PLC Papers Created For:
Conditional Probability 2 Grade 7 Objective: Calculate and interpret conditional probabilities, using expected frequencies with twoway tables, tree diagrams and Venn diagrams Question 1. In a group of students, 45% are girls. 65% of these prefer to play tennis rather than badminton. 10% of the boys prefer to play badminton rather than tennis. One student is chosen at random. Find the probability that this is a boy who prefers to play tennis.... (2) (Total 2 marks)
Question 2. Laura has 9 tins of soup in her cupboard, but all the labels are missing. She knows that there are 5 tins of tomato soup and 4 tins of vegetable soup. She opens three tins at random. Work out the probability that she opens more tins of vegetable soup than tomato soup.... (4)
Question 3 (Total 4 marks) Steve has to catch a flight. The probability of dry weather (D), rain (R) or snow (S) are: P(D) = 0.6, P(R) = 0.35, P(S) = 0.05. If it is dry the probability that Steve will arrive to the airport on time is 0.9. If it rains the probability that he will arrive to the airport on time is 0.6. If it snows the probability that he will arrive to the airport on time is 0.15. Is he more likely to arrive on time to the airport or be late?... (4) (Total 4 marks)
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Boxplots 2 Grade 6 Objective: Interpret and construct box plots Question 1 Dave recorded the length of time 24 pupils took to solve a puzzle. The table shows information about these times in minutes. (a) Work out the number of teachers with a travel time of 3.4 minutes or more. (2) (b) On the grid, draw a box plot to show the information in the table. (2) (Total 4 marks)
Question 2 Jodie measures the lengths of 120 snakes. The lengths were recorded and displayed in the boxplot below. (a) Use the boxplot to fill in the values in this summary table: (3) (b) Calculate the Inter Quartile Range (IQR). (2) (c) One of the snakes measured at 42cm was actually 44cm, what affect would this change have on the median? Decrease Stay the same Increase (1) (Total 6 marks) Total marks /10
Cumulative Frequency 2 Grade 6 Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1 The table below shows information about the heights of 60 students. (a) On the grid, draw a cumulative frequency graph for the information in the table. (3) 60 50 CUMULATIVE FREQUENCY 40 30 20 10 0 140 150 160 170 180 190 200 TIME, T SECS
(b) Find an estimate (i) for the median,... (ii) for the interquartile range.... (Total 6 marks) (3)
Question 2 The table shows information about the lengths, in seconds, of 40 TV adverts. (a) Complete the cumulative frequency table for this information. (1)
(b) On the grid, draw a cumulative frequency graph for your table. (2) 45 40 35 CUMULATIVE FREQUENCY 30 25 20 15 10 5 0 0 10 20 30 40 50 60 70 TIME, T SECS (c) Use your graph to find an estimate for the median length of these TV adverts. seconds (1) (Total 4 marks) Total marks /10
Histograms with unequal class widths 2 Grade 6 Objective: data) Construct and interpret a histogram with unequal class widths (for grouped discrete as well as continuous Question 1 The table shows the length of 678 phone calls made at a call centre Time, secs Frequency 0 < x 20 20 20 < x 60 148 60 < x 120 240 120 < x 300 270 Total 678 a) Draw a fully labelled histogram to show the length of the phone calls. (4)
b) Estimate the number of phone calls that lasted more than 2 minutes. (2) Total for question 6 marks
Question 2 The histogram and the frequency table show some information about the height of some students Height, cms Frequency 130 < x 150 100 150 < x 160 120 160 < x 165 75 165 < x 175 60 175 < x 190 45 Total 400
14 12 10 Frequency Density 8 6 4 2 0 100 120 140 160 180 200 Height, cms a) Use the information to complete the histogram b) Use the histogram to complete the table (2) (2) Total for question 4 marks Total /10
Quartiles and Interquartile Range 2 Grade 5 Objective: Interpolate and calculate quartiles and interquartile range. Question 1 The scores of a maths test are shown below: 37 54 43 57 50 68 69 79 80 77 91 53 96 a) Find the Upper Quartile b) Find the Lower Quartile (2) (1) c) Calculate the Inter-Quartile Range (IQR) (1) d) (i) What is a better measure of spread, Range or Interquartile range (ii) Explain your answer (1).... (1) Total for question 6 marks
Question 2 The table below lists the summary data for the weights of 60 snakes in grams. Weights, kg Minimum 454 L. Quartile 622 Median 660 U. Quartile 812 Maximum 987 a) What is the interquartile range b) Another snake is found to weigh 1340 grams, what effect does this have on (2) (i) The range DECREASE / NO CHANGE / INCREASE (delete as appropriate) (ii) The interquartile range DECREASE / NO CHANGE / INCREASE (delete as appropriate) (1) (1) Total for question 4 marks Total / 10
PLC Papers Created For:
Conditional Probability 2 Grade 7 SOLUTIONS Objective: Calculate and interpret conditional probabilities, using expected frequencies with twoway tables, tree diagrams and Venn diagrams Question 1. In a group of students, 45% are girls. 65% of these prefer to play tennis rather than badminton. 10% of the boys prefer to play badminton rather than tennis. One student is chosen at random. Find the probability that this is a boy who prefers to play tennis. 0.55 x 0.9 Multiply probabilities together M1 0.495 Correct solution A1 oe... (2) (Total 2 marks)
Question 2. Laura has 9 tins of soup in her cupboard, but all the labels are missing. She knows that there are 5 tins of tomato soup and 4 tins of vegetable soup. She opens three tins at random. Work out the probability that she opens more tins of vegetable soup than tomato soup. TVV VTV VVT 5 9 x 4 8 x 3 7 = 5 42 4 9 x 5 8 x 3 7 = 5 42 4 9 x 3 8 x 5 7 = 5 42 VVV 4 9 x 3 8 x 2 7 = 1 21 Correct outcomes chosen Multiplying each probability Adding their probabilities Correct solution M1 M1 M1 A1 P(more vegetable) = 17 42... (4) (Total 4 marks)
Question 3. Steve has to catch a flight. The probability of dry weather (D), rain (R) or snow (S) are: P(D) = 0.6, P(R) = 0.35, P(S) = 0.05. If it is dry the probability that Steve will arrive to the airport on time is 0.9. If it rains the probability that he will arrive to the airport on time is 0.6. If it snows the probability that he will arrive to the airport on time is 0.15. Is he more likely to arrive on time to the airport or be late? P(on time) = (0.6 x 0.9) + (0.35 x 0.6) + (0.05 x 0.15) P(late) = (0.6 x 0.1) + (0.35 x 0.4) + (0.05 x 0.85) M1 M1 P(on time) = 0.76 and P(late) = 0.24 A1 Steve is more likely to be on time. C1... (4) (Total 4 marks) Total /10
Boxplots 2 Grade 6 SOLUTIONS Objective: Interpret and construct box plots Question 1 Dave recorded the length of time 24 pupils took to solve a puzzle. The table shows information about these times in minutes. (a) Work out the number of teachers with a travel time of 3.4 minutes or more. 75% of 24 = (18) M1 (b) On the grid, draw a box plot to show the information in the table. 18 A1 (2) (2) (Total 4 marks)
Question 2 Jodie measures the lengths of 120 snakes. The lengths were recorded and displayed in the boxplot below. (a) Use the boxplot to fill in the values in this summary table: Length, cms Minimum 24 Lower Quartile 38 Median 40 Upper quartile 46 Maximum 54 (3) (b) Calculate the Inter Quartile Range (IQR). 46 38 = (8) M1 8 A1 (2) (c) One of the snakes measured at 42cm was actually 44cm, what affect would this change have on the median? Decrease Stay the same Increase (1) (Total 6 marks) Total marks /10
Cumulative Frequency 2 Grade 6 SOLUTIONS Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1 The table below shows information about the heights of 60 students. (a) On the grid, draw a cumulative frequency graph for the information in the table. (3) 70 60 CUMULATIVE FREQUENCY 50 40 30 20 10 0 140 150 160 170 180 190 200 HEIGHT, CMS
(b) Find an estimate (i) for the median,...172...a1... (ii) for the interquartile range....177 165 = (12)...M1 A1 (Total 6 marks) (3)
Question 2 The table shows information about the lengths, in seconds, of 40 TV adverts. (a) Complete the cumulative frequency table for this information. (1) (b) On the grid, draw a cumulative frequency graph for your table. (2)
CUMULATIVE FREQUENCY 45 40 35 30 25 20 15 10 5 0 0 10 20 30 40 50 60 70 TIME, T SECS (c) Use your graph to find an estimate for the median length of these TV adverts. 37 B1 seconds (1) (Total 4 marks) Total marks /10
Histograms with unequal class widths 2 Grade 6 SOLUTIONS Objective: data) Construct and interpret a histogram with unequal class widths (for grouped discrete as well as continuous Question 1 The table shows the length of 678 phone calls made at a call centre Time, secs Frequency Class Width Freq. Density 0 < x 20 20 20 1.0 20 < x 60 148 40 3.7 60 < x 120 240 60 4.0 120 < x 300 270 180 1.5 Total 678 a) Draw a fully labelled histogram to show the length of the phone calls. 4.5 4 3.5 3 Frequency Density 2.5 2 1.5 1 0.5 0 0 50 100 150 200 250 300 350 Time, secs (4)
b) Estimate the number of phone calls that lasted more than 2 minutes. 4 minutes = 4 x 60 secs = 240 secs 300 240 = 60 mins 60 x 1.5 = (90 calls) M1 90 calls A1 (2) Total for question 6 marks
Question 2 The histogram and the frequency table show some information about the height of some students Height, cms Frequency Class Width Freq. Density 130 < x 150 100 20 5.0 150 < x 160 120 10 12.0 160 < x 165 75 5 15.0 165 < x 175 60 10 6.0 175 < x 190 45 15 3.0 Total 400 16 14 12 Frequency Density 10 8 6 4 2 0 100 120 140 160 180 200 Height, cms a) Use the information to complete the histogram b) Use the histogram to complete the table (2) (2) Total for question 4 marks Total /10
Quartiles and Interquartile Range 2 Grade 5 SOLUTIONS Objective: Interpolate and calculate quartiles and interquartile range. Question 1 The scores of a maths test are shown below: 37 54 43 57 50 68 69 79 80 77 91 53 96 Minimum 37 L. Quartile 53 Median 68 U. Quartile 79 Maximum 96 a) Find the Upper Quartile Write numbers in order M1 b) Find the Lower Quartile 79.5 A1 (2) 51.5 A1 (1) c) Calculate the Inter-Quartile Range (IQR) 79 53 = (26) M1 28 A1 (1) d) (i) What is a better measure of spread, Range or Interquartile range (ii) Explain your answer Interquartile range A1 (1) Range does not allow for outliers whereas Interquartile only look sat middle chunk of data. C1.. (1) Total for question 6 marks
Question 2 The table below lists the summary data for the weights of 60 snakes in grams. Weights, kg Minimum 454 L. Quartile 622 Median 660 U. Quartile 812 Maximum 987 a) What is the interquartile range 812 622 = (190) M1 b) Another snake is found to weigh 1340 grams, what effect does this have on 190 A1 (2) (i) The range DECREASE / NO CHANGE / INCREASE (delete as appropriate) (ii) The interquartile range DECREASE / NO CHANGE / INCREASE (delete as appropriate) (1) (1) Total for question 4 marks Total / 10