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2017 Technology Free exam solutions
Physical Science
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2 Solutions Show all working out to receive full marks 1. The probability that a battery is operational is 0 What is the probability that it is not operational? 1 mark 0 2. A random experiment may result in 1, 2, 3, 4 or 5. If and Pr(4) Pr(5), find the probability of obtaining a 4. 2 marks 13 3 11 I mark 5 2 XC 4 1 13 3. If A and B are events such that Pr(A) 0, Pr(B) 0 and Pr(An 0, find A B 0 a Pr(AnB) 1 mark 0 b B 1 mark 0 2 Solutions Show all working out to receive full marks 1. The probability that a battery is operational is 0 What is the probability that it is not operational? 1 mark 0 2. A random experiment may result in 1, 2, 3, 4 or 5. If and Pr(4) Pr(5), find the probability of obtaining a 4. 2 marks 13 3 11 I mark 5 2 XC 4 1 13 3. If A and B are events such that Pr(A) 0, Pr(B) 0 and Pr(An 0, find A B 0 a Pr(AnB) 1 mark 0 b B 1 mark 0 3 4. Suppose that of the people in Australia, approximately have red hair. Suppose also that of Australians are male, and further that are males with red hair. Use this information to find: R R R M F a the probability that a person selected at random is female and has red hair 1 mark b the probability that a person selected at random is male and does not have red hair. 1 mark 5. The current football fixture has the local team playing at home for of its matches. When the team plays at home, it wins of the time. When the team plays away it wins only of the time. What percentage of games does the team play away and win? 3 marks 0 A O 1 0.4x0.520 1 I 3 4. Suppose that of the people in Australia, approximately have red hair. Suppose also that of Australians are male, and further that are males with red hair. Use this information to find: R R R M F a the probability that a person selected at random is female and has red hair 1 mark b the probability that a person selected at random is male and does not have red hair. 1 mark 5. The current football fixture has the local team playing at home for of its matches. When the team plays at home, it wins of the time. When the team plays away it wins only of the time. What percentage of games does the team play away and win? 3 marks 0 A O 1 0.4x0.520 1 I 5 9. Sketch the graphs of the following two linear inequalities and clearly highlight the area that represents the solution of the two inequalities. 5 marks y area 5 12 1 I X correct lines correct shading Drequired correct area correct yzzxts y? x 4 3 yis S 2 5 9. Sketch the graphs of the following two linear inequalities and clearly highlight the area that represents the solution of the two inequalities. 5 marks y area 5 12 1 I X correct lines correct shading Drequired correct area correct yzzxts y? x 4 3 yis S 2 6 Section Quadratics 14 marks 1. Solve the following equation: 2x2 10x 12 3 marks I or 2. Sketch the graph of the following quadratic equation: y (x 4) 3 4 marks the 2 y (0,13) 4 (4V3,0) 2 X ( 3 ( x 4 ) 2 1 (1 (i T coordinate I Shape 6 Section Quadratics 14 marks 1. Solve the following equation: 2x2 10x 12 3 marks I or 2. Sketch the graph of the following quadratic equation: y (x 4) 3 4 marks the 2 y (0,13) 4 (4V3,0) 2 X ( 3 ( x 4 ) 2 1 (1 (i T coordinate I Shape 8 Section Bivariate Data and Financial 14 marks 1. Examine the graph below that plots the relationship between Hours of exercise per week and resting heart rate. 85 80 75 70 65 60 55 50 45 1 2 3 1 5 6 7 8 9 Hours of Exercise per Week a) What are the units on the 1 mark Hours of exercise per week b) What are the units on the 1 mark Resting heart rate (BPM) c) Which unit is the dependent variable? 1 mark Resting heart rate d) Which unit is the independent variable? 1 mark Hours of exercise e) Using the line of best fit, what would an resting heart rate expected to be if they exercised for 4 hours per week? 1 mark accept 63 64 bpm 8 Section Bivariate Data and Financial 14 marks 1. Examine the graph below that plots the relationship between Hours of exercise per week and resting heart rate. 85 80 75 70 65 60 55 50 45 1 2 3 1 5 6 7 8 9 Hours of Exercise per Week a) What are the units on the 1 mark Hours of exercise per week b) What are the units on the 1 mark Resting heart rate (BPM) c) Which unit is the dependent variable? 1 mark Resting heart rate d) Which unit is the independent variable? 1 mark Hours of exercise e) Using the line of best fit, what would an resting heart rate expected to be if they exercised for 4 hours per week? 1 mark accept 63 64 bpm 9 2. The following scatter plot shows the relationship between the amount of sleep students get the night before a test and the number of mistakes they made. Hours of sleep vs mistakes made 14 12 10 8 6 4 2 0 0 2 4 6 8 10 12 Hours of sleep a) State the type of relationship shown between hours of sleep and mistakes made Strong negative (linear) 1 mark correlation b) What is the independent variable? 1 mark hours of sleep c) What is the dependent variable? 1 mark Mistakes made d) How many hours sleep did the student who made 7 mistakes have? 1 mark G hows of sleep 9 2. The following scatter plot shows the relationship between the amount of sleep students get the night before a test and the number of mistakes they made. Hours of sleep vs mistakes made 14 12 10 8 6 4 2 0 0 2 4 6 8 10 12 Hours of sleep a) State the type of relationship shown between hours of sleep and mistakes made Strong negative (linear) 1 mark correlation b) What is the independent variable? 1 mark hours of sleep c) What is the dependent variable? 1 mark Mistakes made d) How many hours sleep did the student who made 7 mistakes have? 1 mark G hows of sleep
2017 Technology Free exam solutions
Subject: Physical Science
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