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J 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. MatheMatics 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 Questions i n 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 J © EAA 2 1. The diagram below represents the products of ( x + 5) and (3 x + 2). NOT TO SCALE 3x 2 5 x 3x + 2 x + 5 What product is represented by the shaded rectangle? (A) 2 x (B) 6 x (C) x2 (D) 3 x2 2. Jules has a package gift-wrapped, as shown. 10 cm 10 cm 30 cm What is the volume, in cm 3, of the package? (A) 50 (B) 300 (C) 1400 (D) 3000 3. During 2001, Australia exported goods to a total value of $123 000 million. The graph shows the percentage of these goods exported to different parts of the world. 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? (A) 7 380 (B) 12 300 (C) 14 760 (D) 23 370

3 ICAS Mathematics Practice Questions Paper J © EAA 4. Jane was tossing a coin, but one side of the coin was weighted more heavily than the other . Here are the results she obtained. Based on her results, which of these is the best e stim ate o f th e p robabi lit y o f g ettin g 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 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? END OF P APER QUESTION 5 IS FREE RESPONSE. W rite your answer in the boxes provided on the ANSWER SHEET and in the ovals that match your answer .

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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 J 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 J © EAA QUESTIONKEYSOLUTION STRANDLEVEL OF DIFFICUL TY 1 AThe shaded r ectangle has a side of 2 and a side of x. Ther efore, the pr oduct of these two sides is 2 x. Algebra and Pattern Easy 2 DV olume of a box = length × width × height V = 30 × 10 × 10 V = 3000 cm 3 Measur ement Easy 3 A6% of the total pr oducts are exported to China. 6% of 123 000 million = 0.06 × 123 000 million = $7380 million Chance and Data Easy 4 CExperimental P robability equals: Number of times an event has occur red Number of trials 67 + 286 + 581 + 2989 100 + 500 + 1000 + 5000 Applying this formula: Number of times an event has occur red Number of trials 67 + 286 + 581 + 2989 100 + 500 + 1000 + 5000 = 0.59 Ther efore, the best estimate is 0.6. Chance and Data Medium

ICAS Mathematics Practice Questions Paper J © EAA 5190Apart fr om reading 3D coor dinates the main mathematics in this question is Pythagoras’ Theor em. If we look at the mouse and the hawk fr om 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 gr ound 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 fr om the hawk to a new position ‘N’. The mouse can run in any dir ection but wants to maximise the distance fr om the hawk. This means he should run in the same dir ection 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 Measur ement Hard Along the gr ound this gives a distance of 111.8+50=161.8 cm This is just the horizontal distance. F ortunately for the mouse, the hawk is further away than that because it is hovering above the gr ound at a height of 100 cm. W e can show this on a new diagram fr om a differ ent point of view . M H N H 100 2 + 50 2 161.8 2 + 100 2 N H 161.8 cm 100 cm W e can now use Pythagoras’ Theor em again to find the distance fr om 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. T o the near est whole number this is 190. Comment The underl yin g mathemati cs in thi s prob lem i s n ot v er y di fficu lt and boils dow n t o two instan ce s of Pytha goras’ The orem . A s a p rob lem , th oug h, the q u esti on i s m ore di fficu lt. St udent s ha ve t o reali se that P ytha goras’ The orem i s th e app ro priate pie ce of mathemati cs to us e and ha ve t o ex tra ct in formati on p re sented in an unusu al w ay. Al so so me in sig ht i s req uir ed t o u nder stan d in w hat di re cti on the m ous e s hou ld r u n .

ICAS Mathematics Practice Questions Paper J © 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 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