4 Here are the times, in seconds, of five runners in a 100 m race. Tom 11.16, Ed 11.06, Brad 11.44, James 11.47, Derek 11.22

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1 1 a) Write these numbers in words i) 2746 ii) iii) b) Write these in figures i) five thousand and fifty three ii) three hundred and forty five thousand 2 Round these to the nearest integer a) 6.7 b) 57.7 c) Write the following in order, starting with the smallest a) b) Here are the times, in seconds, of five runners in a 100 m race. Tom 11.16, Ed 11.06, Brad 11.44, James 11.47, Derek Who had the fastest time? 5 Round these numbers to the nearest 100 a) 726 b) 4278 c) Round these numbers to 1 decimal place a) 3.79 b) Round these numbers to 2 decimal places a) b) Number : Foundation 8 Round these numbers to 1 significant figure a) 127 cm b) 3756 g c) 62.7 m 9 Dan rounds a number to the nearest 10 and gets 20. Megan rounds the same number to the nearest whole number and gets 15. What could the number be? 10 Calculate the answers to the following by i) writing down the full calculator display ii) rounding your answer to the number of decimal places given a) (1 d.p) b) (2 d.p) c) (1 d.p) d) (2 d.p) e) (3 d.p) f) 2 (1 d.p) 0.5 2

2 Mental Arithmetic: Foundation 1 Work out a) 24 5 = b) 63 8 = c) 98 2 = d) 78 3 = 2 Jill goes shopping with 10. She spends the following amounts in 3 different shops a) How much has she spent altogether? b) How much money does she have left? 3 Work out a) b) c) d) e) f) g) h) Mr H buys 42 boxes of clip on ties. Each box contains 36 ties. How many ties has Mr H bought? 5 Round each of the following to 1 decimal place a) 3.46 b) c) d) Work out a) 4 squared b) the cube of 5 c) the cube root of 64 d) 81 7 Write as a single power of 5 a) b) c) 56 8 Round each the following to 1 significant figure 5 2 d) (5 2 ) 3 a) 123 b) 3504 c) d) e) f) Estimate a) b) Katie is organising a school disco. She needs to buy 10 bottles of squash Shop A have a 3 for the price of 2 offer with each bottle costing Shop B have bottles for 1.20 each or a pack of six for a) How should she buy the squash to spend the least amount of money? You must explain your answer. b) From each bottle of squash she can make 22 drinks. She plans to sell each drink for 45p. How much profit will she make?

3 1 Write each fraction in its simplest form Fractions: Foundation a) b) c) 2 Write down the fraction shaded for each of the following a) b) 3 Work out a) of 24 b) of 20 c) of 18 4 Work out a) of 20 b) of 15 c) of How many halves are there in 2½? Change each of the following mixed numbers to improper fractions a) 1 = b) 2 = c) 3 = 7 Work out a) + = b) + = c) + = 8 9 Emily s recipe for cakes needs of a cup of milk. She has of a cup. How much will she have left? Mrs Cooper is marking a set of 30 books. If she has already marked 14 books what fraction of the books has she got left to do? 10 Work out a) b) c) 11 Write down the reciprocal of a) 2 b) c) three-fifths 12 How much bigger is 2 1 than 2 1? 13 Choose from the list a) 2 fraction that have the lowest product b) 3 fractions that add up to 1

4 FDP: Foundation 1 Copy and complete the table Fraction Decimal Percentage % % 2 Write these decimals in ascending order (smallest to largest) a) b) Jan goes shopping with a 20 note. She buys 2 magazines that cost 2.99 each, a 3.20 ticket for the bus. She then buys a CD for How much money does Jan have left? 4 Work out a) b) a) Tim scores 17 out of 20 in a test. What percentage is this? b) 13 out of 25 people agreed to help at a charity event. What percentage is this? c) 21 out of 40 children arrived on time. What percentage were late? 6 Given that = 11565, work out a) = b) = c) = d) = e) = f) = 7 Which of the following fractions will be recurring decimals when expressed as a decimal?

5 Percentages and Proportion : Foundation 1 Calculate a) 10% of 660 (non-calculator) b) 5% of 660 (non-calculator) c) 15% of 420 (non-calculator) d) 23% of 450 e) 85% of 800 f) 3% of a) Increase 48 by 15% (non-calculator) b) Increase 50 by 35% (non-calculator) c) Increase 360 by 4% d) Increase 1250 by 12% 3 a) Decrease 60 by 10% (non-calculator) b) Decrease 45 by 5% (non-calculator) c) Decrease 53 by 4% d) Decrease 94 by 22% 4 Tina earns 6.40 per hour and works 35 hours per week. Her rent is 84 per week. From next month her new hourly rate of pay will rise by 5% but her rent is increasing by 4 per week. How will this change the amount she has to spend after paying her rent and by how much? 5 The value of Facebook shares changed from $27.10 on the 8 th June 2013 to $30.01 on the 15 th June. Calculate the percentage change(correct to 1 decimal place). 6 A 600g packet of biscuits costs How much would a 250g packet cost? 7 It takes 5 workers 12 days to paint a large bridge. How long would it take 4 workers? 8 Which is the best value for money A 300ml bottle of shower gel priced 2.25 or a 125ml bottle of shower gel priced 90p 9 Helia invested 4000 for 3 years with a compound interest rate of 1.5%. What was her investment worth at the end of this period?

6 Ratio : Foundation 1 A box of chocolates contains milk, plain and white chocolates in the ratio 4 : 3 : 2 respectively What fraction of the chocolates are a) milk chocolate b) white chocolate 2 Write each of these ratios as simply as possible a) 2 : 12 b) 18 : 24 c) 0.8 : Four of these ratios area the same. Which? 1 : : : : 55 2 : 5 3 : The simplest version of all of the ratios below is 1 : 4 Copy and complete a) 2 :. b) 5 :. c). : 28 d). : Divide 60 in the ratio 5 : 7 6 The ratio of staff to toddlers in a nursery should be 1 : 4. If there are 24 toddlers in a nursery how many staff will be needed? 7 The ratio of fat : sugar : flour in a crumble topping in 2 : 3 : 5 respectively. a) How much sugar do you need to make 200g of topping mixture? b) How much topping mixture could you make if you had plenty of flour and sugar but only 30g of fat? 8 Beth invested 3500 in a business and Rick invested 2500 a) At the end of the year Beth and Rick share the profit of in the ratio of their investments. How much money will Rick receive? b) Next year, when the profit is shared in the same ratio Rick gets What was the total profit for the year?

7 Factors, Multiples and Primes : Foundation 1 Write down all of the factors of Here is a list of numbers. 90, 108, 210, 306, 495, 501 Which of the numbers in the list are multiples of 5 3 Here is a list of numbers 2, 3, 4, 6, 9, 11, 12, 15, 17, 18 a) Which of the numbers are prime numbers? b) Which of the numbers are square numbers? c) Which of the numbers has the most factors? Show how you decide. 4 a) List the factors of 24 b) What is the highest common factor of 24 and 56 5 Find the lowest common multiple of 12 and Express 120 as a product of primes 7 The highest common factor of two numbers is 8. Give three possible pairs of numbers. 8 Ben says that if you write 40 as a product of primes the answer is Is he correct? Explain your answer.

8 Basic Algebra : Foundation 1 Simplify a) a + a + a + a c) 12c - 5c + 4c b) 2y + y + 7y d) 5t - 4t + 3t - 6t 2 If p = 4 and t = 7, find the value of a) 2p + t b) 5p - 2t Simplify a) p + 2s + 4p + 2s b) 3a + 7b + 2a + 2b c) 8s + t - 3s + 2t d) 5x - y - 2x - 6y Write an expression that simplifies to 10x - 3y If x = 8 and y = -1 a) Show that 2x + 3y = 13 b) Write down an expression involving x and y that has a value of Multiply out a) 2(a + 3) b) 3(2c + 3) c) r(5r + 4) Factorise a) 2a + 10 b) 3xy + 10y c) 15e + 20e Expand and simplify a) 4(a + 2) + 3(a + 4) b) 3(3x + 4) + 2( 2x - 1) c) 4(2r + 5) - 3( r - 2) d) y(y + 5) + 2y(y - 2) Here are 2 formulae A : V = 3x + 5 B : V =2(x + 6) Find a value of x such that a) A is greater than B b) B is greater than A You must show your workings. Rearrange the formulae to make y the subject a) y + a = c b) 2y + e = f c) j = 4y - 3k

9 ALGEBRA and QUADRATICS : Foundation 1 Simplify a) 3a + 4a + a c) 6a 2a + a b) 5y + y + 2y d) 6b + 2b 7b 2 Simplify a) 2p + s + 3p + 2s b) 5a + 2b + 2a + 3b c) 4s + t - 3s + 3t d) 4x - y - 2x - 4y 3 Multiply out a) 5(2a + 3) b) 4(2c - 3) c) w(2w + 4) 4 Factorise a) 4a + 10 b) 7xy + 12y c) 15e + 20e 2 5 Solve using trial and improvement the equation x 2 + x = 65, giving your answer correct to 1 decimal place. 6 Solve using trial and improvement the equation 2x 3 5x = 250, giving your answer correct to 1 decimal place. (Try x = 5) 7 a) Copy and complete the table for y = x 2 5 x y -5 b) Plot the graph of y = x 2-5 c) When x = 1.5, what is the value of y? d) Use your graph to find the solutions of the equation x 2-5 = 0 8 a) Copy and complete the table for y = x 2 2x 4 x b) Plot the graph of y = x 2-2x -4 c) Use your graph to find the solutions of the equation x 2-2x -4 = 0 d) Use your graph to find the solutions of the equation x 2-2x -4 = 4

10 Solving Equations : Foundation 1 Solve a) 2x = 12 b) x + 4 = 7 c) x 3 = 10 2 Solve a) = 5 b) = 2 c) 2x + 1 = 9 d) 5x 2 = 13 3 The angles in a triangle add up to 180 a) Write down an equation in terms of x b) Solve your equation to find the value of x 4 Solve a) 4(2x + 1) = 28 b) 4(x 2) = 10 c) 4x + 1 = 2x + 17 d) 5x 4 = 2x Solve a) 4(x + 2) = 2x + 9 b) 2 5x = 3(2 x) Harry thinks of a number, adds 9 and doubles the result. His answer is 34 a) Write this as an equation b) Solve your equation to find Harry s number 7 Solve a) 4 = 5 b) = 6

11 Sequences : Foundation 1 Draw the next diagram in this sequence. 2 Write down the 5th, 8th and 10th terms in the following sequences. a) 0, 5, 10, 15,. b) 2, 5, 8, 11, 3 Write down the term-to-term rule for the following sequences. a) 4, 7, 10, 13,.. b) 1, 2, 4, 8, 16,.. c) 1, 2, 4, 7, 11,.. 4 Write down the missing terms in the sequence 3,, -1, -3,,, -9, 5 Write down the first three terms of the sequence whose nth term is n The nth term of a sequence is 4n + 3. Alice says that the 10th term is double the 5th term. Is she correct? Show how you decide. 7 Write down the nth term for each of the following sequences a) 4, 11, 18, 25,.. b) 6, 9, 12, 15,.. c) 95, 90, 85, 80,. d) -5, 0, 5, 10,..

12 Angles: Foundation 1 Here is a list of angles A B C D From the list write down a) an acute angle b) an obtuse angle c) a reflex angle 2 Estimate the size of the following angles a) b) 3 Calculate the size of the angle x in each of the following a) b) c) 4 Jake says that the triangle sketched below is a right angled triangle Is he correct? Explain how you decided

13 5 Calculate x and y Grade D 6 Calculate the size of angle x Grade D 7 Work out the size of the angles marked. Give reasons for your answers. Grade C

14 Area and Perimeter : Foundation 1 Work out the area and perimeter of the following a) b) 2 Which of these rectangles has the largest area? Show how you decide 3 Which of these shapes has the largest area? Show how you decide. 4 Ajay has a square room with a side length 4m. He buys a circular rug of radius 1.5m. What area of the floor will not be covered by the rug?

15 5 The rear wheel of Emma s bicycle has a diameter of 65 cm. She cycles 3.2 km to school each morning. How many complete revolutions will her wheel do during the journey? 6 These two shapes have the same area. Calculate the length L 7 Turf Supplies charge 15 for delivery and 5.50 per square metre of turf (you cannot buy part of a square metre) How much will it cost Jake to turf his lawn shown in the diagram below? 8 A circular table has an area of 7500 cm 2. Find it s circumference correct to the nearest cm.

16 Measures and Accuracy : Foundation 1 Round each of the following to the degree of accuracy stated a) correct to 2 decimal places b) correct to 2 significant figures c) correct to 3 significant figures d) correct to 2 decimal places 2 In solving problems involving time a calculator gate the following answers. Change the calculator time displayed into hours and minutes a) b) c) The top speed of a brown garden snail is 13 mm per seconds. What is its speed in metres per hour? 4 The maximum recorded speed to a Lion is 72 km/h. At this speed how far would the lion travel in 2 minutes? 5 A rectangular tank measures 2 m 1.2 m 0.8 m. Initially it is full of water. The tank is punctures and water leaks through the hole at a rate of 25 ml per second. How long will it take for the tank to empty? 6 Drew drove to Newcastle. At the start of the journey the mileometer showed miles. When she arrived in Newcastle it showed miles. The journey took 2 hours and 30 minutes Calculate the average speed for her journey. 7 What is the smallest and largest these measures could have been before they were rounded? a) 32 cm given to the nearest cm b) 240 cm given to the nearest 10 cm c) 15.7 seconds given to 1 decimal place

17 Pythagoras : Foundation 1 Use your calculator to work out a) b) c) Calculate the area of the following squares a) b) 10.5 cm 11cm 3 Work out the area of the missing square a) b) Area =.. 205cm 2 81 cm 2 Area = 144 cm cm 2 4 Find the length of x. a) b) c) 9 cm x 17 cm x 6.5 cm 3.3 cm 12 cm 8 cm

18 1 How many lines of symmetry does each of the following have? Rotations and Reflections: Foundation 2 What is the order of rotational symmetry of each of the following? 3 Copy and complete the following using the dotted lines as lines of symmetry 4 a) Copy the axes and figure A b) Draw the reflection of A in the line x = 4 Label this figure B A c) Draw the reflection of A in the line y = x Label this figure C

19 5 a) Copy the axes and figure X b) Draw figure X after a rotation of 90 clockwise about centre (0,0) X 6 Shape F can be mapped onto shape G by a single transformation. Describe fully this transformation 7 Shape X can be mapped onto shape Y by a single transformation. Describe fully this transformation Y X

20 Translations and Enlargement: Foundation 1 Which of the shapes are CONGRUENT to the shaded triangle? A E B C D 2 Write down the coordinates of the points P, Q, R and S 3 Copy the grid below. Show the position of L after a translation by vector [ 3 4 ]

21 4 Enlarge the figure shown by scale factor 3 4 Describe the translation that maps a) A to B b) B to C C B A 5 Describe fully the enlargement that maps A on to B B A 6 Enlarge shape A by scale factor 2, centre (0,0)

22 Volume and Surface Area : Foundation 1 Work out the volumes of the 2 figures shown. Assume that each cube has a volume of 1 cm 3 a) b) 2 Which box has the largest volume? Show how you decide. 3 These two cuboids have the same volume. Calculate the length L 4 Calculate the surface area of the cuboid Heanor Gate Science College

23 5 Calculate the volume following a) b) c) 6 A cube has a surface area of 150 cm 2. Calculate the volume of the cube 7 A rectangular swimming pool measures 12 m by 20 m with a depth of 1.5 m. a) The inside walls of the pool are to be painted using a special paint. Each tin of paint costs and will cover 20 m 2. How much will the paint cost? b) The pool is to be filled with water to within 20 cm of the top. How many litres of water are needed? 8 A cylinder with a height of 10 cm has a volume of 950 cm 3. Find the radius of the cylinder correct to 1 decimal place 9 a) How many mm 2 are there in 6 cm 2? b) How many cm 2 are there in 0.5 m 2? c) How many cm 3 are there in 2 m 3? Heanor Gate Science College

24 Probability : Foundation 1 Choose words from the box below that fit the following outcomes Impossible Unlikely Even Chance Likely Certain a) A fair coin will land on tails b) A fair dice when rolled will land on a 6 c) Schools in the UK will be closed for a year 2 A bag contains the following counters 4 red 5 green 1 blue What is the probability of picking a) a red counter b) a black counter c) a blue or red counter? 3 To win a prize the spinner must land on the grey sections. Which of the spinners would you choose and why? 4 The table shows the probability of getting colours on a four coloured spinner Colour Pink Yellow Orange Purple Probability a) What is the probability of getting purple? b) What is the probability of getting either orange or pink? c) What is the probability of not getting yellow? 5 A biased dice is rolled 200 times. The table shows the outcome Score Frequency a) Estimate the probability of scoring a 5 b) Estimate the probability of getting less than 3

25 6 A doctors surgery keeps a record of how long patients wait before their appointment. Time Number of patients Less than 5 minutes 17 More than 5 minutes but less than 10 minutes 18 More than 10 minutes 5 a) What is the probability that a patient chosen at random will wait more than 10 minutes? b) During a week 240 patients have appointments. How many would you expect to wait more than 5 but less than 10 minutes? 7 The table shows the probabilities that a student will chose a certain drink Orange Water Tropical Lemon Other A student is three times as likely to pick orange, than lemon. a) What is the probability that a student chooses Orange? b) What is the probability that the student doesn t choose Tropical? c) What is the probability that the student chooses Tropical or Lemon? 8 Two dice are rolled and the score is the difference between the numbers shown. a) Copy and complete the sample space to show all possible outcomes b) What is the probability of getting a score of 3? c) What is the probability of the score being an odd number?

26 Representing Data : Foundation 1 The data shows the type of transport used by people going to the cinema on a Friday evening. Number of people Walk Car Bus Cycle a) Draw a bar chart to show this data b) How many people went by car or bus? 2 The pictogram shows the number of TV s owned by families in a street. 0 TV s 1 TV 2 TV s More than 2 TV s Key represents 4 families a) How many families did not have a TV? b) How many families had 2 TV s? c) How many families lived in the street?

27 3 The data shows the mobile phone networks used by student in class 9FG Number of pupils T-mobile O2 Vodafone Three Other a) How many pupils are in the class? b) What fraction of the pupils use T-mobile? c) Draw a pie chart to represent the data. 4 A survey was carried out to investigate the most popular make of phone use by students 120 If 35 pupils have a Samsung phone, how many students took part in the survey? 5 25 students were asked how long they spent on their maths homework. Time t (in minutes) Frequency 0 t < t < t < t < t < t < t < 35 0 Draw a frequency polygon to represent this data.

28 6 The dual bar chart shows the number of orders received as and phone by a small company during a week in January 2012 a) Which day did the company receive more phone orders than orders? b) Why do you think there were no phone orders on 2 of the days? c) The manager says that more than half of the orders are taken by . Is this true? You must show how you decide. A similar study was carried out in January The results are shown below Frequency Frequency d) Comment on the differences and similarities between the 2012 and the Suggestions reasons for your observations.

29 Summary Statistics : Foundation 1 A local football team plays 10 games and lets in the numbers of goals shown below Find the a) mode b) median c) mean d) range 2 Mrs Bates gives her class a test each week for 10 weeks. a) Dan s weekly results were 4, 2, 4, 5, 5, 9, 6, 6, 8, 1 Calculate the mean and range. b) Ellie s weekly results were 4, 4, 7, 5, 5, 7,6, 4, 3, 5 Calculate the mean and range. c) Compare the results of the two students. 3 The data shows the time taken, to the nearest minute to change a wheel on a car Draw a stem and leaf diagram and use this to work out the median and range. 4 Copy the table and tick the correct boxes for each of the following data sets Quantitative Qualitative Discrete Continuous Primary Secondary The amount of rainfall recorded each day The number of red smarties in 100 packets The earnings of the top goal scorers in the Premiership 5 The table shows some information about storms in the USA Number of rumbles of thunder per minute Mean 3.1 Median 3 Mode 3 This table shows the number of rumbles of thunder per minute during a storm in the UK Number per minute Frequency Compare the UK storm to the storm in the USA.