Cambridge International Examinations Modal Paper Cambridge ...€¦ · Cambridge International...

Click here to load reader

  • date post

    30-Apr-2020
  • Category

    Documents

  • view

    23
  • download

    0

Embed Size (px)

Transcript of Cambridge International Examinations Modal Paper Cambridge ...€¦ · Cambridge International...

  • 1

    ©EdueLanka 2018 IGCSE MAFA 019

    Cambridge International Examinations – Modal Paper

    Cambridge International General Certificate of Secondary Education

    First Semester Examination for Lycium International syllabus content

    CANDIDATE :

    MODULE CODE :

    MATHEMATICS

    Paper 2 (Extended) March 2018

    1 hour 30 minutes

    Candidates answer on the Question Paper.

    Additional Materials: Electronic calculator Geometrical instruments

    Tracing paper (optional)

    READ THESE INSTRUCTIONS FIRST

    Write your Module No. and name on all the work you hand in.

    Write in dark blue or black pen.

    You may use an HB pencil for any diagrams or graphs.

    Do not use paper clips, glue or correction fluid.

    DO NOT WRITE IN ANY BARCODES.

    Answer all questions.

    If working is needed for any question it must be shown below that question.

    Electronic calculators should be used.

    If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to

    three significant figures. Give answers in degrees to one decimal place.

    For 𝜋, use either your calculator value or 3.142.

    At the end of the examination, fasten all your work securely together.

    The number of marks is given in brackets [ ] at the end of each question or part question.

    The total of the marks for this paper is 70.

  • 2

    ©EdueLanka 2018 IGCSE MAFA 019

    1) A train leaves Zurich at 23 40 and arrives in Vienna at 08 36 the next day.

    Work out the time taken.

    ..................... h ..................... min [1]

    2) From a sample of 20 batteries, 6 are faulty.

    Work out the percentage of faulty batteries.

    .............................................. % [1]

    3) Calculate (1.765 – 0.0723)14, giving your answer correct to 4 significant figures.

    ....................................................[2]

    4) Omar changes 2000 Saudi Arabian riyals (SAR) into euros (€) when the exchange rate is €1 = 5.087

    SAR. Work out how much Omar receives, giving your answer correct to the nearest euro.

    € ...................................................[2]

    5) Find the lowest common multiple (LCM) of 32 and 48.

    ................................................... [2]

  • 3

    ©EdueLanka 2018 IGCSE MAFA 019

    6) y - c = mx

    Find the value of y when m = −2, x = −7 and c = −3.

    y = .................................................. [2]

    7) 𝐸 = 𝑚𝑐2

    Write c in terms of E and m.

    x = .................................................. [2]

    8)

    Triangle ABC is isosceles and AC is parallel to BD.

    Find the value of a and the value of b.

    a = ..................................................

    b = .................................................. [2]

    9)

  • 4

    ©EdueLanka 2018 IGCSE MAFA 019

    The front of a house is in the shape of a hexagon with two right angles.

    The other four angles are all the same size.

    Calculate the size of one of these angles.

    ............................................ [2]

    10)

    A, B, P and Q lie on the circle, centre O.

    Angle APB = 48°.

    Find the value of

    (a) x,

    x = .................................................. [1]

    (b) y.

    y = .................................................. [1]

    11) Simplify (81𝑚8)1

    4

    ................................................... [2]

  • 5

    ©EdueLanka 2018 IGCSE MAFA 019

    12) Write the following in order of size, smallest fi rst.

    0.52, 0.5, 0.53, √0.53

    .................. < .................. < .................. < .................. [2]

    13)

    The diagram shows a rectangular garden divided into different areas.

    FG is the perpendicular bisector of BC.

    The arc HJ has centre D and radius 20 m.

    CE is the bisector of angle DCB.

    Write down two more statements using loci to describe the shaded region inside the garden.

    The shaded region is

    • nearer to C than to B

    • ......................................................................................................................................................

    • ...................................................................................................................................................... [2]

    14) 3, 1, -1, -3, …

    (a) Find the next term in this sequence.

    ................................................... [1]

    (b) Find the nth term of the sequence.

    ................................................... [2]

  • 6

    ©EdueLanka 2018 IGCSE MAFA 019

    15) Without using a calculator, work out

    21

    7 ÷ 3

    3

    4

    Show all your working and give your answer as a fraction in its lowest terms.

    ................................................... [3]

    16) Five angles of a hexagon are each 114°.

    Calculate the size of the sixth angle.

    .

    .................................................. [3]

    17)

    A, B, C, D and E are points on a circle.

    Angle ABD = 58°, angle BAE = 85° and angle BDC = 19°.

    BD and CA intersect at N.

    Calculate

    (a) angle BDE,

  • 7

    ©EdueLanka 2018 IGCSE MAFA 019

    Angle BDE = ............................................... [1]

    (b) angle AND.

    Angle AND = ............................................... [2]

    18) A car, 4.4 metres long, has a fuel tank which holds 65 litres of fuel when full.

    The fuel tank of a mathematically similar model of the car holds 0.05 litres of fuel when full.

    Calculate the length of the model car in centimetres.

    ......................................... cm [3]

    19) y is directly proportional to the positive square root of x.

    When x = 9, y = 12.

    Find y when x = 1

    4

    y = .................................................. [3]

    20)

  • 8

    ©EdueLanka 2018 IGCSE MAFA 019

    The Venn diagram shows the numbers of elements in each region.

    (a) Find n ( A ∩ 𝐵′ ).

    ................................................... [1]

    (b) An element is chosen at random.

    Find the probability that this element is in set B.

    ................................................... [1]

    (c) An element is chosen at random from set A.

    Find the probability that this element is also a member of set B.

    ................................................... [1]

    (d) On the Venn diagram, shade the region (A ∪ B)’. [1]

    21)

    Calculate the area of this trapezium.

    ........................................... cm2 [4]

    22) Factorise completely.

    (a) 2a + 4 + ap + 2p

    ................................................... [2]

    (b) 162 – 8t2

    ................................................... [2]

  • 9

    ©EdueLanka 2018 IGCSE MAFA 019

    23)

    Scale: 1 cm to 8 m

    The rectangle ABCD is a scale drawing of a rectangular football pitch.

    The scale used is 1 centimetre to represent 8 metres.

    (a) Construct the locus of points 40 m from A and inside the rectangle. [2]

    (b) Using a straight edge and compasses only, construct the perpendicular bisector of DB. [2]

    (c) Shade the region on the football pitch which is more than 40 m from A and nearer to D than to B.

    [2]

    24)

    (a) Calculate the area of triangle ABC.

    ........................................... cm2 [2]

    (b) Calculate the length of AC.

  • 10

    ©EdueLanka 2018 IGCSE MAFA 019

    AC = ........................................... cm [4]

    25) Solve the equation.

    7 − 5(2 − 3𝑥)

    11= 12

    n = ................................................ [2]

    26) If A = (2 30 5

    ) and B = (1 03 4

    ) find 2A – B.

    ................................................ [3]

    End of Paper 02 (Extended)

  • ©EdueLanka 2018 IGCSE MAFA 019

    Cambridge International Examinations – Modal Paper

    Cambridge International General Certificate of Secondary Education

    First Semester Examination for Lycium International syllabus content

    CANDIDATE :

    MODULE CODE :

    MATHEMATICS

    Paper 4 (Extended) March 2018

    2 hours

    Candidates answer on the Question Paper.

    Additional Materials: Electronic calculator Geometrical instruments

    Tracing paper (optional)

    READ THESE INSTRUCTIONS FIRST

    Write your Module No. and name on all the work you hand in.

    Write in dark blue or black pen.

    You may use an HB pencil for any diagrams or graphs.

    Do not use paper clips, glue or correction fluid.

    DO NOT WRITE IN ANY BARCODES.

    Answer all questions.

    If working is needed for any question it must be shown in a separate paper which is provided.

    Electronic calculators should be used.

    If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to

    three significant figures. Give answers in degrees to one decimal place.

    For 𝜋, use either your calculator value or 3.142.

    At the end of the examination, fasten all your work securely together.

    The number of marks is given in brackets [ ] at the end of each question or part question.

    The total of the marks for this paper is 130. Shown marks are approximations.

  • 1

    ©EdueLanka 2018 IGCSE MAFA 019

    1)

    (a) Kristian and Stephanie share some money in the ratio 3 : 2. Kristian receives $72.

    i. Work out how much Stephanie receives. [2]

    ii. Kristian spends 45% of his $72 on a computer game. Calculate the price of the computer game. [1]

    iii. Kristian also buys a meal for $8.40. Calculate the fraction of the $72 Kristian has left after buying the

    computer game and the meal. Give your answer in its lowest terms. [2]

    iv. Stephanie buys a book in a sale for $19.20. This sale price is after a reduction of 20%. Calculate the original

    price of the book. [3]

    (b) Boris invests $550 at a rate of 2% per year simple interest. Calculate the amount Boris has after 10 years.[3]

    (c) Marlene invests $550 at a rate of 1.9% per year compound interest. Calculate the amount Marlene has after 10

    years. [2]

    (d) Hans invests $550 at a rate of x% per year compound interest. At the end of 10 years he has a total amount of

    $638.30, correct to the nearest cent. Find the value of x. [3]

    2) A tennis club has 560 members.

    (a) The ratio men : women : children = 5 : 6 : 3.

    i. Show that the club has 240 women members. [2]

    ii. How many members are children? [1]

    (b) 𝟓

    𝟖 of the 240 women members play in a tournament. How many women members do not play in the

    tournament? [2]

    (c) The annual membership fee in 2013 is $198 for each adult and $75 for each child.

    i. Calculate the total amount the 560 members pay in 2013.[2]

    ii. The adult fee of $198 in 2013 is 5.6% more than the fee in 2012. Calculate the adult fee in 2012.[3]

    (d) The club buys 36 tennis balls for $9.50 and sells them to members for $0.75 each. Calculate the percentage

    profi t the club makes. [3]

    (e) A tennis court is a rectangle with length 23.7 m and width 10.9 m, each correct to 1 decimal place. Calculate

    the upper and lower bounds of the perimeter of the court.

    Upper bound ........................................... m

    Lower bound ........................................... m [3]

    3)

  • 2

    ©EdueLanka 2018 IGCSE MAFA 019

    A, B and C lie on the circle centre O, radius 8.5 cm.

    AB = BC = 10.7 cm.

    OM is perpendicular to AB and ON is perpendicular to BC.

    (a) Calculate the area of the circle. [2]

    (b) Write down the length of MB. [1]

    (c) Calculate angle MOB and show that it rounds to 39° correct to the nearest degree. [2]

    (d) Using angle MOB = 39°, calculate the length of the major arc AC. [3]

    (e) The tangents to the circle at A and at C meet at T. Explain clearly why triangle ATB is congruent to triangle

    CTB. [3]

    4)

    (a) The diagram shows triangle LMN with LM = 12 cm, LN = 15 cm and MN = 21 cm.

    i. Calculate angle LMN. Show that this rounds to 44.4°, correct to 1 decimal place. [4]

    ii. Calculate the area of triangle LMN. [2]

    (b) The diagram shows triangle PQR with PQ = 6.4 cm, angle PQR = 82° and angle QPR = 43°. Calculate the

    length of PR.

  • 3

    ©EdueLanka 2018 IGCSE MAFA 019

    5)

    Sidney draws the triangle OP1 P2. OP1 = 3 cm and P1 P2 = 1 cm. Angle OP1 P2 = 90°.

    (a) Show that OP2 = √10 cm. [1]

    (b) Sidney now draws the lines P2 P3 and OP3. Triangle OP2 P3 is

    mathematically similar to triangle OP1 P2.

    i. Write down the length of P2 P3 in the form √𝑎

    𝑏 where a and b are integers. [1]

    ii. Calculate the length of OP3 giving your answer in the form 𝑐

    𝑑 where c and d are integers [2]

    (c) Sidney continues to add mathematically similar triangles to his drawing. Find the length of OP5. [2]

    (d)

    i. Show that angle P1OP2 = 18.4°, correct to 1 decimal place.[2]

    ii. Write down the size of angle P2OP3. [1]

    iii. The last triangle Sidney can draw without covering

    his first triangle is triangle OP(n–1) Pn.

    Calculate the value of n. [3]

  • 4

    ©EdueLanka 2018 IGCSE MAFA 019

    6)

    In the diagram, BCD is a straight line and ABDE is a quadrilateral. Angle BAC = 90°, angle ABC = 30° and angle CAE

    = 52°. AC = 15.7 cm, CE = 16.5 cm and CD = 23.4 cm.

    (a) Calculate BC. [3]

    (b) Use the sine rule to calculate angle AEC. Show that it rounds to 48.57°, correct to 2 decimal places. [3]

    (c)

    i. Show that angle ECD = 40.6°, correct to 1 decimal place. [2]

    ii. Calculate DE. [4]

    (d) Calculate the area of the quadrilateral ABDE. [4]

    In the pentagon ABCDE, angle EAB = angle ABC = 110° and angle CDE = 84°. Angle BCD = angle DEA = x°.

    i. Calculate the value of x. [2]

    ii. If BC = CD. Calculate angle CBD. [1]

    iii. This pentagon also has one line of symmetry. Calculate angle ADB. [1]

    7)

    (a) A, B and C lie on a circle centre O. Angle AOC = 3y° and angle ABC = (4y + 4)°. Find the value of y.[4]

  • 5

    ©EdueLanka 2018 IGCSE MAFA 019

    (b) In the cyclic quadrilateral PQRS, angle SPQ = 78°.

    i. Write down the geometrical reason why angle QRS = 102°. [1]

    ii. Angle PRQ : Angle PRS = 1 : 2. Calculate angle PQS. [3]

    (c) The diagram shows two similar figures.

    The areas of the figures are 5 cm2 and 7.2 cm2.

    The lengths of the bases are l cm and 6.9 cm.

    Calculate the value of l.

    End of Paper 4 (Extended)