Top 40 Topics 01 10 Topic Date completed Exam Q s completed 01. Two Way Tables 02. Scatter Graphs 03. Stem and Leaf 04. Product of Prime Factors 05. Trial and Improvement 06. Questionnaires 07. Averages from a Table 08. Averages from Grouped Data 09. Cumulative Frequency 10. Box Plots
01 - TWO WAY TABLES Q1. The two-way table gives some information about how 100 children travelled to school one day. Walk Car Other Total Boy 15 14 54 Girl 8 16 Total 37 100 (a) Complete the two-way table. (3) One of the children is picked at random. (b) Write down the probability that this child walked to school that day.... (1) Q2. Ali asked 200 students which sport they like best. They could choose swimming or tennis or athletics. The two-way table shows some information about their answers. Swimming Tennis Athletics Total Female 19 Male 36 42 Total 79 54 200 Complete the two-way table. (Total 3 marks)
Q3. A teacher asked 30 students if they had a school lunch or a packed lunch or if they went home at lunch. 17 of the students were boys 4 of the boys had a packed lunch 7 girls had a school lunch 3 of the 5 students who went home were boys Work out the number of students who had a packed lunch Q4. Janice asks 100 students if they like biology or chemistry or physics best. 38 of the students are girls. 21 of these girls like biology best. 18 boys like physics best. 7 out of the 23 students who like chemistry best are girls. Work out the number of students who like biology best.
Q1. Six pupils took a spelling test. 02 - SCATTER GRAPHS Time spent revising (minutes) 10 15 35 40 45 50 Number of mistakes made in the test 14 11 5 5 2 3 Plot the data on the scatter diagram. A pupil revised for 25 minutes. Use a line of best fit to estimate the number of mistakes he made.
Q2. The table shows the population (in tens of thousands) of 10 English counties and the grant (in millions of pounds) they each received to prevent flooding. Population (10,000s) Grant ( millions) 29 58 108 34 115 19 136 25 47 49 8 17 34 10 34 7 41 9 12 17 The first six points have been plotted on this scatter diagram. a) Complete the scatter diagram. b) Describe the relationship shown in the scatter diagram. c) Draw a line of best fit on your scatter diagram. (1) (1) d) Another country has a population of 80,000. Use your line of best fit to estimate the grant for this country. (1)
Q3. Harriet reads eight books. For each book she records the number of pages and the time she takes to read it. The scatter graph shows information about her results. a) Describe the relationship between the number of pages in a book and the time Harriet takes to read it. (1) b) Harriet reads another book. The book has 150 pages. Estimate the time it takes Harriet to read it.
03 - STEM AND LEAF Q1. Here are the ages, in years, of 15 teachers. 35 52 42 27 36 23 31 41 50 34 44 28 45 45 53 Draw an ordered stem and leaf diagram to show this information. You must include a key. Key: (3) Q2. Here are the speeds, in miles per hour, of 16 cars. 31 52 43 49 36 35 33 29 54 43 44 46 42 39 55 48 Draw an ordered stem and leaf diagram for these speeds. (3)
Q3. Anna hits some tennis balls. The speeds (mph) of the balls are shown. 46 55 64 48 51 57 65 60 53 72 61 59 52 53 49 (a) Show the data in an ordered stem and leaf diagram. Remember to complete the key. Key:...... represents... mph (b) Work out the median speed Q4. Here are the weights in grams, to the nearest gram, of 15 eggs. 33 46 41 54 51 38 60 44 55 51 62 55 52 37 63 (a) Complete the ordered stem and leaf diagram to show this information. You must include a key. (4) (1) Key: (3)
Meg is going to pick at random one of the eggs. (b) Work out the probability that this egg will have a weight of more than 45 grams. Q5. Jim did a survey on the lengths of caterpillars he found on a field trip. Information about the lengths is given in the stem and leaf diagram. 1 3 5 7 7 2 0 6 8 8 8 9 Key: 5 2 means 5.2 cm 3 1 5 5 5 5 6 8 9 4 1 5 5 2 (a) Work out the median. (b) Work out the range.... cm (c) Work out the mode.... cm... cm
04 - PRODUCT OF PRIME FACTORS Q1. Write 84 as a product of its prime factors. Q2. Express 180 as a product of its prime factors. Q3. Write 360 in the form 2 a x 3 b x 5 c Q4. The number 1104 can be written as 3 x 2 c x d, where c is a whole number and d is a prime number. Work out the values of c and d.
05 TRIAL AND IMPROVEMENT Q1. The equation x 3 + 3x = 41 has a solution between 3 and 4 Use a trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show all your working. Answer x =... (4 marks) Q2. Use trial and improvement to find a solution to the equation x 3 + 6x = 29 Continue the table of results. Give your solution to 1 decimal place. x x 3 + 6x Comment 2 20 Too small
Q3. Use trial and improvement to solve this problem. x 3 2x = 7 Give your answer to 1 decimal place. Show all your trials and their outcomes. Q4. The equation 2x 2 + x = 7 has a solution between x = 1 and x = 2. Use trial and improvement to find this solution correct to 1 decimal place.
Q5 a) Show that the equation x 3 + 3x - 7 = 0 has a solution between x = 1 and x = 2. b) Using trial and improvement, find this solution correct to 1 decimal place. Show all your trials and their outcomes. Q6. The equation x 3 6x = 72 has a solution between 4 and 5 Use a trial and improvement method to find this solution. Give your answer correct to one decimal place. You must show all your working.
06 QUESTIONNAIRES Q1. Gary wants to find out how much time teenagers spend listening to music. He uses this question on a questionnaire. How many hours do you spend listening to music? 1 to 5 5 to 10 10 to 20 Over 20 a) Write down two things wrong with this question. 1 2 b) Design a better question for Gary s questionnaire to find out how much time teenagers spend listening to music. Q2. Sam wants to find out the type of films people like best. He is going to ask whether they like comedy, action, science fiction or musical films best. a) Design a suitable table for a data collection sheet he could use to collect this information. Sam collects his data by asking 10 students in his class at school. This might not be a good way to find out the types of film people like best. b) Give one reason why.
Q3. 200 students in year 11 took a mathematics test. Kamini wants to find out whether these students like mathematics. For her sample she asks the 20 students who got the highest marks in the test. This is not a good sample to use. a) Write down one reason why. She uses this question on her questionnaire. What do you think of mathematics? Excellent Very good Good b) Write down one thing that is wrong with this question. Kamini also wants to find out how many hours students spend on their mathematics homework. c) Design a suitable question that Kamini could use on her questionnaire. You must include some response boxes.
07 AVERAGES FROM A TABLE Q1. The table shows the marks scored in a mental arithmetic test by 30 students. Mark Frequency 4 3 5 1 6 2 7 8 8 6 9 5 10 5 a) Which mark is the mode? b) Which mark is the median? c) What is the range of the data? d) Calculate the mean mark Q2. Faisal carries out a survey of 100 students in year 11. He asks each student how many cars there are at their household. The results are shown in the table. Mark Frequency 0 6 1 17 2 52 3 22 4 3 Total 100 Work out the mean number of cars at each household.
Q3. Bianca asked 32 women about the number of children they each had. The table shows information about her results. Number of Frequency children 0 9 1 6 2 7 3 8 4 2 More than 4 0 a) Find the mode b) Calculate the mean
08 AVERAGES FROM GROUPED DATA Q1. 90 people each exercised for 30 minutes. Each person s recovery time was measured. The results are summarised in this table. Recovery time (m minutes) Number of people 0 < m 4 2 4 < m 8 7 8 < m 12 29 12 < m 16 26 16 < m 20 16 20 < m 24 10 Calculate an estimate of the mean recovery time. minutes (4) Write down the modal class. (1) Q2. Caleb measured the heights of 30 plants. The table gives some information about the heights, h cm, of the plants. Height (h cm) of plants Frequency 0 < h 10 2 10 < h 20 8 20 < h 30 9 30 < h 40 7 40 < h 50 4 Work out an estimate for the mean height of the plants. (4) In which class interval does the median lie? (1)
Q3. The table shows some information about the weight, in grams of 60 eggs. Weight (w grams) of plants Frequency 0 < w 30 0 30 < w 50 14 50 < w 60 16 60 < w 70 21 70 < w 100 9 Calculate an estimate for the mean weight of an egg. (4)
09 CUMULATIVE FREQUENCY Q1. This table shows the distribution of the times, in hours and minutes, taken by 100 runners to complete a half marathon. Time (t hours and minutes) Number of runners (frequency) 1 h < t 1 h 10 min 6 1 h 10 min < t 1 h 20 min 24 1 h 20 min < t 1 h 30 min 44 1 h 30 min < t 1 h 40 min 20 1 h 40 min < t 1 h 50 min 5 1 h 50 min < t 2 h 1 a) Complete the cumulative frequency table below Time (t hours and minutes) Cumulative Frequency t 1 h 0 t 1 h 10 min 6 t 1 h 20 min 30 t 1 h 30 min t 1 h 40 min t 1 h 50 min t 2 h 100 (1) b) On the grid, draw a cumulative frequency diagram for the times. (3)
c) Use the cumulative frequency diagram to find an estimate of the number of runners who took longer than 1 hour 35 minutes. Q2. A garage keeps records of the costs of repairs to customers cars. The table gives information about these costs for one month. Cost ( C) Frequency 0 < C 200 7 200 < C 400 11 400 < C 600 9 600 < C 800 10 800 < C 1000 8 1000 < C 1200 5
(a) Write down the modal class interval. (1) (b) Complete the cumulative frequency table. Cost ( C) 0 < C 200 0 < C 400 0 < C 600 0 < C 800 0 < C 1000 0 < C 1200 Cumulative Frequency (1) (c) On the grid, draw a cumulative frequency diagram for your table.
(d) Use the graph to find an estimate for the number of repairs which cost more than 700.... Q3. A fisherman catches 50 fish. The table shows information about the lengths of the fish. Length (l, inches) Frequency Cumulative frequency 5 < l 10 6 6 10 < l 15 20 26 15 < l 20 13 20 < l 25 8 25 < l 30 3 a) Complete the table. (1) b) Draw a cumulative frequency diagram for the data. (3)
Q4. The cumulative frequency diagram shows the distribution of heights, in cm, of 400 students in a school. Use the diagram to find an estimate of a) The median height. (1) b) The number of students with height less than 124cm. (1) c) The number of students with height more than 147cm.
Q5. The following table shows a grouped frequency distribution of the number of reward points collected by 60 different customers at a supermarket. Number of points collected 1-20 21-40 41-60 61-80 Number of customers 4 12 34 10 a) Complete the following cumulative frequency table. Number of points collected 20 40 60 80 Number of customers 4 (1) b) Draw a cumulative frequency diagram to show this information (3) c) Calculate the interquartile range.
10 BOX PLOTS Q1. The box plot represents the distribution of the speeds, in km/h of vehicles on a road during the daytime. (a) (i) What is the median speed? (ii) Work out the interquartile range of the speeds. (1) This box plot represents the distribution of the speeds, in km/h, of vehicles on the same road at night. (b) Make two comparisons between the speeds of vehicles during the daytime and at night.
Q2. Four students Adil, Dev, Freddie and Shane, each kept a record of their scores at cricket one season. The table summarises Adil s scores. Score Lowest 10 Lower quartile 24 Median 40 Upper quartile 60 Highest 110 (a) Draw a box plot to summarise Adil s scores. The box plot summarises Dev s scores. (b) State one similarity and one difference between Adil s and Dev s scores. Similarity: Difference:
Q3. Here is some information about waiting times, in minutes at a school canteen. Minimum Lower Quartile Median Upper Quartile Maximum 0 2.2 4.2 7.6 9.5 Draw a box plot to show this information. A new queuing system is introduced. The box plot shows information about waiting times with the new system. Compare the waiting times of the new and old systems.
Q4. Here are the times, in seconds that 15 people waited to be served at Rose s garden centre. 5 9 11 14 15 20 22 25 27 27 28 30 32 35 44 On the grid, draw a box plot for this information. Q5. All the students in Mathstown School had a test. (3) The lowest mark was 18 The highest mark was 86 The median was 57 The lower quartile was 32 The interquartile range was 38 On the grid, draw a box plot to show this information. (3)
Q6. The box plot gives information about the distribution of the weights of bags on a plane. (a) Jean says the heaviest bag weighs 23 kg. She is wrong. Explain why. (b) Write down the median weight. (1) kg (1) (c) Work out the interquartile range of the weights. kg (1) There are 240 bags on the plane. (d) Work out the number of bags with a weight of 10 kg or less.