3 3 a k 4 4 4 4 4 4 4 4 4 4 4 4 4 E l 5 5 5 5 5 5 5 5 5 5 5 5 5 c P 6 6 6 6 6 6 6 6 6 6 6 6 6 d n 7 7 7 7 7 7 7 7 7 7 7 7 7 e o 8 8 8 8 8 8 8 8 8 8 8 8 8 I S 9 9 9 9 9 9 9 9 9 9 9 9 9 J T A A A A A A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C C C C C C a a a a a a a a a a a a a a a a a a a a a a a a E E E E E E E E E E E E E E E E E E E E E E E E c c c c c c c c c c c c c c c c c c c c c c c c d d d d d d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e e e e e e e e e e e I I I I I I I I I I I I I I I I I I I I I I I I J J J J J J J J J J J J J J J J J J J J J J J J h h h h h h h h h h h h h h h h h h h h h h h h i i i i i i i i i i i i i i i i i i i i i i i i M M M M M M M M M M M M M M M M M M M M M M M M k k k k k k k k k k k k k k k k k k k k k k k k l l l l l l l l l l l l l l l l l l l l l l l l P P P P P P P P P P P P P P P P P P P P P P P P Q n n n n n n n n n n n n n n n n n n n n n n n R o o o o o o o o o o o o o o o o o o o o o o o S S S S S S S S S S S S S S S S S S S S S S S S T T T T T T T T T T T T T T T T T T T T T T T T r r r r r r r r r r r r r r r r r r r r r r r r s s s s s s s s s s s s s s s s s s s s s s s s t t t t t t t t t t t t t t t t t t t t t t t t u u u u u u u u u u u u u u u u u u u u u u u u v v v v v v v v v v v v v v v v v v v v v v v v Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ – – – – – – – – – – – – – – – – – – – – – – – – / / / / / / / / / / / / / / / / / / / / / / / / Are you male or female? Male Female Does anyone in your home usually speak a language other than English? Ye s No School name: Town / suburb: Today’s date: / / Postcode: PA PE R J *202512* EXAMPLE 1: Debbie Bach FIRST NAME LAST NAME ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD EXAMPLE 2: Chan Ai Beng FIRST NAME LAST NAME ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD EXAMPLE 3: Jamal bin Abas FIRST NAME LAST NAME ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD EEEE EEE EE EEE EE EEE EEEEE EEE EEEEEE EEE EEEE FIRST NAME to aSSear on certificate LAST NAME to aSSear on certificate PAPER M SAMPLE

MULTIPLE CHOICE Questions 1 to 35 Example: 4 + 6 = (A) 2 (B) 9 (C) 10 (D) 24 The answer is 10 , so fill in the oval C , as shown. a C B A 1 A B C a 11 A B C a 21 A B C a 31 A B C a 2 A B C a 12 A B C a 22 A B C a 32 A B C a 3 A B C a 13 A B C a 23 A B C a 33 A B C a 4 A B C a 14 A B C a 24 A B C a 34 A B C a 5 0 M M 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 PA PE R J TO ANSWER THE QUESTIONS START USE A PENCIL DO NOT USE A COLOURED PENCIL OR PEN M PA PE R A For details on how we handle your personal information, please see our Privacy Policy on our website at unswglobal.unsw.edu.au SAMPLE

ICAS Mathematics Practice Questions Paper J Β© EAA QUESTION KEY SOLUTION STRANDLEVEL OF DIFFICULTY 1A The shaded rectangle has a side of 2 and a side of x. Therefore, the product of these two sides is 2 x. Algebra and Pattern Easy 2D Volume of a box = length Γ— width Γ— height V = 30 Γ— 10 Γ— 10 V = 3000 cm 3 Measurement Easy 3A 6% of the total products are exported to China. 6% of 123 000 million = 0.06 Γ— 123 000 million = $7380 million Chance and Data Easy 4C Experimental Probability equals: Number of times an event has occurred Number of trials 67 + 286 + 581 + 2989 100 + 500 + 1000 + 5000 Applying this formula: Number of times an event has occurred Number of trials 67 + 286 + 581 + 2989 100 + 500 + 1000 + 5000 = 0.59 Therefore, the best estimate is 0.6. Chance and Data Medium 7 Β© UNSW Global Pty Limited

Β© UNSW Global Pty Limited 8 ICAS Mathematics Practice Questions Paper J Β© EAA 5 190Apart from reading 3D coordinates the main mathematics in this question is Pythagoras’ Theorem. If we look at the mouse and the hawk from above we would see this: M H N H 100 2 + 50 2 161.8 2 + 100 2 N H 161.8 cm 100 cm The line shows the hawk’s path. The distance along the ground of this path (the horizontal component) is M H N H 100 2 + 50 2 161.8 2 + 100 2 N H 161.8 cm 100 cm . This is about 111.8 cm. The mouse runs 50 cm away from the hawk to a new position β€˜N’. The mouse can run in any direction but wants to maximise the distance from the hawk. This means he should run in the same direction as the line NH in the diagram below. M H N H 100 2 + 50 2 161.8 2 + 100 2 N H 161.8 cm 100 cm 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 than that because it is hovering above the ground at a height of 100 cm. We can show this on a new diagram from a different point of view. M H N H 100 2 + 50 2 161.8 2 + 100 2 N H 161.8 cm 100 cm We can now use Pythagoras’ Theorem again to find the distance from the hawk to the mouse. M H N H 100 2 + 50 2 161.8 2 + 100 2 N H 161.8 cm 100 cm This gives an answer of 190.2 cm. To the nearest whole number this is 190. Comment The underlying mathematics in this problem is not very difficult and boils down to two instances of Pythagoras’ Theorem. As a problem, though, the question is more difficult. Students have to realise that Pythagoras’ Theorem is the appropriate piece of mathematics to use and have to extract information presented in an unusual way. Also some insight is required to understand in what direction the mouse should run. m. m m. m. m m m.

ICAS Mathematics Practice Questions Paper J Β© EAA Level of difficulty refers to the expected level of difficulty for the question. Easy more than 70% of candidates will choose the correct option Medium about 50–70% of candidates will choose the cor rect option Medium/Hard about 30–50% of candidates will choose the cor rect option Hard less than 30% of candidates will choose the cor rect option 9 Β© UNSW Global Pty Limited

Β© 2019 Copyright. Copyright in this publication is owned by UNSW Global Pty Limited, unless other wise indicated or licensed from a third party. This publication and associated testing materials and products may not be reproduced, published or sold, in whole or part, in any medium, without the permission of UNSW Global Pty Limited or relevant copyright owner. 1 All international schools registered with UNSW Global (which have an 8-digit school code star ting with 46) should sit the papers according to the Australian year levels. 2 Indian Subcontinent Region: India, Sri Lanka, Nepal, Bhutan and Bangladesh. 3 Middle East Region: United Arab Emirates, Qatar, Kuwait, Saudi Arabia, Bahrain, Oman, Turkey, Lebanon, Tunisia, Morocco, Libya, Algeria, Jordan and Pakistan. 4 Pacific Region: Vanuatu, Papua New Guinea and Fiji.5 Southern Africa Region: South Africa, Botswana, Lesotho, Swaziland, Zimbabwe and Namibia. PA PE R J THE FOLLOWING YEAR LEVELS SHOULD SIT THIS PAPER Australia 1 Year 12 Brunei Pre-University 2 Egypt Year 12 Hong Kong Form 6 Indian Subcontinent 2 Class 12 Indonesia N/A Malaysia Upper 6 Middle East 3 Class 12 New Zealand/ Pacific 4 Year 13 Singapore Junior College 1 Southern Africa 5 Grade 12