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Kỳ thi Toán học Úc (AMC) là một trong những sàn đấu quốc tế lớn về Toán học bằng tiếng Anh, dành cho tất cả học sinh tiểu học và trung học. Kỳ thi đã thu hút tổng cộng hơn 15 triệu lượt thí sinh từ 40 quốc gia trên thế giới tranh tài kể từ khi cuộc thi này được tổ chức.Không cần dùng máy tính, không học bài máy móc, cuộc thi Toán học Úc (Australian Mathematics Competition – AMC) được thiết kế rõ ràng để thí sinh làm bài nhanh chóng, thể hiện kiến thức và tư duy Toán học.
Upper Primary Division Questions to 10, marks each Which of these numbers is the largest? (A) 12 000 (B) 100 (C) 102 000 (D) 201 (E) 200 Cody has $42 and Chris has $26 How much they have together? (A) $68 (B) $24 (C) $64 (D) $28 (E) $72 Which of these shapes is a square? (A) (B) (D) (E) (C) Which of these numbers can be divided by without any remainder? (A) 58 (B) 52 (C) 54 (D) 50 (E) 56 (C) 18 (D) (E) 62 What is 71 − 63? (A) 12 (B) 68 Thirty-six thousand, six hundred and three is written as (A) 36 000 603 (B) 360 603 (C) 360 063 (D) 30 663 (E) 36 603 UP How many lines of symmetry can be drawn for the shape? (A) (B) (D) (C) (E) Brian arrives at the station at 10:07 but is 15 minutes late for his train At what time did his train depart? (A) 09:22 (B) 09:52 (C) 10:22 What percentage of the square is shaded? (A) (B) 25 (C) 15 (D) 80 (E) 50 (D) 10:52 (E) 10:15 10 If I can walk km in 10 minutes, how far can I walk in an hour and a half? (A) 10 km (B) 36 km (C) km (D) km (E) 12 km Questions 11 to 20, marks each 11 Frank’s pencil is 15 cm long How long is it in metres? (A) 0.015 m (B) 0.15 m (C) 1.5 m (D) 15 m (E) 150 m UP Z Y 12 Five coins lie on a table as shown in the diagram In what order were they placed? X V W (A) Z, V, W, Y, X (B) Y, X, Z, W, V (D) X, Y, Z, W, V (C) X, W, V, Z, Y (E) Z, Y, W, V, X ❜❜❜ 13 An ant walks once around the top edges of this box, How far does it walk? (A) 20 cm (B) 14 cm cm (C) 16 cm 14 Jenny made a solid using only pentagonal faces as illustrated If each pentagon has an area of 30 cm2 , what is the surface area of the solid that Jenny built? (A) 300 cm2 (B) 30 cm2 (C) 150 cm2 (D) 180 cm2 (E) 360 cm2 cm (D) 24 cm cm (E) 10 cm UP 15 Chris thinks of a number, multiplies it by and then adds This gives him a result of 19 What was his original number? (A) (B) 12 (C) 15 (D) (E) 61 16 This picturegraph shows the number of people at the zoo for these days Saturday Sunday = 50 people Monday How many people attended the zoo on Monday? (A) 150 (B) (C) 250 (D) 125 (E) 300 17 A torch uses batteries every hours How many packs of batteries will you need to run the torch for 30 hours? (A) (B) (C) 18 A square is divided up into two smaller squares and two rectangles as shown If the areas of the two smaller squares are 16 cm2 and 25 cm2 , what is the area of the shaded rectangle? (B) 20 cm2 (C) 22 cm2 (A) 18 cm2 (D) 24 cm2 (E) 28 cm2 (D) (E) UP 19 There are 10 telegraph poles in a straight road, 100 m apart The distance from the first to the last is (A) 900 m (B) 1000 m (C) 800 m (D) 100 m (E) 1100 m 20 A cube has the numbers to written on its faces in such a way that the numbers on opposite faces always add up to Which of the cubes below could NOT be that cube? (A) (B) (C) 3 (D) (E) Questions 21 to 30, marks each of them have brown hair and 20% have black hair The rest have blond hair How many have blond hair? 21 There are 20 children at a party, (A) (B) (C) (D) 12 (E) 18 B 22 If A and B are points halfway along the sides of the square, what is the area shaded? A (A) cm2 (B) cm2 (C) cm2 (D) 10 cm2 (E) 12 cm2 cm cm UP 23 Arjun wants to cover his wardrobe door with photos of his friends The pictures are all 10 cm by 15 cm His wardrobe door is 0.6 m by 1.8 m How many photos will he need if he wants to leave no spaces? (A) 72 (B) 12 (C) 120 (D) 24 (E) 60 P Q R S 24 In the cube shown in the diagram, the shape QRT W would be W T (A) (B) (E) (D) V (C) 25 A chocolate bar is blocks wide and blocks long Jim breaks a row of the short side and eats it Mary then breaks a row off the long side and eats it What fraction of the block remains? (B) (C) (D) (E) (A) 12 26 John tells the truth on Monday, Tuesday, Wednesday and Thursday He lies on all other days Dieter tells the truth on Monday, Friday, Saturday and Sunday He lies on all other days One day they both said, “Yesterday I lied’ The day they said that was (A) Monday (B) Wednesday (D) Friday (E) Saturday (C) Thursday UP 27 A rectangular sheet of paper is folded in half and then folded in half again A piece is cut out of the folded paper as shown The sheet is then smoothed out to its original size again Which one of the following could it be? (A) (B) (D) (E) 28 In the diagram, tennis ball, (C) is a squash ball, is a cricket ball, is a is a football and the scales show what balances How many squash balls will balance a football? (A) (B) (C) (D) (E) UP 29 Equilateral triangles of the same size are joined along edges (so that their vertices touch) What is the smallest number of triangles needed to form a hexagon (a six-sided shape)? (A) (B) (C) 30 Four 10 c coins lie on a table as shown Keeping in contact with the other three coins, the shaded coin is rolled around the other three coins until it returns to its starting place Through what angle does the shaded coin turn, on its axis, in rolling once around the other three coins? (A) 360◦ (B) 540◦ (D) (C) 720◦ *** (E) (D) 900◦ (E) 1080◦ Upper Primary Division Questions to 10, marks each Which of these numbers is the largest? (A) (B) 800 (C) 200 (D) 80 (E) 280 Which clock shows the time 2:45? (A) (B) (D) (C) (E) Ben cuts an equilateral triangle into two identical pieces Which of these shapes could be one of those pieces? (B) (A) (D) (C) (E) UP How many faces does this solid have? (A) (B) (D) (C) (E) 12 Most of the numbers on this scale are missing 44 62 P Assuming that the scale is uniform, the point P corresponds to a reading of (A) 47 (B) 48 (C) 50 (D) 52 (E) 56 (E) 0.7 Which of the following is less than one half? (A) 12 (B) 52% (C) 0.65 A net of a cube is shown in the diagram When this net is made into a cube, the letter opposite H is (A) G (B) T (C) P (D) M (E) K (D) H G M P K T Instead of multiplying 25 × 84, Brendan calculated 100 × 84 From this result, what can he to get the correct answer? (A) Divide by (B) Multiply by (D) Add 75 (C) Subtract 75 (E) Divide by UP Felicity has a combination lock for her bike like the one below It has the numbers to on each tumbler It clicks every time she moves the tumblers one number forward or back, including a click as the tumbler moves between and She found the lock in the position 9–0–4 shown Her combination is 5–8–7 9 What is the least number of clicks needed to get the lock to her combination? (A) 20 (B) 18 (C) 17 (D) (E) 10 Which number multiplied by itself is equal to times 20? (A) 10 (B) 20 (C) 25 (D) 100 (E) 120 Questions 11 to 20, marks each 11 Greg sees a clock in the mirror, where it looks like this What is the actual time? (A) 4:10 (B) 4:50 (C) 5:10 (D) 6:50 21 (E) 7:10 12 In these two number sentences + + + = 12 + + + = 20 what is the value of (A) (B) ? (C) (D) (E) UP 13 In this sum, each of the letters X, Y and Z represents a different digit Which digit does the letter X represent? (A) (B) (C) (D) X X (E) + X Y Y Z X 14 A maths student made the following pattern: 11 15 16 15 11 The numbers down the sides of the pattern increase by and each of the other numbers is found by adding the two numbers above it What will be the sum of all the numbers on the next line in this pattern? (A) 128 (B) 138 (C) 148 (D) 158 (E) 168 15 The school bought 18 boxes of primary school paint for $900 Each box had a number of bottles, each worth $2.50 How many bottles were in each box? (A) 15 (B) 20 (C) 45 (D) 50 (E) 125 16 One year in June, there were four Wednesdays and five Tuesdays On which day was the first of June? (A) Monday (B) Tuesday (C) Thursday (D) Friday (E) Saturday 17 What percentage of this shape is shaded? (A) 40% (D) 52% (B) 48% (C) 50% (E) 66% UP 18 At 10 am the school flagpole cast a shadow m long Next to the flagpole, the 0.5 m tap cast a shadow of 0.3 m How tall is the flagpole in metres? (A) (B) (D) 10 (C) ? (E) 12 0.5 m 6m 0.3 m 19 This shape can be folded up to make a cube Which cube could it make? (A) (D) C9 (C) 1= (B) C= C (E) = C9 20 The area of the large rectangle is 300 square metres It is made up of four identical smaller rectangles What is the width of one of the small rectangles in metres? (A) (B) (C) (D) 10 (E) 12 = UP Questions 21 to 25, marks each 21 Which one of the patterns below would be created with these folds and cuts? (A) (B) (C) (D) 22 The whole numbers from to are to be placed in the seven circles in the diagram In each of the three triangles drawn, the sum of the three numbers is the same Two of the numbers are given What is X + Y ? (A) (B) (D) X (C) (E) 23 A square ABCD with a side of cm is joined with a smaller square EF GC with a side of cm as shown What is the area of the shaded shape BDF E? (A) 12 cm2 (B) 14 cm2 (D) 18 cm2 (C) 16 cm2 (E) 24 cm2 (E) Y A B E D F C G UP 24 In this year of 2017, my family is in its prime: I am 7, my brother is 5, my mother is 29 and my father is 31 All of our ages are prime numbers What is my father’s age the next year that my family is in its prime, when all of our ages are again prime? (A) 37 (B) 41 (C) 43 (D) 47 (E) 61 25 A triangular prism is to be cut into two pieces with a single straight cut What is the smallest possible total for the combined number of faces of the two pieces? (A) (B) (D) 10 (C) (E) 11 For questions 26 to 30, shade the answer as a whole number from to 999 in the space provided on the answer sheet Question 26 is marks, question 27 is marks, question 28 is marks, question 29 is marks and question 30 is 10 marks 26 Two rectangles overlap to create three regions, each of equal area The original rectangles are cm by 15 cm and 10 cm by cm as shown The sides of the smaller shaded rectangle are each a whole number of centimetres What is the perimeter of the smaller shaded rectangle, in centimetres? 15 10 UP 27 Jonathan made a tower with rectangular cards cm long and cm wide, where each row has one more card than the row above it The perimeter of a tower with levels is 18 cm, as shown What will be the perimeter of a tower with 10 levels, in centimetres? 28 All of the digits from to are used to form two 5-digit numbers What is the smallest possible difference between these two numbers? 29 A jigsaw piece is formed from a square with a combination of ‘tabs’ and ‘slots’ on at least two of its sides Pieces are either corner, edge or interior, as shown corner piece (two straight sides at right angles) edge piece (one straight side) interior piece (no straight sides) We treat two shapes as the same if one is a rotation of the other, without turning it over How many different shapes are possible? 30 A 3×3 grid has a pattern of black and white squares A pattern is called balanced if each × subgrid contains exactly two squares of each colour, as seen in the first example The pattern in the second example is unbalanced because the bottom-right × subgrid contains three white squares Counting rotations and reflections as different, how many balanced × patterns are there? balanced unbalanced ... beginning and the end of a two-digit number, its value is increased by 1190 What is this two-digit number? *** Upper Primary Division Questions to 10, marks each Which number is made up with hundred,... (C) 720◦ *** (E) (D) 900◦ (E) 1080◦ Upper Primary Division Questions to 10, marks each Which of these numbers is the largest? (A) (B) 800 (C)... looking for all the edge pieces How many of these edge pieces should she expect to find? *** Upper Primary Division Questions to 10, marks each Which of these numbers is the largest? (A) 132 542 (B)