[PDF] 2019 Reach and ICAS Practice Questions Mathematics Paper I.pdf | Plain Text

Mathematics PA PE R I 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

1. Terry is in Station Rd and is going to aparty in West St, which runs parallel toStation Rd. The angles between some ofthe streets are shown. West St Smith Rd Oak St Station Rd z° x° w° w° y° y° (A) w = y (B) x = w (C) y= x (D) z= y West St Station Rd Smith Rd NOT TO SCALE Which of these statements must be true? West St Smith Rd Oak St Station Rd z° x° w° w° y° y° (A) w = y (B) x = w (C) y = x (D) z = y West St Station Rd Smith Rd NOT TO SCALE 2. A company uses this formula to predict total profit P based on the number of products x sold. P = n 2 + 60n – 4000 How many products are sold if there is zero profit? (A) 0 (B) 40 (C) 100 (D) 4000 3. 7.101 (3.019 – 0.798) – What is the value of this expression correct to three significant figures? (A) 3.19 (B) 3.197 (C) 3.20 (D) 3.200 4. This scatter diagram shows the relationship between the air temperature T and the number of people P visiting a beachside shopping centre. Number of people (P) Air temperature (T ) (A) P =5 T 2 (B) P = –5 T (C) P = – (D) P = —5 T —T 5 Which formula could describe the relationship between the air temperature and the number of people? Number of people (P) Air temperature (T ) (A) P = 5T 2 (B) P = – 5T (C) P = – (D) P = —5 T —T 5 © UNSW Global Pty Limited 2

5.* Mario knows that a number is divisible by nine if the sum of its digits is divisible by nine. He has eight cards with the digits 1 to 8 written on them as shown. Mario selects three of these cards to make a three-digit number that is divisible by nine. He then replaces these three cards and repeats this selection procedure to select different three-digit numbers divisible by nine. How many even three-digit numbers is it possible for him to find in this way? 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 © UNSW Global Pty Limited * Free response questions are only applicable to some assessments.

5.* Mario knows that a number is divisible by nine if the sum of its digits is divisible by nine. He has eight cards with the digits 1 to 8 written on them as shown. Mario selects three of these cards to make a three-digit number that is divisible by nine. He then replaces these three cards and repeats this selection procedure to select different three-digit numbers divisible by nine. How many even three-digit numbers is it possible for him to find in this way? © 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 I *202511* 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 I 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

7 © UNSW Global Pty Limited ICAS Mathematics Practice Questions Paper I © EAA QUESTIONKEYSOLUTION STRANDLEVEL OF DIFFICULTY 1 A West St Smith Rd Oak St Station Rd z° x° w° w° y° y° (A) w = y (B) x = w (C) y = x (D) z = y West St Station Rd Smith Rd NOT TO SCALE Station Rd and West St are parallel, while Smith Rd crosses them. This results in angle y and angle w, that are alternate, being equal. Therefore, statement A is the correct statement. Space and Geometry Easy 2 BThis is a quadratic equation. It factorises to (n + 100)(n − 40) = 0 The solutions for this equation are n = − 100 and n = 40. As n is the number of products, it cannot be negative. Hence, n = 40 is the correct solution. Alternatively, substituting the options will show that n = 40 gives P = 0. Algebra and Patterns Easy 3 CThe result of the calculation is 3.197208465. This number rounded to three significant figures is 3.20. Number and Arithmetic Medium 4 DThe diagram shows an inverse relation between the air temperature, T, and the number of people, P. As T increases, P decreases. Note that the relation is not linear. Option A is a quadratic equation that gives a parabola when graphed, where the relation is positive (considering positive values of T). This does not describe the given data. Options B and C are both linear equations that give straight lines sloping downwards when graphed. Again, these do not describe the given data. Option D is an equation that gives a hyperbola when graphed. For small values of T, P has a large value. As the values of T increase, the values of P decrease. This correctly describes the given data. Chance and Data Medium

ICAS Mathematics Practice Questions Paper I © EAA 5 18Numbers to be considered are numbers with a digit sum that is divisible by 9. So the sum of the digits must be multiples of 9: 9, 18, 27... The highest digit sum that can be obtained from the numbers 1 to 8 is 8 + 7 + 6 = 21. So only numbers whose digits sum to 9 or 18 need to be considered. The numbers must be even, so they must be of the form: _ _ 2, _ _ 4, _ _ 6 and _ _ 8. Take for example _ _ 2. To make this number’s digits sum to 9, the first two digits must sum to 7. We can therefore have 342, or 432. We cannot have 252 or 522 as the number 2 cannot be used twice. This table summarises the solutions. Possible numbers Sum to 9 Solutions Sum to 18 Solutions First two digits sum to: First two digits sum to: _ _ 2 7 432 16 - 342 162 612 _ _ 4 5 234 14684 324 864 _ _ 6 3 126 12486 846 216 756 576 _ _ 8 1 - 10 468 648 738 378 Therefore there are 18 possible numbers that Mario can find. Note: This is one possible method. The question can be solved using other methods. Chance and Data Hard 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 correct option Medium/Hard about 30–50% of candidates will choose the correct option Hard less than 30% of candidates will choose the correct option © UNSW Global Pty Limited 8



© 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 I THE FOLLOWING YEAR LEVELS SHOULD SIT THIS PAPER Australia 1 Year 11 Brunei Pre-University 1 Egypt Year 11 Hong Kong Form 5 Indian Subcontinent 2 Class 11 Indonesia Year 12 Malaysia Form 5 & Lower 6 Middle East 3 Class 11 New Zealand/ Pacific 4 Year 12 Singapore Secondary 4 & 5 Southern Africa 5 Grade 11