Maths

GCSE Mathematics Specimen Papers and Mark Schemes For first teaching from September 2010 For first examination in Summer 2011 For first award in Summer 2012 Subject Code: 2210 Foreword The awarding bodies have prepared new specifications to comply with revised GCSE criteria. The specimen examination papers accompanying new specifications are provided to give centres guidance on the structure and character of the planned examinations in advance of the first examination.It is intended that the specimen papers and mark schemes contained in this booklet will help teachers and students to understand, as fully as possible, the markers’ expectations of candidates’ responses to the types of questions set at GCSE level. These specimen papers and mark schemes should be used in conjunction with CCEA’s GCSE Mathematics specification. GCSE Mathematics Specimen Papers and Mark Schemes Contents Specimen Papers Unit T1 Mathematics (Foundation Tier) Unit T2 Mathematics (Foundatio n Tier) Unit T3 Mathematics (Higher Tier) Unit T4 Mathematics (Higher Tier) Unit T5 Mathematics (Foundation Tier) Paper 1Unit T5 Mathematics (Foundation Tier) Paper 2 Unit T6 Mathematics (Higher Tier) Paper 1 Unit T6 Mathematics (Higher Tier) Paper 2 1 3 23 43 63 83 93 107 121 Mark Schemes General Marking Instructions Unit T1 Mathematics (Foundation Tier) Unit T2 Mathematics (Foundation Tier) Unit T3 Mathematics (Higher Tier) Unit T4 Mathematics (Higher Tier) Unit T5 Mathematics (Foundation Tier) Paper 1 Unit T5 Mathematics (Foundation Tier) Paper 2 Unit T6 Mathematics (Higher Tier) Paper 1 Unit T6 Mathematics (Higher Tier) Paper 2 133 135 137 143 149 157 163 167 171 175 Subject Code QAN 2210 500/7925/6A CCEA Publication  © 2010 You may download further copies of this publication from www. ccea. org. uk SPECIMEN PAPERS DIVIDER PAPER FRONT 1 SPECIMEN PAPERS DIVIDER PAPER BACK 2 Centre Number 71 Candidate Number General Certificate of Secondary Education 2011 Mathematics For Examine r’s use only Question Marks Number Unit T1 (With calculator) Foundation Tier [CODE] SPECIMEN EXAMINATION PAPER TIME 1 hour 30 minutes INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Write your answers in the spaces provided in this question paper.Answer all twenty five questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. You may use a calculator for this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 100. Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. Functional elements will be assessed in this paper. Quality of written communication will be assessed in questions 6 and 23. You should have a calculator, ruler, compasses and a protractor.The formula sheet is overleaf. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 T otal Marks 3 Foundation Tier Formulae Sheet Area of trapezium = 1 (a + b)h 2 Volume of prism = area of cross section ? length 4 Answer all questions 1 (a) Write 80% as a decimal Answer _____________ [1] Answer ___________ % [1] Answer_____________________ [1] Answer_____________ [1] Answer_____________ [1] (b) Write 0. 35 as a percentage (c) Write 48 million in figures (d) 5729 people attended a football match. Write the number 5729 to (i) the nearest 10 (ii) the nearest 100 2 (a)Find the next 2 terms in the sequence and explain the rule you used: 6, 11, 16, 21, _____, ______ Rule _________________________________________________ [3] (b) Find the next term in the sequence 0. 2, 0. 4, 0. 8, 1. 6, _______ [1] 5 3 The diagram shows a tiled patio in the shape of a rectangle 3 by 16, covered with 48 square tiles. Write down the length and width of 2 other possible rectangles which can be covered with 48 of these square tiles. Answer__________ by__________ __________ by__________ 4 [1] [1 ] Michael recorded the colours of cars in the school car park in a tally chart. ColourTally Frequency Red |||| 4 Blue || 2 Yellow ||| Black |||| || White |||| |||| Silver |||| Green |||| (a) Complete the frequency column. [1] (b) On the grid opposite, draw a frequency diagram to show this information. [3] 6 (c) What is the most popular colour of car in the car park? Answer_________________ (d) [1] Using the frequency table, write down the fraction of the total cars which are yellow. Answer_________________ 7 [1] 5 (a) (i) Shade the major segment in the circle below [1] (ii) (b) PQ is called a _________________ of the circle. (i) Shade the minor sector in the circle below. 1] [1] (ii) OS is called a _______________ of the circle. 8 [1] 6 The table below shows the percentage of pupils at a High School who obtained a grade C or better in GCSE Mathematics during the past five years. Year % of pupils (a) 2004 75 2005 78 2006 82 2007 84 2008 90 Which year showed the smallest improvement? Answer______________ (b) [1] Your quality of written communication will be assessed in this question The school wants to show this information using a statistical diagram. Which type of diagram would you use? Answer__________________________ [1] Give a reason for your answer. _______________________________________________________________ ________________________________________________________________ 7 [2] Here is a list of numbers 25 27 32 35 8 21 9 (a) From the list write down those numbers which are (i) multiples of 5 Answer____________ (ii) [1] Answer____________ [1] factors of 54 9 (b) From the list of numbers (i) calculate the mean Answer_____________ Answer_____________ (ii) 8 [2] [2] find the median In a mid season sale a clothing shop has 20% off all its items. Clare bought a dress which originally cost ? 50 and a hat which originally cost ? 25 (a)How much did she save in the sale? Answer ? _____________ Answer ? _____________ (b) 9 [2] [1] Answer_____________ [2] What wa s her total bill? Simplify 5p ? 2r ? 3p + 5r 10 10 (a) Jo bought 6 roses at 67p each. What change did she get from a ? 5 note? Answer ? _____________ (b) Five kilograms of potatoes and two kilograms of onions cost ? 4. 10 in total. The potatoes cost 62p per kilogram. How much would it cost in total to buy one kilogram of potatoes and one kilogram of onions? Answer ? _____________ 11 [2] [4] The brick shown below is in the form of a cuboid, measuring 6. 4 metres by 3. metres by 2. 6 metres. Calculate the volume of the brick. Answer_____________ 11 [3] 12 Calculate (a) the square root of 1. 44 Answer_____________ Answer_____________ (e) 13 [2] Answer_____________ (d) [1] Answer_____________ (c) [1] Answer_____________ (b) [1] [2] the cube of 2. 8 2. 32 ? 1. 69 3 of 125 5 5. 62 ? 3. 4 The table below gives the maximum and minimum temperatures of six different cities in Europe in March. City Belfast Minimum 2 ° C Dublin ?1 ° C 9 ° C London 4 ° C 16 ° C Edinburgh 0 ° C 11 ° C Barcelona 10 ° C 19 ° C 8 ° C 20 ° C Paris (a) Maximum 10 ° C Which minimum temperature was the lowest?Answer____________________ ° C 12 [1] (b) In two of these cities the temperatures had increased from minimum to maximum by 12 ° C. Write down the names of these two cities. Answer____________________ and ____________________ [2] What is the difference in minimum temperature between Dublin and Paris? (c) Answer_____________ ° C 14 [1] Answer_______________ [1] Answer_____________ % [1] Answer_____________ % [1] Results of a Year 12 Physics test 9 8 7 6 5 4 2 0 2 7 4 6 Key 5 4 (a) 5 1 5 8 6 7 6 8 9 7 9 8 9 9 means 54% How many pupils sat the Physics test? (b) What is the modal percentage mark? c) What is the range of percentage marks? 13 15 The diagram shows the plan for a rectangular garden. Calculate (a) the area of the garden Answer____________m2 [2] Answer____________m2 [2] (b) the area of the plot for the trees A border needs to be dug around the perimeter of the garden. (c) Calculate the perimeter of the garden. Answer____________m 14 [2] 16 The diagram shows a pizza which has been divided into 8 equal parts. The shaded parts are eaten. (a) Write down, as a fraction in its lowest terms, the fraction that is eaten. Answer_____________ Answer___________ % (b) 17 [2] [1]What percentage is left uneaten? Which fractions from the list given below are not equivalent to 2 ? 3 8 10 16 4 12 , , ,, 12 15 28 6 16 Answer_____________ 15 [2] 18 In a survey 300 men were asked which sport they liked best. The pie-chart below shows the results. (a) Measure the angle which represents Basketball. Answer_____________? (b) [1] What fraction of men chose Rugby as their favourite sport? Answer_____________ (c) [1] Answer_____________ [2] How many men chose Hurling as their favourite sport? 16 19 (a) Expand 3(x + 1) Answer______________ [2] Answer_____________ [2] (b) Solve 2y + 3 = 19 0 In the diagram the point P (? 4, 4) has been plotted. (a) Plot the follow ing points on the diagram, labelling clearly Q (? 2, ? 3), R (5, ? 3) and S (3, 4) [3] (b) Join up the points in order and name the quadrilateral formed. Answer____________________ 17 [1] 21 (Diagram not drawn accurately) Calculate (a) x x = ___________? [1] y = ___________? [1] (b) y 22 Draw the net of the matchbox tray (no lid) shown in the diagram, which has base 5cm by 3cm and height 2cm, on the square grid provided. [3] 18 23 Your quality of written communication will be assessed in this question Fred has just won ? 00. 1 1 of it to his son, James. He has promised of it to his daughter, Kathy and 5 4 How much will he have left after he gives Kathy and James their shares? Show clearly each step of your working out. Answer ? _____________ 19 [4] 24 The positions of two towns A and B are shown on the grid. (a) A third town C is 3km east and 2km north of A. Using a scale of 1cm = 0. 5km, show the position of C. (b) [2] How far is C from A? Answer_____________km 20 [3] 25 The follow ing information shows how Sinead spends her time on a Saturday. Activity Cleaning Watching TV Number of hours 2 Using Shopping he Exercising Internet 5 4 3 2 Sleeping 8 Draw a pie chart to illustrate this data. [4] 21 ___________________________________________ THIS IS THE END OF THE QUESTION PAPER ___________________________________________ 22 Centre Number 71 Candidate Number General Certificate of Secondary Education 2011 Mathematics Unit T2 (With calculator) Foundation Tier [CODE] SPECIMEN EXAMINATION PAPER TIME 1 hour 30 minutes INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Write your answers in the spaces provided in the question paper.Answer all twenty three questions. Any working should be clearly shown in the spaces provided since marks may be awarded for partially correct solutions. You may use a calculator for this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 100. Figures in b rackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. Functional Elements will be assessed in this paper. Quality of written communication will be assessed in questions 5 and 17. You should have a calculator, ruler, compasses and protractor. The formula sheet is overleaf.For Examiner’s use only Question Marks Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Total Marks 23 Foundation Tier Formulae Sheet Area of trapezium = 1 (a + b)h 2 Volume of prism = area of cross section ? length 24 Answer all questions 1 Five kilograms of potatoes and two kilograms of onions cost ? 4. 10 in total. The potatoes cost 62p per kilogram. How much would it cost in total to buy one kilogram of potatoes and one kilogram of onions? Answer ? _____________ 2 Answer_____________ (a) [4] [2] Answer_____________ [2] Simplify 5p ? 2r ? 3p + 5r (b) Expand ?2(2y ? 3) 25 3 Calculate a) the cube of 2. 8 Answer______________ Answer__ ____________ (b) (c) [1] [1] Answer______________ [2] 2. 32 + 1. 69 5. 62 ? 3. 4 26 4 Results of a Year 12 Physics test 9 8 7 6 5 4 2 0 2 7 4 6 Key 5 4 (a) 5 1 5 8 6 7 6 8 9 7 9 8 9 9 means 54% How many pupils sat the Physics test? Answer_____________ (b) [1] What is the modal percentage mark? Answer___________% Answer___________% (c) 5 [1] [1] What is the range of percentage marks? Quality of written communication will be assessed in this question Fred has just won ? 900 1 1 He has promised of it to his daughter Kathy, and of it to his son James. 4 How much will he have left after he gives Kathy and James their shares? Show clearly each step of your working out. Answer ? ______________ 27 [4] 6 The positions of two towns A and B are shown on the grid. (a) A third town C is on a bearing of 120? from B and at a distance of 2. 5 km from B. Using a scale of 1 cm = 0. 5km, show the position of C. [3] (b) How far is C from A? Answer _____________ km [2] 28 7 The following information sho ws how Sinead spends her time on a Saturday. Activity Cleaning Watching TV Shopping Number of hours 2 5 4 Using the Exercising Internet 3 2 Sleeping 8Draw a pie chart to illustrate this data. [4] 8 Solve (a) x = 15 4 Answer x = _____________ (b) [1] Answer y = _____________ [2] 6y ? 2 = 13 29 9 Write down the next two numbers in the sequence 11, 10, 8, 5, ____, _____ Answer________, _________ 10 [2] In the diagram the volume of the cuboid is 48cm3. It holds exactly 48 sugar cubes each 1cm by 1cm by 1cm. The length of the cuboid is 4cm and the breadth is 3cm. (a) What is the height of the cuboid? Answer_____________ (b) Write down the dimensions of another cuboid that the 48 cubes could fit into exactly. Answer______cm by______cm by______cm 1 (a) [3] Find the value of [1] 3. 8 ? 6. 2 giving your answer correct to 1 decimal place. 9. 1 ? 2. 7 Answer_____________ 30 [2] (b) A plasma TV has a marked price of ? 790 In a sale its price is reduced by 15% What is the sale price of the TV? A nswer ? _____________ (c) [3] Mary’s family drink 3 cartons of orange juice in 5 days. How many cartons would Mary need to buy to last a full week? Answer _____________cartons 12 [3] Write down an expression for the total cost of x bars of chocolate at 35p each and y bottles of water at 50p each. Answer_______________________ 31 [2] 13Draw the graph of y = 4x–3 on the grid below. [3] 14 (Diagram not drawn accurately) The quadrilateral shown has angles x, 79? , 3x, and 97? Work out the value of x Answer x = _________________o 32 [4] 15 (a) (Diagram not drawn accurately) In the triangle ABC shown above BC = 8. 5 cm and AX = 6. 4 cm. Calculate the area of the triangle ABC. Answer___________________cm2 [2] (b) (Diagram not drawn accurately) ABCDE is a regular pentagon, with O as its centre. Calculate the size of angle AOB. Answer Angle AOB = _____________? 33 [2] 16 Find the area of a circle with a diameter of 3 metres.Take ? = 3. 14 Answer___________________m2 17 (a) [2] The speeds, in miles per hour, of the cars passing the gates of a primary school during lunch hour are recorded in the table below. Speed (mph) No. of cars 0–5 2 6–10 5 11–15 34 16–20 61 21–25 29 26–30 4 Represent this information using a bar chart. [3] 34 (b) Which is the modal class interval? Answer________________ (c) [1] Your quality of written communication will be assessed in this question Katy wants to know how many times a month, on average, the people in her town go to the cinema. She asks 200 people in her school.Explain why Katy’s sample may not be representative of the people in her town. _______________________________________________________________ _______________________________________________________________ 35 [2] 18 (a) Write 72 as a product of prime factors Answer______________ (b) [2] Find the lowest common multiple (LCM) of 72 and 108 Answer______________ Answer______________ (c) 19 [2] [2] Find the highest comm on factor (HCF) of 72 and 108 Susan puts ? 1700 in her bank account at 4. 2% simple interest each year. Calculate the total amount in her bank account after 3 years. Answer ? ________________ 36 [3] 0 (a) Expand and simplify 4(2 – 3x) + 3(x + 4) Answer________________ Answer________________ [2] Answer x =________________ (b) [2] [3] Answer________________ [2] Expand x ( x 2 – 6) (c) Solve for x 7x + 18 = 2(x – 6) 21 (a) ? A regular polygon has an exterior angle of 18 Find the number of sides in the polygon. 37 (b) The diagram shows a play tent in the shape of a triangular prism. Calculate the volume of the tent. Answer_____________________cm3 38 [6] 22 A teacher recorded the number of hours 50 students used the internet over a 7 day period. The information is shown in the table below. Number of Hours 0? h