Year 9 Practice Test
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Define census.
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Data collected on an entire population.
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Define survey.
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Data collected on a set members of a group.
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Give an example of quantitative data on a black and white sheep dog.
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The dog has two ears OR 4 legs (Numerical information)
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Give an example of continuous data of a cat.
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She weighs 5.4 kg for example. (It takes on a certain values)
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Which of the following is discrete data? a) Sam is 160 cm tall. b) Sam weighs 60 kg. c) Sam has one brother. d) Sam ran 100m in 10.2 s
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c) Sam has one brother.
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A spinner is made up of a piece of card in the shape of a regular pentagon, with a toothpick pushed through its centre. The five triangles are numbered from 1 to 5. The spinner is spun until it lands on one of the five edges of the pentagon. What is the probability that the number it lands on is odd?
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There are three odd numbers (1, 3 and 5), so the Number of ways it can happen = 3. There are five numbers altogether, so the Total number of outcomes = 5. So the probability the number is odd = 3/5.
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Each of the letters of the word MISSISSIPPI are written on separate pieces of paper that are then folded, put in a hat, and mixed thoroughly. One piece of paper is chosen (without looking) from the hat. What is the probability it is an I?
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There are 4 I's in the word MISSISSIPPI, so the Number of ways it can happen = 4 There are 11 letters altogether in the word MISSISSIPPI, so the Total number of outcomes = 11 So the probability the letter chosen is an I = 4/11 = 36%
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A fair coin is tossed three times. What is the probability of obtaining one Head and two Tails? (A fair coin is one that is not loaded, so there is an equal chance of it landing Heads up or Tails up.) Draw a tree diagram.
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Represent 'Heads up' by H and 'Tails up' by T. There are 8 possible ways the coins can land: (H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H) and (T, T, T) Of these, 3 have one Head and two Tails: (H, T, T), (T, H, T) and (T, T, H) So: The Number of ways it can happen = 3 The Total number of outcomes = 8 3/8
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A ladder 5 m long, leaning against a vertical wall makes an angle of 65? with the ground. a) How high on the wall does the ladder reach? b) How far is the foot of the ladder from the wall? c) What angle does the ladder make with the wall?
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a) The height that the ladder reach is PQ PQ = sin 65? × 5 = 4.53 m b) The distance of the foot of the ladder from the wall is RQ. RQ = cos 65? × 5 = 2.11 m c) The angle that the ladder makes with the wall is angle P
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A helicopter, flying at a constant altitude of 91 m, sights the middle of a landing pad at an angle of depression of 16 degrees. How far, in metres, must the helicopter travel to be directly over the landing spot at an altitude of 91 m? Draw a diagram to assist you.
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The helisopter must travel 317m.
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A train leaves Paddistone Station and travels 40 km on a bearing of 060 degrees from true north to Tarrigal Station. How far East of Paddistone is Tarigal station?
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36.64km
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A 10 metre long ladder rests against a vertical wall so that the distance between the foot of the ladder and the wall is 2 metre. Find the angle the ladder makes with the wall and height above the ground at which the upper end of the ladder touches the wall.
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Let AB be the ladder, BC the horizontal ground and AC the vertical wall. Step 1: From the triangle ACB sin A = BCAB = 210 = 0.2 or A = sin?1(0.2) = 0.2013 =; A = 0.2 The ladder makes an angle of 0.2 with the wall Step 2: Again, cos A = ACAB =; cos A = AC10 =; AC = 10 cos(0.2) = 10 x 0.98 = 9.8 Hence the ladder reaches 9.8 m up the wall.
