0322_SHSPT_MATHEMATICAL_REASONING_QUESTION_PAPER.docx

# Problem Solving ## Problem 1 A diagram of a scale with three packages on it. Package 1 is labeled 1, package 2 is labeled 2, and package 3 is labeled 3. The scale shows a total weight of 1.1 kg. Three packages are weighed together. Their total mass is shown on the scale. Package 1 has a mass of...

# Problem Solving ## Problem 1 A diagram of a scale with three packages on it. Package 1 is labeled 1, package 2 is labeled 2, and package 3 is labeled 3. The scale shows a total weight of 1.1 kg. Three packages are weighed together. Their total mass is shown on the scale. Package 1 has a mass of 850 g. Package 2 has a mass of 225 g. What is the mass of package 3? - A 975 g - B 1175 g - C 1425 g - D 1525 g - E 2425 g ## Problem 2 A diagram of six empty circular pots in a tray. To the right of the tray are five potted plants, each with a red blossom. At a garden shop, Claire is packing plants into boxes. Each box holds 6 plants. She has 149 plants. She wants to fill 27 boxes. How many more plants does she need? - A 1 - B 5 - C 7 - D 13 - E 17 ## Problem 3 A diagram with a square, a triangle, and a circle. ### Diagram Rules - Multiply the number in the square by 4. - Multiply the number in the triangle by 3. - Find the difference between these two results and write it in the circle. The number in the square is greater than one. The number in the square is 2. The number in the triangle is 14. What is the number in the square? - A 2 - B 4 - C 5 - D 8 - E 20 ## Problem 4 A diagram of a pizza divided into 10 slices. The pizza has two slices shaded in blue, four slices shaded in red, and four are empty. Rana eats 2/10 of the pizza. Penny eats 2/10 of the pizza. Joshua eats 5/10 of the pizza. Which of these statements is/are correct? - They eat the whole pizza. - Joshua eats the least pizza. - Penny eats twice as much pizza as Joshua. - A statement 1 only - B statement 2 only - C statements 1 and 2 only - D statements 1 and 3 only - E statements 2 and 3 only ## Problem 5 Which of the following calculations shows how to work out the number of seconds in 24 days? - A 24 x 24 - B 24 x 60 - C 24 x 24 x 60 - D 24 x 60 x 60 - E 24 x 24 x 60 x 60 ## Problem 6 A column chart, showing the number of children in six classes at a school. The column for class 6 has not been drawn. There are 30 children in class 3. There are a total of 160 children in six classes in a school. The column graph shows the number of children in classes 1 to 5. The column for Class 6 has not been drawn. There are 30 children in Class 3. How many children are in Class 6? - A 21 - B 26 - C 32 - D 41 - E 42 ## Problem 7 A diagram of a balance scale, with two squares and one triangle on the left side and three triangles on the right side. Each square and triangle is a separate object. The total mass of the objects on the left side of the balancing scales is the same as the total mass of the objects on the right. Each square has equal mass. Each triangle has equal mass. If the mass of each triangle is 6 grams, what is the mass of each square? - A 3 g - B 7 g - C 8 g - D 9 g - E 18 g ## Problem 8 A table showing the time taken by five racing drivers to complete one lap of a motor racing circuit. | Name | Time (seconds) | |---|---| | Smith | 58.117 | | Cruz | 58.208 | | Adams | 58.046 | | Batra | 58.2 | | Evans | 58.31 | Who were the fastest three drivers, in order, starting with the fastest? - A Evans, Cruz, Batra - B Evans, Cruz, Smith - C Batra, Evans, Adams - D Adams, Smith, Evans - E Adams, Smith, Batra ## Problem 9 A diagram shows a boy standing at point P facing east. The boy will turn clockwise to face a house at point H. The angle between north and the line connecting P and H is 60 degrees. A boy is standing at point P, facing east. He turns clockwise to face a house which is at point H. What is the angle of his turn? - A 30° - B 60° - C 150° - D 210° - E 300° ## Problem 10 Alex had $76. He spent some of it in a shop. Then he gave half of what he had left to Charlie. Charlie spent a quarter of what Alex gave him on lunch. Charlie spent $9 on lunch. How much did Alex spend in the shop? - A $4 - B $12 - C $14 - D $36 - E $40 ## Problem 11 A rectangular prism is made from identical small cubes. Each small cube is solid and looks like this from the side: a square. The three diagrams below show three different faces of the rectangular prism. Diagram1: A 2x2 square of cubes. Diagram2: A 2x3 rectangular prism of cubes. Diagram 3: A 3x3 square of cubes. How many small cubes is the rectangular prism made from? - A 20 - B 30 - C 31 - D 62 - E 900 ## Problem 12 Jennifer sells bunches of flowers. She wants to make a picture graph to show the data in the table. | Day | Number of bunches of flowers sold | |---|---| | Monday | 24 | | Tuesday | 28 | | Wednesday | 36 | She wants to use these pictures only in her picture graph: - Picture of a whole flower - Picture of half a flower She will not draw any other fractions of a flower. Which of these keys can she use to represent the data correctly? - Key X: represents 4 bunches - Key Y: represents 8 bunches - Key Z: represents 12 bunches - A None of them - B Key X or key Y only - C Key X or key Z only - D Key Y or key Z only - E Key X, Y, or Z ## Problem 13 Three different numbers are chosen from the numbers 3, 5, 6, and 8. They are then added together. Which of these statements is/are correct? - The total cannot be a multiple of 8. - The total can be a multiple of 3. - The total is always odd. - A None of them - B Statement 1 only - C Statement 2 only - D Statement 3 only - E Statements 2 and 3 only ## Problem 14 The diagram shows a triangle inside a rectangle. The area shaded grey is 84 cm². The length of the rectangle is 12 cm and the width is 11 cm. The hypotenuse of the triangle is the diagonal of the rectangle, and one vertex of the triangle is at one of the corners of the rectangle. What is the area of the triangle? - A 33 cm² - B 37 cm² - C 42 cm² - D 48 cm² - E 52 cm² ## Problem 15 Seo-Jung has been recording rainfall for the last 5 weeks by collecting it in a container. The container was empty at the start of week 1. Seo-Jung recorded the amount of rain in the container at the end of each week. No water was lost during the 5 weeks. The diagrams show what he recorded: - Week 1-5: Bars with the following measurements in mL: 10, 20, 10, 20, 30 During which two weeks was there exactly the same amount of rainfall? - A Week 1 and week 2 - B Week 1 and week 4 - C Week 2 and week 3 - D Week 2 and week 4 - E Week 3 and week 5 ## Problem 16 Brody is thinking of a quadrilateral. The quadrilateral has: - No parallel sides. - Two sides of 5 cm and two sides of 8 cm. - Exactly one right angle. How many lines of symmetry does Brody's quadrilateral have? - A 0 - B 1 - C 2 - D 3 - E 4 ## Problem 17 A gardener has a box of bulbs to plant in a garden. The garden has three sections. - She plants 2/3 of the bulbs in the first section. - She plants 4/3 of the remaining bulbs in the second section. - She has 6 bulbs left, which she plants in the third section. How many bulbs were in the box at the start? - A 16 - B 18 - C 24 - D 32 - E 48 ## Problem 18 A cube painted around one vertex. Which of the following diagrams could be a net for this cube? - Diagram 1: A 2x2 square with a square sticking off the side. The top square and the side square are shaded. - Diagram 2: A 3x3 square with the top left corner and the square above it shaded. - Diagram 3: A 3x3 square with the top left corner and the square to the right shaded. - A Diagram 1 only - B Diagram 2 only - C Diagram 3 only - D Diagrams 1 and 2 only - E Diagrams 1 and 3 only ## Problem 19 A bag contains three colors of disc: red, blue, and yellow. There are an equal number of red discs and blue discs. There are twice as many blue discs as yellow discs. One disc is selected without looking. What is the probability of selecting a blue disc? - A 1/5 - B 1/4 - C 1/3 - D 2/5 - E 2/3 ## Problem 20 Here is part of a menu from a cafe. The prices have been torn off. MENU Burger $ Chips $ Drinks $ - Burger and a drink cost $6.00 in total. - Chips and a drink cost $3.75 in total. - A burger, chips, and a drink cost $8.50 in total. How much does a burger and chips cost in total? - A $2.25 - B $4.75 - C $7.25 - D $7.75 - E $9.75 ## Problem 21 Jason's clock was working normally until 7:05 am. At 7:05 am, he dropped the clock. For the rest of the day, the clock's hands turned twice as fast as normal. At 3:25 pm that day, what time did the clock show? - A 7:05 - B 8:55 - C 9:55 - D 10:55 - E 11:55 ## Problem 22 I have an equal number of $1 and $2 coins. The total value of the coins is $54. $1 coins weigh 9 grams and $2 coins weigh 7 grams. What is the total weight of all my coins? - A 144 g - B 288 g - C 414 g - D 432 g - E 576 g ## Problem 23 Two statues are 8 kilometres 23 metres apart. A map-maker incorrectly labels the distance between the statues on a map. The incorrect distance is 23 km 8 m. What is the difference between the correct and incorrect distances? - A 14 km 85 m - B 14 km 985 m - C 15 km 15 m - D 15 km 85 m - E 15 km 985 m ## Problem 24 Jedda draws a map of an island showing areas where there are only hills, only bush, or both. These three areas cover the whole island. - The total area of the island is 164 km². - The total area where there are hills is 132 km². - The total area where there is bush is 80 km². What area of the island has both hills and bush? - A 24 km² - B 32 km² - C 48 km² - D 52 km² - E 84 km² ## Problem 25 A display has three lights that flash at different intervals. - The red light flashes every 2 minutes. - The green light flashes every 3 minutes. - The blue light flashes every 5 minutes. The lights all flash together at 7:00 am. How many times between 7:01 am and 9:59 am the same morning do the green and blue lights flash together without the red light also flashing? - A 6 - B 8 - C 9 - D 11 - E 12 ## Problem 26 Three planks of wood all have the same length. They are placed next to each other as shown. - 40 cm to the left of the first plank - 5 cm between planks - 135 cm to the right of the last plank What is the length of one plank of wood? - A 45 cm - B 50 cm - C 60 cm - D 75 cm - E 85 cm ## Problem 27 Alison shaded 3 small squares in a grid. She wants to shade extra squares to make a pattern with exactly four lines of symmetry. What is the smallest number of extra squares she needs to shade? - A 3 - B 5 - C 7 - D 9 - E 13 ## Problem 28 Merindah sold drinks at the class barbecue. The drinks were orange or lemon. She sold 33 drinks altogether. Which of these statements cannot be correct? - She sold ten more orange drinks than lemon drinks. - She sold twice as many orange drinks as lemon drinks. - She sold five more lemon drinks than orange drinks. - A Statement 1 only - B Statement 2 only - C Statement 3 only - D Statements 1 and 2 only - E Statements 2 and 3 only ## Problem 29 This shape is a trapezium with two right angles. The height of the trapezium is 3 cm, the shorter length is 2 cm, and the longer length is 6 cm. Anna has a square piece of card with side length 24 cm. What is the greatest possible number of these trapeziums Anna can cut out from this card? - A 16 - B 24 - C 32 - D 48 - E 64 ## Problem 30 Jamal makes a number sequence. He chooses the 1st number in the sequence. Then he follows these two rules, one after the other, repeatedly: - Subtract 100 to get the next number in the sequence. - Add 10 to get the next number in the sequence. The 6th number in the sequence is 8451. What is the 1st number in Jamal's sequence? - A 8171 - B 8181 - C 8711 - D 8721 - E 8731 ## Problem 31 A robot is facing south-east. It makes 58 quarter-turns clockwise, then 93 quarter-turns anti-clockwise. In which direction is the robot now facing? - A North - B North-east - C North-west - D South-east - E South-west ## Problem 32 This shape is made from rectangles. The diagram is made up of five rectangles: - A 14x16 rectangle, with a 5x1 rectangle sticking out of the left side and a 2x1 rectangle sticking out of the right side. - This rectangle has a 3x3 rectangle sticking out of the bottom and a 3x2 rectangle sticking out of the bottom right side. What is the perimeter of this shape? - A 44 cm - B 52 cm - C 60 cm - D 64 cm - E 68 cm ## Problem 33 Timothy writes down the number 24. He reverses the digits to make the number 42. He then works out that 42 is 18 more than his starting number, 24. Nicole writes down a whole number between 10 and 99. She also reverses the digits of her number. She finds that this makes a number that is 72 more than her starting number. What was the last digit of Nicole's starting number? - A 2 - B 3 - C 5 - D 7 - E 9 ## Problem 34 Harry has a large, solid cube made from 64 small cubes. He removes some small cubes. He now sees this view when he looks at any of the six faces: a 3x3 square with one square removed from the center. How many small cubes are in the object now? - A 16 - B 32 - C 36 - D 40 - E 72 ## Problem 35 Aaron and Tom have a game where they each spin a spinner with the numbers 1, 2, and 3 on it once, and whoever spins the higher number wins. They play this game 8 times. - Aaron spins two 1s, three 2s, and three 3s. - Tom spins two 1s, five 2s, and one 3. There are no draws. How many games does Aaron win? - A 2 - B 4 - C 5 - D 6 - E It is not possible to tell.