Mathematics Pre Spm

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    MATHEMATICS PRE-SPM

    EXERCISE (10 OCTOBER 2011)

    1. Solve the following quadratic equation:7 5

    2

    4

    xx

    x

    2. Calculate the value ofp and ofq that satisfy the following simultaneous linear equations:2 14

    39

    2

    p q

    p q

    3. The Venn diagram in the answer space shows sets P, Q and R such that the universal setP Q R .

    On the diagrams in the answer space, shade

    (a) 'P Q (b) ' ( )P Q R

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    4. Solve the following quadratic equation:2 3

    22

    xx x

    5. Calculate the value ofx and ofy that satisfy the following simultaneous linear equations:1

    3 72

    2 2

    x y

    x y

    6. (a) State whether the following compound statement is true or false.

    2 4 2m m m or 25 5

    (b)Write down two implications base on the following compound statement:13 is a prime number if and only if 13 is divisible by 1 and itself

    (c)Make a general conclusion by induction for the sequence of numbers 1, 10, 25, 46, .whichfollows the following pattern.

    2

    2

    2

    2

    1 3 1 2

    10 3 2 2

    25 3 3 2

    46 3 4 2

    .... ....................

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    7. Diagram below shows a parallelogram PQRS drawn on a Cartesian plane. QS is parallel toy-axis. Theequation of straight line SR is 2 2x y .

    (a)State the x-intercept of the straight line SR.(b)State the equation of the straight line QS.(c)Find the equation of the straight line PQ.

    8. Diagram below shows a combined solid consist of a cuboid and a right pyramid, which are joined atthe planeEFGH. J is vertically above the planeEFGH.

    The volume of a combined solid is 372 cm. Calculate:

    (a)The volume, in cm, of the right pyramid.(b)The heights, in cm, of the right pyramid.

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    9. Diagram below shows two sectors OBCand OADE, both with centre O.

    It is given that OA =AB = 7 cm, 80DOE . Using22

    7 , calculate

    (a)The perimeter, in cm, of the whole diagram.(b)The area, in cm, of the shaded region.

    10. Diagram below shows four labeled cards in box P and three labeled cards in box Q.

    A card is picked at random from each of the boxes.

    (a)List the sample space.(b)List all the outcomes of the events and find the probability that

    (i) both cards are labeled with a number,(ii) one card is labeled with letter M or the other card is labeled with number 7.