Module Bengkel Matematik SPM 2013

7/27/2019 Module Bengkel Matematik SPM 2013

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REGION INEQUALITIES

1. On the graph provided, shaded the region which satisfies the three inequalities

y 2x + 8 ,y x andy < 8

[3 marks]

2. On the graph in the answer space, shade the region which satisfies the three inequalities

y - 2x + 10 , x < 5 andy 10.

[3 marks]


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3. On the graph in the answer space, shade the region which satisfies the three inequalities y -x + 6 ,

y 2x4 and x > 1

[3 marks]

4. On the graph in the answer space, shade the region which satisfies the three inequalities

[3 marks]


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MATRICES

1. SPM11P2SAQ8

(a) It is given that ( ) ( ), where M is a 2 2 matrix. Find M.

(b) Write the following simultaneous linear equations as matrix equation:

Hence, using matrix method, calculate the value ofx andy.

[6 marks]

Answer:

(a)

(b)


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2. SPM10P2SAQ11

The inverse matrix of( ) is (

).

(a) Find the value ofm and ofk.(b) Write the following simultaneous linear equations as matrix equation.


[6 marks]

Answer:

(a) m= ..

k = ..

(b)


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3. SPM09P2SAQ7

It is given that matrixA = ( ).

(a) Find the inverse matrix ofA.(b) Write the following simultaneous linear equations as matrix equation:


[6 marks]

Answer:

(a)

(b)


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4. SPM08P2SAQ8

The inverse matrix of( ) is (

).

(a) Find the value ofm and k.(b) Write the following simultaneous linear equations as matrix equation:


[6 marks]

Answer:

(a)

(b)


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GRADIENT AND AREA UNDER A GRAPH

1. Diagram 1 shows the distance-time graph of the journeys taken by Ali and Azmi.

Diagram 1

The straight line OB represents Alis journey from town X to town Y, while the straight line FG

represents Azmis journey from town Y to town X. Ali and Azmi uses the same route.

(a) State the distance in km, of town Y from town X.(b) Find the time Ali and Azmi meet each other during their journey.(c) Find the distance when they meet from town Y.(d) Calculate Azmis speed.

[6 marks]

Answer:

(a)

(b)

(c)

(d)


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2. Diagram 2 shows a displacement-time graph for the journey of a car from town A to town C passing

town B and then back to town A.

Diagram 2

(a) Calculate the speed in kmh-1 for the journey from town A to town B.(b) State the length of time in hour, for the car is stationary.(c) Calculate the average speed in kmh-1 for the total distance of the car.

[6 marks]

Answer:

(a)

(b)

(c)


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3. Diagram 3 shows the speed-time graph of a particle for a period of 15 s.

Diagram 3

(a) State the distance, in m, the particle moves with constant speed.(b) Calculate the rate of change of speed, in ms -2, in the first 6 s.(c) Calculate the value of k, if the total distance travelled in the first 15 s is 139 m.

[6 marks]

Answer:

(a)

(b)

(c)


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4. Diagram 4 shows the speed-time graph of a particle for a period of 17 seconds.

Diagram 4

(a) Calculate the value of u, if the total distance travelled in the first 8 seconds is 164 m.(b) State the length of time, in seconds, that particle move with uniform speed.(c) Calculate the average speed, in ms-1, for a period of 20 seconds.

[6 marks]

Answer:

(a)

(b)

(c)


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5. Diagram 5 shows a velocity-time graph for a particle.

Diagram 5

(a) State the time, in seconds, the particle moves with constant velocity.(b) Calculate the rate of change of velocity, in ms

-2

, of the particle in the last 5 seconds.(c) Find the value of u if the total distance travelled after 15 seconds is 190 m.

[6 marks]

Answer:

(a)

(b)

(c)


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PROBABILITY II

1.NS11P2SAQ8

Diagram 6 shows four numbered cards in box P and three cards labeled with letters in box Q.

Diagram 6

A card is picked at random from box P and then a card is picked at random from box Q.

By listing the sample of all the possible outcomes of the event, find the probability that

(a) A card with a prime number and the card labeled with vowel are picked.(b) A card with a number which is multiple of 2 or the cards labeled consonant are picked.

[5 marks]

Answer:

(a)

(b)


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2.JHR11P2SAQ7

Diagram 7 shows a number spinner and three cards labeled with letters P, Q and R in a box.

The spinner is spin and a card is picked at random from the box.

Diagram 7

By listing all the possible outcomes of the event, find the probability that

(a) The spinner shows number 3 and the card labeled Q is picked,(b) The spinner shows numbers which are multiple of 2 or the card labeled P is picked.

[5 marks]

Answer:

(a)

(b)


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3.KLT12P2SAQ10

Diagram 8 shows five cards labeled with digits.

Diagram 8

All these cards are put into a box. A two-digit code is to be formed by using any two of these cards. Two

cards are picked at random, one after, without replacement.

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

(i) the code begins with the letter 3,(ii) the code consists of two even digits or two odd digits.

[6 marks]

Answer:

(a)

(b) (i)

(b) (ii)


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4. There are 2 Physics teachers, 2 Chemistry teachers and 1 Biology teacher in a staff room. Two teachers

in staff room are chosen at random. Calculate the probability that

(a) The first is a Physics teacher and the second teacher is a Biology teacher,(b) Both of the teachers are teaching the same subject.

[5 marks]

Answer:

(a)

(b)

5. SPM06P2SAQ7In a quiz contest, there are three categories of questions consisting of 5 questions on

sport, 3 questions on entertainment and 7 questions on general knowledge. Each question is placed inside

an envelope. All of the envelopes are similar and put inside a box.

All the participants of the quiz contest are requested to pick at random two envelopes from the box.

Find the probability that the first participant picks

(a) the first envelope with a sport question and the second envelope with an entertainment question,(b) two envelopes with questions of the same category.

[5 marks]

Answer:

(a)

(b)

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Module Bengkel Matematik SPM 2013