Cambridge Lower Secondary Maths STAGE 8: STUDENT’S BOOK REVIEW UNITS All the questions and answers in this material have been written by the authors. This material has not been through the Cambridge International endorsement process. Review units Review 1A Chapters 1–4 Chapter 1 Negative numbers 1 Problem solving Ramesh has these number cards. –4 –9 8 –8 5 Show how Ramesh can use his cards to complete these number statements. + a) 2 =1 b) – =1 Find the missing number in each statement. a) 9 × –3 = ………… b) –66 ÷ –6 = ………… c) 60 ÷ ………… = –15 d) 3 × –2 = ………… ÷ 4 Chapter 2 Place value and rounding 1 Here are four powers of 10. 104 107 106 103 Use these powers of 10 each exactly once to complete these sentences. ………….. is equal to ten thousand ………….. is greater than one million ………….. is smaller than …………… 2 3 Work out a) 250 × 0.01 b) 0.042 ÷ 0.1 c) 450 ÷ 0.01 d) 0.32 × 0.1 e) 5.6 × 0.01 f) 1.9 ÷ 0.1 Use these numbers to complete these number statements. Use each number exactly once. 0.045 0.54 0.0554 0.102 …………. < 0.12 0.036 < …………. < …………. < 0.06 0.504 ≠ ………….. Online resources 1 4 Round each number to the accuracy shown. a) 457 476 to the nearest thousand b) 10.104 to the nearest whole number c) 2.154 to 1 decimal place d) 0.3476 to 2 decimal places Chapter 3 Fractions, decimals and percentages 1 Maria has some money. She spends 44% of her money on a coat 22.5% of her money on some shoes 3 200 of her money on some socks. a) Write 44% as a fraction in its simplest form. b) Write 22.5% as a decimal. c) Write 2 as a percentage. Use division to convert these fractions to recurring decimals. a) 3 3 200 8 9 b) 2 15 c) 1 18 Write each set of fractions in order of size starting with the smallest. a) 2 3 17 27 5 9 b) 3 16 1 6 5 24 Chapter 4 Mental methods 1 2 Given that 21 × 28 = 588, work out: a) 21 × 14 ……….. b) 42 × 28 ……….. c) 22 × 28 ……….. d) 588 ÷ 21 ……….. Decide if these statements are true or false. a) 3 2 13 25 = 0.56 b) 1.3 = 103% c) 2 54 = 280% Use the numbers statements: 1 1 1000 , 10 , 180, 1000 and 10 000 each exactly once to complete these a) 1 kg = ……….. g b) 1 mm = ………. cm d) 1 millilitre = ………….. litre e) half turn = ………… ° Stage 8: Review units c) 1 m2 = ……….. cm2 Review 1B Chapters 5–8 Chapter 5 Expressions 1 Here are four cards. A Perimeter 2a 2b C 3m n 1 B 3x x 12 n D 2n 1 a) Which card shows a function? b) Which card shows a formula? c) Which card shows an equation? 2 Simplify each of these expressions using powers. a) t × t × t b) t × t × t × t × t c) 6 × t × t 3 Write down if each statement is true or false. Correct any statement which is false. a) 3n − 8m + 1 − n + 5m = 2n + 13m +1 b) 6n × 4n = 24n2 c) 4t (2t+ 3) = 6t2 + 7t 4 Noor has n dollars. Omar has 6 dollars less than Noor. Preema has 4 times as much money as Omar. Write down an expression in terms of n for the amount of money that a) Preema has b) the three people have in total. Chapter 6 Sequences and functions 1 Find the position-to-term rule and the 40th term for each of these sequences. a) 9, 15, 21, 27, …. b) –2, 3, 8, 13, … c) The sequence with first term 14 and term-to-term rule ‘add 3’. 2 These three patterns are made from circular tiles. They are the first three terms in a ­sequence of patterns. Pattern 1 Pattern 2 Pattern 3 Online resources 3 a) Draw Pattern 4 in this sequence. b) Find the position-to-term rule to find the number of counters needed to make any pattern. c) Find the number of counters needed to make Pattern 20. d) Ollie has 30 counters. What is the largest pattern in this sequence he can make? 3 a) Here is a function. x 2x − 9 . Complete this number machine to match the function. x …… …… 2x 9 b) Here is a number machine. 5 2 Complete this function to match the number machine. x ………. Chapter 7 Shapes 1 These two triangles are congruent. 3.2 cm c 129° 4 cm b cm 6.5 cm 29° a cm 4 cm Not to scale Write down the values of a, b and c. 2 Which of these triangles has a hypotenuse measuring 20 cm? 16 cm 15 cm 25 cm 12 cm 20 cm 4 cm 7.5 cm 20 cm Triangle A 8.5 cm Triangle B Triangle C Not to scale 4 Stage 8: Review units 3 Problem solving a) The diagonals of a quadrilateral measure 5 cm and 6 cm. The acute angle between the diagonals is 80°. Samira says that the quadrilateral could be a rectangle. Explain how you can tell that she is wrong. b) The diagonals of a different quadrilateral both measure 11 cm. The diagonals meet at right angles. Tom says the quadrilateral must be a square. Is he correct? Explain your answer. 4 Decide if these statements are true or false. Diagram Statement The two shaded angles are alternate angles. The two shaded angles are corresponding angles. The two shaded angles are equal. Chapter 8 Midpoints 1 Find the midpoint of the line segment joining these points. a) (3, 2) and (11, 20) b) (–3, 11) and (9, 2) c) (–5, 9) and (1, –3) d) (0, 5) and (–7, –10) Online resources 5 Review 1C Chapters 9–12 Chapter 9 Scale drawing and measures 1 Ella makes a scale drawing of her bedroom. She uses a scale of 1:50. a) If her bed is 2m long, how long will it be on her scale drawing? b) She calculates that the width of her bedroom will need to be 12 cm. How wide is her bedroom? 2 3 Match the object to the units that would be used to measure it: Length of a car m2 Area of a football pitch cm2 Volume of a swimming pool km2 Area of a piece of paper m3 Volume of a box of chocolates m Area of a forest cm3 Some people take part in a race. a) The race is 8 laps of a track that is 400m metres long. How many kilometres is the race? b) Rosa has 5 litres of water. She pours it into cups to give to the people in the race. If each cup can hold 180 ml of water, how many complete cups can she fill? Chapter 10 Data collection 1 Josi wants to find out if older students exercise more than younger students at her school. a) Which two of the following would it be most useful to collect data about The age of the student The name of the student The number of hours the student exercises each week The football team the student supports b) Josi decides to write a questionnaire and hand it out in the school sports clubs. Give one disadvantage of this approach. 2 Sayed is collecting data about the books in a library. Decide if each of the following types of data are discrete or continuous: The number of words in the title The number of pages in each book The width of each book The mass of each book 6 Stage 8: Review units 3 Barry does an experiment to find out how long (in minutes) it takes students to solve some mathematical problems. His results are: 5 min 4 min 8 min 6 min 12 min 3 min 6 min 9 min 5 min 7 min 15 min 11 min 14 min 19 min 7 min 5 min 9 min 9 min 18 min 11 min a) Copy and complete the frequency table for this data, filling in the missing class interval as well as the data. b) What is the modal class? c) How many students had a time of more than 10 minutes? 4 Time (minutes) 0<t≤5 5 < t ≤ 10 Tally Frequency 15 < t ≤ 20 Total The two-way table gives information about the number of left handed and right ­handed students in two classes. Fill in the missing numbers Boys Girls Total Right Handed 16 34 Left Handed 9 16 Total 23 27 a) How many students were asked altogether? b) How many boys are left handed? c) What fraction of the girls are right handed? Chapter 11 Averages and spread 1 Pete has an apple tree in his garden. He weighed some of the apples he picked from the tree. Here are his results to the nearest gram. 86 g 78 g 80 g 86 g 111 g 93 g 92 g 99 g 94 g 94 g 100 g 91 g 88 g 103 g What is 94 g a) the mode b) the median c) the mean d) the range? d) Which average would he use if he wanted to show off how big his apples are? Chapter 12 Probability 1 If the probability that Ernest will get homework tomorrow is 35%, what is the probability that Ernest will not get homework? 2 If you pick a letter at random from the word MATHEMATICAL what is the probability that you will choose: a) A vowel b) A letter that is not a vowel (a consonant) c) The letter M d) A letter that is also in the word TEAM Online resources 7 Review 2A Chapters 13–17 Chapter 13 Types of number 1 Decide if these statements are true or false a) 1 is a prime number b) A list of all the factors of 76 is 1, 2, 4, 19, 38, 76 c) The highest common factor of 54 and 72 is 4 d) 112 is a common multiple of 8, 14 and 18 e) The lowest common multiple of 2 × 3 × 5 and 2 × 3 × 7 is 210 2 3 Write each number as a product of its prime factors a) 68 b) 130 c) 270 d) 504 Match each expression in the left-hand column with its answer in the right-hand column 182 − 172 − 12 225 3 400 − 2 11 6 + 132 − 3 1 20 256 − 3 12 + 113 18 Chapter 14 Fractions 1 Ivan has written these fractions. 2 23 1 2 7 8 11 12 3 34 Using these fractions, each exactly once, to complete the following calculations: a) __ − c) 2 19 9 1 5 3 = − __ = 2 5 = 17 × 2 5 b) 1 41 × 19 = c) 19 ÷ 8 43 1 3 = 29 = 1__ d) 3__ − __ 23 + 2 56 = __ = __ = 1__ Correct the errors in these calculations a) 17 × 3 b) __ + 7 4 = 6 4 = 36 5 = 7 54 × 19 = 26 × 7 4 = 6 × 19 4 104 7 = 95 5 = 23 24 = 13 67 Work out a) 4% of 3200 kg b) 32% of $1400 c) 61% of 4300 ml d) 93% of 1250 cm Stage 8: Review units 4 Tom wrote down these values 250 m $7500 973 litres 165.5 cm Find the answers to Tom’s calculations 5 6 a) 250 m increased by 3% b) 973 litres decreased by 8% c) $7500 increased by 45% d) 165.5 cm decreased by 84% Match the proportion on the left with an equivalent value on the right 15 out of 165 1 9 27 minutes out of 3 hours 0.125 56 apples out of 504 apples 15% 0.66 cm out of 528m 1 11 Write each set in order of size, starting with the largest 7 8 26 out of 32 83.2% 0.8751 b) 38 minutes out of 1.5 hours 25.3% 65 250 0.294 c) 65.25% 99 cm out of 1.5 m 224 350 0.6552 a) Chapter 15 Using known facts 1 2 Decide if these statements are true or false a) 6 × 0.9 = 54 b) 0.008 × 4 = 0.032 d) 0.0065 ÷ 5 = 0.013 e) 0.0006 × 7 = 0.042 c) 7.2 ÷ 9 = 0.8 Work out a) 1 12 of 84000 c) 4% of 400 b) 5 9 of 63 d) 55% of 8000 Chapter 16 Solving word problems mentally 1 Using each direct proportion, complete the statements a) 40 pencils cost $6. ___ pencils cost $15. b) Mohammed is paid $54 for 9 hours work. If Mohammed works 31.5 hours he earns ___. c) Peter can walk 3km in 15 minutes. In 105 minutes Peter can walk ___. d) The mass of 4 magazines is 560g. 2.52kg is the mass of ___ magazines. Online resources 9 Chapter 17 Decimals 1 Work out a) 35 742 + 84 928 b) 584 294 − 2945 + 211 411 c) 98.42 − 39.548 d) 13.28 − 7.9105 + 4.801 e) 56 543.2 + 456.701 − 4537.28 2 Amir wrote these answers 47.4 0.1 0.006 0.66 Using these calculations, write down the non-calculator methods used to find the answers. 0.92 ÷ 7 0.0453 ÷ 8 284.4 ÷ 6 5.943 ÷ 9 Review 2B Chapters 18–21 Chapter 18 Formulae 1 a) Write a formula for the perimeter, P, of this shape. 2a Use your formula to calculate the perimeter of the shape when a = 4, b b = 2 and c = 2 3b b) Pierre charges a fixed fee of $24 + $25 per hour for each electrical item he repairs. 3b Write a formula for the total cost C for a repair that takes h hours. Use your formula to find the total cost of a repair lasting 4 hours. c c c 2 F = 1.8 + 32C is the formula for converting temperatures given in degrees Celsius (°C), C, to degrees Fahrenheit (°F), F. Use the formula to convert the following temperatures from °C into °F. a) 8°C 3 b) 12°C c) 45°C d) 68°C Using a = 2, b = 3 and c = –4, find the value of v for these formulae a) v = a + b2 − 3 b) v = 15 − b2 + c2 c) v = a3 + c d) v = 4a2 − 2b + c 10 Stage 8: Review units Chapter 19 Straight-line graphs 1 a) Match the equation on the left with the correct table of values on the right. y=x−2 x y –2 –1 –1 1 0 3 1 5 y = 2x + 3 x y 0 2 1 2.5 2 3 3 3.5 y = 4 − 3x x y –2 –4 0 –2 2 0 4 2 1 2 x y –4 16 –3 13 –2 10 –1 7 y= x+2 b) Using the correct table of values from question 4, draw the graphs of y = 2x + 3 2 1 2 y= x+2 y = 4 − 3x Decide if these statements are true or false a) The graph of y = 4x is not a straight line b) Alan draws a curve. He says that the equation of the curve cannot be 2x − 3 = 7. c) The graph of y = x pass through the point (0, 0) d) On a set of axes, the co-ordinates (–1, 1) and (0, 3) lie on the line y = 5x e) The graphs of equations of the form y = mx + c are always straight lines Chapter 20 Nets and constructions 1 Draw a sketch of the net of each of these shapes. a) 2 b) c) Construct on plain paper a) The perpendicular bisector of a line segment 8 cm long. Mark the midpoint with the letter P. b) The perpendicular bisector of a line segment 6.5 cm long. Mark the midpoint with the letter Q. c) The angle bisector of 56°. d) The angle bisector of 125°. Online resources 11 Chapter 21 Symmetry and transformations 1 Complete these sentences a) A square has ___ lines of symmetry. b) An isosceles triangle has ___ rotational symmetry. c) A regular hexagon has rotational symmetry of order ___. d) A parallelogram ___ lines of symmetry. 2 Peter has drawn a translation, reflection and rotation. However, each transformation has errors. Redraw each one so that it is correct. Mirror line Review 2C Chapters 22–25 Chapter 22 Imperial units of measurement 1 Max and Olga are discussing the distance between Moscow and St. Petersburg. Max says it is 450 miles and Olga says that it’s 688 km. a) How many miles is 688 km? b) The actual distance between Moscow and St. Petersburg is 705 km. Whose estimate was closer? Explain your answer. Chapter 23 Area, surface area and volume 1 Calculate the areas of the following shapes: b) a) 5 cm 5 cm 5 5 cm cm 8 cm 88 cm cm c) 5 cm 5 cm 5 cm 3 cm 3 cm 3 cm 8 cm d) 9 cm 9 cm 9 cm 5 cm 5 cm 5 cm 9 cm 5 cm 7 cm 7 cm 7 cm 3 cm 3 3cm cm Stage 8: Review units 3 cm 3 cm 3 cm 3 cm 7 cm 7 cm 7 cm 7 cm 12 5 cm 5 cm 5 cm 12 cm 12 cm 12 12cm cm 5 cm 3 cm 4 cm 4 cm 4 4cm cm 3 cm 7 cm 5 cm 2 Dariya has a cuboid with a length of 6 cm and width of 5 cm. The volume is 120 cm3. a) What is the height of the cuboid? b) What is the surface area of the cuboid? 3 5 cm 6 cm Here are the nets of two shapes. What is the surface area of each shape? a) b) 5 cm 8 cm 6 cm 4 cm 6 cm 5 cm 5 cm 12 cm Chapter 24 Displaying and interpreting data 1 Jessica measures the thickness of 60 books and gets the result shown in the table below. Thickness, t (mm) 0≤t<5 5 ≤ t < 10 10 ≤ t < 15 15 ≤ t < 20 20 ≤ t < 25 25 ≤ t < 30 Frequency 5 8 15 17 10 5 60 Draw a frequency diagram to illustrate this data 2 The table and pie chart below show the same data about the favourite sports of 60 people. Sport Swimming Football Basketball Frequency 11 28 Favourite sports of 60 people 168º 84º Tennis Total Angle 60 42º 360º Complete the table and the pie chart. Football Basketball Online resources 13 3 The stem and leaf diagram below shows the heights of 25 statues in a city to the nearest 10 cm. Stem 1 2 3 4 5 Leaf 7 1 0 0 6 9 4 2 0 7 5 8 8 3 6 6 6 6 9 1 4 5 6 8 9 Key 1| 7 represents 1.7 metres a) What is the height of the tallest statue? b) What is the median height of the statues? c) What the range of the heights of the statues? 4 The frequency diagram below shows time taken for students to travel to school on a particular day. Time taken for students to travel to school 70 a) How many students took part in the survey? 60 b) How many students took more that 30 minutes to travel to school? 50 Frequency c) What percentage of students can get to school in less than 20 minutes? 40 30 20 10 0 0 5 10 20 30 40 Travel time (minutes) 50 Rory collects data on the number of songs on 10 albums recorded by each of two rock bands. Median Mean Range Band A 18.5 19.6 5 Band B 18 18.4 8 a) Compare the average number of songs on albums by the two bands. b) Which band is more consistent in the number of songs on their albums? How do you know? 14 Stage 8: Review units Chapter 25 Mutually exclusive outcomes 1 A group of students are on an activity holiday. On a particular day they have the choice of the following activities. They must choose one morning activity and one afternoon activity. Morning Afternoon: • Horse Riding (HR) • Swimming (Sw) • Climbing (C) • Kayaking (K) • Archery (A) • Sailing (Sa) List all the possible combinations of activities that they could choose. Review 3A Chapters 26–29 Chapter 26 Calculations 1 2 Write each set in order of size, starting with the smallest a) 43 − 49 ( − 5)3 13.322 b) 105 33 − 3 −27 5×5×5×5 144 c) 3 × 3 × 4 × 5 × 5 36 (–8)2 52 − 3 216 9 Work out a) 3 + 3 × 4 − 5 b) (4 − 3 + 7) × 4 d) 33 ÷ 2 × 1.5 − 23 e) 2.8 + 145 ÷ 5 − 5 × 5 c) 54 ÷ (6 × 3) + 42 Chapter 27 Ratio and proportions 1 San has written these numbers 3 1.6 16 750 3 4 Use the numbers to complete these statements 2 a) 64 : __ = 4 : 1 b) 150 : 450 = 1 :__ c) 600 g : 150 g : __ g = __ : 1: 5 d) __ l : 4000 ml : 2.4 l = 2 : 5 : __ Red, green and blue paint are mixed in the ratio 5:3:4. Sanjit uses the three colours to create 4500ml of the paint. Sanjit uses this method to find how much he needs of each colour. Find and correct the errors in his method. 4500 ÷ 10 = 375 Red = 5 × 375 = 2625 ml Green = 4 × 375 = 1125 ml Blue = 4 × 370 = 1500 ml Online resources 15 3 a) 8 tins of meat cost $6.80 Find the cost of 14 tins of meat. b) Pierre mixes butter, sugar and flour in the ratio 2 : 1 : 3. He uses 130g of butter. How much sugar and flour does Sanjit use in the mixture? Chapter 28 Mental calculations with fractions and integers 1 Work out a) 30 × d) 2 1 4 × b) 1 6 3 5 2 6 × 90 e) 4 ÷ 1 5 c) 1 2 × 1 5 f) 2 ÷ 1 5 Match the calculation on the left with the correct answer on the right 9 + 2050 + 951 + 650 5 7 × ( 81 + 43 ) 8 5 × 1 4 21 × +5− 1 4 2 5 ÷2 Chapter 29 Calculations with decimals 1 Decide if these statements are true or false a) 25.2 × 0.7 = 176.4 b) 0.06 × 2.88 = 0.1728 c) 0.024 g ÷ 0.03 g = 0.0008 g d) 99.045 × 0.04 = 3.9618 e) $38.42 ÷ 0.17 = 226 Review 3B Chapters 30–32 Chapter 30 Equations 1 For each problem, construct an equation to solve it. a) Peter’s age is 7. When you multiply Ann’s age by 5 and subtract the result from 45 you get Peter’s age. Find Ann’s age. b) The area of a rectangle is 28 cm2. The length of the rectangle is (3x − 4)cm and the width of the rectangle is 8 cm. What is the value of x? 16 Stage 8: Review units c) Tim thinks of a number. He multiples it by 14 then adds 2. Pierre thinks of the same number. He multiples it by 2 and then subtracts the result from 4. He gets the same answer as Tim. What is the number Tim and Pierre had chosen? d) The lengths of two adjacent sides of a square are 2(x − 4) and 7(3 + 2x). Find the value of x. Chapter 31 nth term of sequences 1 Write an expression for the number of squares in Pattern n of each sequence. a) Pattern 1 Pattern 3 Pattern 2 b) Pattern 1 Pattern 2 Pattern 3 c) Pattern 1 Pattern 2 Pattern 3 d) Pattern 1 Pattern 2 Pattern 3 Online resources 17 Chapter 32 Geometrical reasoning and proof 1 Dot has written three geometrical proofs but each of them contains errors. Correct each proof. a) A proof to show that the sum of the angles in the triangle is 180º d° c° e° a = d because of corresponding angles b = c because of alternate angles a° The sum of the angles in the triangle b° =a+b+c =d+c+c = 180º b) A proof to show that the sum of the angles in the quadrilateral is 180º q° The sum of the angles in the quadrilateral is: c° r° =p+q+r+s d° = (a + d) + q + (d + s) + c a° =a+q+d+b+s+c p° b° s° = 180º + 170º = 360º c) A proof to show that the exterior angle of a triangle is equal to the sum of the two interior opposite angles. c = 170 − a − b b° d = 190 − c c° d = 190 − (170 − a − b) d = 190 − 170 + c + b d=a+b 18 Stage 8: Review units a° d° 2 Find the size of each of the lettered angles marked below, stating the geometrical reason for each step of your working out. b) a) 95° 27° s p 40° r q c) d) 35° 75° 105° 45° s t 65° a 80° 85° Review 3C Chapters 33–36 Chapter 33 Circles 1 Using plain paper a) Draw a circle with radius 4cm. b) Construct a triangle with sides measuring 7.4 cm, 6.5 cm, 4.9 cm c) Construct a triangle PQR with PQR = 90˚, QR = 4.7 cm, PR = 7.2 cm 2 Liam wrote down these names for the parts of a circle segment chord diameter sector arc radius semicircle circumference Using words from Liam’s list, add labels to this circle. Online resources 19 3 Work out, correct to 1 decimal place a) The circumference of a circle with radius = 4.8 cm b) The area of a circle with diameter = 52 mm c) The circumference and area of a circle with radius = 0.85 cm d) The area of the shaded part of this diagram 5 cm 5 cm 2.5 cm 4 Andrew drew these two pie charts comparing the transport used by students to get to school. Benbridge Academy Silverstone Academy Car Walk Bus Cycle 200 students 300 students a) Which school has about a quarter of its students cycling to school. b) Just over half of the students at Silverstone Academy walk to school. About what proportion of students walk to school at Benbridge Academy? c) Compare the proportion of students in each school who use a car. d) Andrew says that the same number of students, at each school, use the bus. Explain why he is incorrect. 20 Stage 8: Review units Chapter 34 Enlargement 1 Three shapes are drawn onto cm squared paper. A B C a) Pierre says that shape B is an enlargement of shape A by a scale factor of 2. Explain why he is incorrect. b) Copy shape A on to cm squared paper. Enlarge shape A by a scale factor of 2. c) What is the scale factor of the enlargement which maps shape A onto shape C? 2 Copy each shape onto cm squared paper. Enlarge each shape by the given scale factor from the centre of enlargement O. b) a) c) O O O Scale factor 2 O O O O O Scale factor 3 factor 2 Scale factor 2 factor Scale factor 2 factor Scale 3 factor Scale Scale 3 Scale 2 O Scale factor 2 Online resources 21 Chapter 35 Real-life graphs 1 Claire drives from Town A to Town B, a journey of 300 km. She stops twice on the journey. 300 Distance (km) 250 200 150 100 50 0 13:00 14:00 15:00 Time 16:00 17:00 a) How long does Claire stop altogether during the journey? b) What is the distance between the first and second stops? c) Claire arrives at Town B at 17:00. Complete the distance-time graph for her journey. d) Which part of the journey did Claire drive slower? Give a reason for your answer. 2 A student cycles from Town A to Town B. Another student runs for 10km away from Town B 20 Distance (km) Town A Runner 10 Cyclist 0 Town B 14:00 14:30 15:00 Time a) What is the distance between Town A and Town B? b) At what time did the two students pass each other? c) Explain why the cyclist travels at a faster speed? 22 Stage 8: Review units Chapter 36 Experimental probability 1 Sanjit throws a fair die 100 times. He obtains the following results Number Number of times thrown 1 25 2 5 3 25 4 15 5 20 6 10 Alan throws the same die 250 times. He obtains the following results. Number Number of times thrown 1 40 2 30 3 35 4 45 5 50 6 50 a) For Sanjit’s experiment, calculate the experimental probability of throwing a 6. b) For Alan’s experiment, calculate the experimental probability of throwing a 3. c) What is the theoretical probability of throwing any number on a fair die? Give a reason for your answer. d) Which experiment has more accurate results? Give a reason for your answer. Online resources 23