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

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 IN\bORMATION. Use a 2B or B pencil. Do NOT use a pen. Ru\b out any mistakes completely. You MUST record your answers on the ANSWER SHEET. Mathe M atics Mark only ONE answer for each question. Your score will \be the num\ber 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 possi\ble options. On your ANSWER SHEET fill in the oval that matches your answer. \bREE-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. Practice Qu e stions in t e r n a t i o n a l c o m p e t i t i o n s and assessments for sc\bools

ICAS Mathematics Practice Questions Paper I © EAA 2 1. T erry is in Station Rd and is going to a party in West St, which runs parallel to Station Rd. The angles between some of the 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 \bOT 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 \bOT TO SCALE 2. A company uses this formula to predict total profit P based on the number of products n 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 =  5T 2 (B)  P =  – 5T (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

ICAS Mathematics Practice Questions Paper I © EAA 4 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 P APER W rite your answer in the boxes provided on the ANSWER SHEET and in the ovals that match your answer . QUESTION 5 IS FREE RESPONSE.

I PAPE R The follo wing year levels should sit THIS Paper: Austr alia Year 11 Br unei Pre-Univ ersit y 1 Indonesia Year 12 Mala ysia For m 5 & Lo wer 6 Ne w Zealand Year 12 Y ear 11 Singapor e Secondary 4 & 5 South Africa Grade 11 THE UNIVERSITY OF NEW SOUTH WALES Edu ca tio n al A ssessmen t A ust rali a eaa.uns w.edu.au Acknowledgment Copyright in this booklet is owned by Educational Assessment Australia, UNSW Global Pty Limited, unless otherwise indicated. Every effort has been made to trace and acknowledge copyright. Educational Assessment Australia apologises for any accidental infringement and welcomes information to redress the situation. © 2012 Educati onal Asses sment A us trali a. EAA is an education group of UNSW Global Pty training and consulting services and a wholl y o wned enterprise of the Universit y of New South Wales . ABN 62 086 41 8 582

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D C B A D C B A D C B A D C B A 1 2 3 4 START Your pri vac y is assured as EAA fully complies with appropriate Austr alian pri vac y legislation. Visit www .eaa.unsw.edu.au for more details. 0 1 2 3 5 6 7 8 9 4 0 1 2 3 5 6 7 8 9 4 0 1 2 3 5 6 7 8 9 4 5 In te rn atio n al C om pe tit io n s and A ss e ssm ents fo r S ch o ols M P A PER I TO ANSWER THE QUESTIONS MUL TIPLE CHOICE FREE RESPONSE Example: 6 + 4 = Example: 6 + 6 = (A) 2 ● The answer is 12, so WRITE your (B) 9 answer in the boxes. (C) 10 ● Write only ONE digit in each box, (D) 24 as shown, and in the correct oval, as shown. The answer is 10, so in the oval , as shown. C D C B A 0123 56789 4 0123 56789 4 0123 56789 4 1 2

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 \bOT 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 518N um ber s to b e consider ed 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 fr om the numbers 1 to 8 is 8 + 7 + 6 = 21. So only numbers whose digits sum to 9 or 18 need to be consider ed. The numbers must be even, so they must be of the form: _ _ 2, _ _ 4, _ _ 6 and _ _ 8. T ak e for e xample _ _ 2. T o make this number’s digits sum to 9, the first two digits must sum to 7. W e can ther efore have 342, or 432. W e cannot have 252 or 522 as the number 2 cannot be used twice. This table summarises the solutions. P ossible numbers Sum to 9 Solutions Sum to 18 Solutions F irst two digits sum to: F irst two digits sum to: _ _ 2 7432 16- 342 162 612 _ _ 4 5234 14684 324 864 _ _ 6 3126 12486 846 216 756 576 _ _ 8 1 -10468 648 738 378 Ther efore ther e 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 Har d Level of difficulty refers to the e xpected level of difficulty for the question. Easy more than 70% of candidates will choose the cor rect option Medium about 50–70% of candidates will choose the cor rect option Medium/Har d about 30–50% of candidates will choose the cor rect option Har d less than 30% of candidates will choose the cor rect option