PAPER. Practice Questions. Mathematics. International Competitions and Assessments for Schools STUDENT S NAME:

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1 ractice uestions nternational ompetitions and ssessments for chools U U. U : ead the instructions on the and fill in your, and. Use a or pencil. o use a pen. ub out any mistakes completely. ou U record your answers on the. athematics ark only answer for each question. our score will be the number of correct answers. arks are deducted for incorrect answers. U- U: Use the information provided to choose the answer from the four possible options. n your fill in the oval that matches your answer. - U: rite your answer in the boxes provided on the answer sheet and fill in the oval that matches your answer. ou may use a ruler and spare paper. calculator is required.

2 . erry is in tation d and is going to a party in est t, which runs parallel to tation d. he angles between some of the streets are shown... (..) hat is the value of this expression correct to three significant figures? ak t z y est t mith d x w tation d (). (). (). ().. his scatter diagram shows the relationship between the air temperature and the number of people visiting a beachside shopping centre. hich of these statements must be true? () w = y () x = w () y = x () z = y. company uses this formula to predict total profit based on the number of products n sold. = n + n ow many products are sold if there is zero profit? () () () () umber of people () ir temperature ( ) hich formula could describe the relationship between the air temperature and the number of people? () = () = () = () = athematics ractice uestions aper

3 U. rite your answer in the boxes provided on the and in the ovals that match your answer.. ario knows that a number is divisible by nine if the sum of its digits is divisible by nine. e has eight cards with the digits to written on them as shown. ario selects three of these cards to make a three-digit number that is divisible by nine. e then replaces these three cards and repeats this selection procedure to select different three-digit numbers divisible by nine. ow many even three-digit numbers is it possible for him to find in this way? athematics ractice uestions aper

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5 to appear on certificate to appear on certificate re you male or female? ale emale oes anyone in your home usually speak a language other than nglish? es o chool name: own suburb: odays date: ostcode: ay onth ear (optional) U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U : ub out all mistakes completely. rint your details clearly in the boxes provided. ake sure you fill in only one oval in each column. : ebbie ach : han i eng : amal bin bas U U nternational ompetitions and ssessments for chools U ** aper

6 our privacy is assured as fully complies with appropriate ustralian privacy legislation. isit for more details. nternational ompetitions and ssessments for chools U U xample: + = xample: + = () he answer is, so your () answer in the boxes. () rite only digit in each box, () as shown, and in the correct oval, as shown. he answer is, so in the oval, as shown.

7 U U U mith d y est t w tation d pace and eometry asy tation d and est t are parallel, while mith d crosses them. his results in angle y and angle w, that are alternate, being equal. herefore, statement is the correct statement. his is a quadratic equation. t factorises to (n + )(n ) = he solutions for this equation are n = and n =. s n is the number of products, it cannot be negative. ence, n = is the correct solution. lternatively, substituting the options will show that n = gives =. lgebra and atterns asy he result of the calculation is.. his number rounded to three significant figures is.. umber and rithmetic edium he diagram shows an inverse relation between the air temperature,, and the number of people,. s increases, decreases. ote that the relation is not linear. ption is a quadratic equation that gives a parabola when graphed, where the relation is positive (considering positive values of ). his does not describe the given data. ptions and are both linear equations that give straight lines sloping downwards when graphed. gain, these do not describe the given data. ption is an equation that gives a hyperbola when graphed. or small values of, has a large value. s the values of increase, the values of decrease. his correctly describes the given data. hance and ata edium athematics ractice uestions aper

8 umbers to be considered are numbers with a digit sum that is divisible by. o the sum of the digits must be multiples of :,,... he highest digit sum that can be obtained from the numbers to is + + =. o only numbers whose digits sum to or need to be considered. he numbers must be even, so they must be of the form:,, and. ake for example. o make this numbers digits sum to, the first two digits must sum to. e can therefore have, or. e cannot have or as the number cannot be used twice. his table summarises the solutions. ossible numbers um to um to irst two digits sum to: olutions irst two digits sum to: olutions hance and ata ard - - herefore there are possible numbers that ario can find. ote: his is one possible method. he question can be solved using other methods. evel of difficulty refers to the expected level of difficulty for the question. asy edium ediumard ard more than % of candidates will choose the correct option about % of candidates will choose the correct option about % of candidates will choose the correct option less than % of candidates will choose the correct option athematics ractice uestions aper