Choose a circle to show how much each sentence is like you Very Unlike Me Unlike Me Like Me Very Like Me 1 2 3 4 01. I like maths at school. 02. I am good at maths. 03. My teacher thinks I am good at maths. 04. My Mum and Dad think I am good at maths. 05. I enjoy doing maths in my own time (not at school). 06. I enjoy doing things in maths that I haven't tried before. Page 1
Practice Questions These practice questions are to help you understand how to show your answer for different types of questions. P01. Who is holding a card with an even number on it? Ben Eru Aroha Davina P02. Complete this number pattern. 2, 4,,, 10 Page 2
P03. What fraction of this circle is shaded? P04. Match the sentence with the correct shape. 1. I have three sides 2. I have 4 sides a. b. c. Page 3
P05. Which numbers make this number sentence TRUE? 1 2 3 4 5 P06. Put the numbers 1, 2, 3, and 4 in the boxes to order these numbers from biggest (1) to smallest (4). 3 7 2 0 P07. Select whether the following statements are True or False. In the number 213, the value of 1 is ten. In the number 504, the value of 5 is fifty. TRUE FALSE Page 4
01. What is the volume of the rectangular prism? 30 units 3 50 units 3 55 units 3 60 units 3 02. About how much will an average alligator have grown by the time it is ten years old? 6 zags 9 zags 10 zags 17 zags Page 5
03. In the figure below, WXYZ is a parallelogram. If the area of triangle WXY is 22 square centimetres, what is the area of WXYZ? 11 square centimetres 22 square centimetres 33 square centimetres 44 square centimetres 04. What is the area of the rectangular poster shown below? 50 sq cm 80 sq cm 100 sq cm 600 sq cm Page 6
05. A triangle that has sides with length 6, 6, and 10 is called acute. right. scalene. isosceles. equilateral. 06. The rectangle shown below has an area of 51 square centimetres and a length of 10.2 centimetres. What is the perimeter of the rectangle? 15.2 cm 20.2 cm 30.4 cm 40.8 cm 07. Put the numbers 1, 2, 3 and 4 in the boxes to order these four events from 1 - LEAST likely to occur to 4 - MOST likely to occur. The sun rising in the morning A person living to be 100 years old Selecting a red ball from a bag of black balls A regular coin landing tails up when tossed Page 7
08. During an experiment, Roscoe tossed a fair coin 10 times and got 6 "heads". What is the probability the coin will land showing heads on Roscoe's next toss? 1 2 6 10 4 6 6 4 Use the following information to answer questions 09 to 10. Ivan was on holiday on Waiheke Island. Page 8
09. What direction is Surfdale from Stonyridge? north south east west 10. What is north west of Blackpool? Oneroa Village Ferry Terminal Church Bay Palm Beach End of Section 11. Which of the following could be the amount of concrete a concrete truck can hold? 5 L 5 m 2 5 m 3 5 ha Page 9
12. A cube can also be classified as a rectangular prism. square-based pyramid. cylinder. rhombus. 13. A rectangular picture is pasted on to a sheet of white paper as shown below. What is the area of the white paper NOT covered by the picture? 165cm 2 500cm 2 1900cm 2 2700cm 2 Page 10
14. The diagram below shows ΔPQR on a coordinate plane. Which of the following is the result of a reflection of ΔPQR? Page 11
15. A cylindrical water container is 1.2 metres high and has a diameter of 4.6 metres. Approximately how many cubic metres of water will the container hold when it is half full? 4.33 9.97 29.93 39.87 Use the following information to answer questions 16 to 17. The school field is being hired out as a car park for a local event. 16. Which is the closest estimate of how many cars could be parked close together on the school field? 100 400 1300 1600 17. Explain your answer. Page 12
End of Section 18. The length of CP is 50 100 175 200 19. Patrick made a spinner. What is the likelihood of the arrow on Patrick's spinner landing on yellow? Impossible Poor chance Even chance Good chance Certain Page 13
20. The calculation 3 2 + 4 2 + 7 2 gives you the length HG CB FD EA 21. Which is closest to the height of a cone that has a slant height of 16 centimetres and a radius of 6 centimetres? 10 cm. 14.8 cm. 20 cm. 17.1 cm. Page 14
22. If trapezium KLMN shown below is reflected across the x-axis to form trapezium K'L'M'N', what is the resulting coordinate of point M'? (-4, 5) (-4, -5) (4, -5) (4, 5) 23. Mark wants to compare theoretical and experimental probabilities. He plans to roll two cubes with faces numbered 1 through 6 and add the numbers showing on the top face of each cube. Mark performed 100 trials of this experiment and recorded the results in the table below. The experimental probability can be used as an approximation for the theoretical probability. How could Mark alter his experiment so that the experimental probability is likely to be closer to the theoretical probability? Use one cube. Perform more trials. Use new cubes. Throw the cubes from a tall building. Page 15
24. What is the probability that a teacher chosen at random will be a male? 1 2 9 20 13 32 15 32 25. A coin was tossed 60 times and it came up heads 32 times. The relative frequency of a tail coming up was: 15 8 7 8 8 15 7 15 8 7 26. A landing pad for a helicopter is in the shape of a circle with a radius of 7 metres. Which of the following is closest to the area of the landing pad? 44 square metres 154 square metres 205 square metres 308 square metres Page 16
27. Pipelines from an oil well to a storage tank can be represented by vectors. Which of these vectors is the longest? ( 4) 3 ( 2 5 ) ( 1 6 ) ( 4 0) ( 5) 1 28. A rectangle has a perimeter of 44 cm and an area of 72 square cm. What are the lengths of the sides of the rectangle? 2 cm and 36 cm 4 cm and 18 cm 8 cm and 9 cm 11 cm and 11 cm 29. The sum of the interior angles of a polygon is the same as the sum of its exterior angles. What type of polygon is it? quadrilateral hexagon octagon decagon Page 17
30. To determine the distance across a pond. Harry made the measurements shown in the diagram. Which is closest to the distance from R to S? 3.48 m 19.7 m 20.3 m 113.4 m 31. Triangles ABC and DEF are similar triangles. What is the length of side AC? 2 4 4.5 5.5 32 Page 18
32. Alice stood in front of a large mirror and rotated her left hand clockwise. When she looked at her reflection in the mirror which of the following did she observe about her image? Her image's right hand moving anticlockwise. Her image's left hand moving anticlockwise. Her image's right hand moving clockwise. Her image's left hand moving clockwise. 33. Which of the following solids has a regular cross section? Sphere Cone Prism Pyramid 34. When playing a board game, you spin two spinners with congruent sectors numbered 1 through 7 as shown. If the sum of the two numbers you spin is 12, 13, or 14, you win. What is the probability of winning? 21 49 10 49 15 49 6 49 Page 19
35. PQ and QR are shown. Given the system of vectors PQ and QR, which of the following represents the resultant vector PR? ( 3 3) ( -1 5) ( 2 8) ( -2 5) 36. In the diagram below, lines p and r are parallel. Line s is a transversal that is NOT perpendicular to lines p and r. Which angle is NOT congruent to 5? 1 2 3 7 Page 20
37. The soccer stadium wall casts a shadow that extends 150 metres from its base when the edge of the shadow forms a 23 degree angle with the ground. What is the height of the stadium wall to the nearest metre? 59 metres 64 metres 138 metres 353 metres 38. From school, Larry drove 3 kilometres east and 4 kilometres north to Bob's house. After dropping Bob off, Larry drove 4 kilometres west and 3 kilometres north to his home. Which vector represents Larry's drive to his home from school? ( 3 4) ( 4 3) ( 5 5) ( -1 7) Page 21
39. The lengths of the two short sides of a right triangle are 5 centimetres and 10 centimetres. Which of the following measures is closest to the length of the hypotenuse? 11.2 cm 11.4 cm 11.6 cm 11.8 cm 40. The area of the shaded triangle in the diagram below is 1 square unit. Which is closest to the area of triangle ABC? 2 square units 3 square units 4 square units 5 square units Page 22
41. The chart below shows the number of tiles for each letter in a word game. There are a total of 100 letter tiles in the game. Susan is the first player to select one letter tile. What is the probability that she will select either a M, A, T, or H letter tile as her first selection? 1 45 4 100 4 45 19 100 42. In the circle below, AB, CD are chords intersecting at E. If AE = 5, BE = 12, and CE = 6, what is the length of DE? 7 9 10 13 Page 23
43. A spinner with 3 equal sectors, as shown, was spun 100 times and the results recorded in the table below. Which one of the following statements is correct: The proportion of blue outcomes should increase with 200 spins. The frequencies will be more even with fewer spins. The frequencies will be more even with more spins. The number of spins does not effect the proportion of frequencies. 44. A number cube with faces numbered 1 through 6 will be tossed once, and the arrow on a spinner with equally sized regions labeled A through E will be spun at the same time. What is the probability that the number facing up on the cube will be less than 3 and the arrow will land on a region labeled A or E? 17 30 3 11 2 15 1 15 Page 24
45. If QRS and XYZ are complementary, which must be TRUE? One of the angles can measure between 90º and 180º. The sum of the measures of the angles is 90º. The sum of the measures of the angles is 180º. Both angles must measure more than 90º. 46. Which of the following could be the lengths of the sides of a triangle? 1, 2, 1 2, 3, 1 3, 5, 4 7, 15, 7 47. The trapezium pictured below has the measurements shown. Which measure is closest to the perimeter of the trapezium? 41 cm 59 cm 64 cm 66 cm Page 25
48. Which statement is TRUE for the given triangle? sin θ = sin θ = sin θ = sin θ = 4 sin 65 5 5 sin 65 4 4 5 sin 65 4 4 sin 65 Page 26