hussenhmhuda.files.wordpress.com · Web viewIII : The minimum total profit for both shirts is RM3 600. (a) Write three inequalities, other than x > 0 and y > 0, which satisfy all

PAPER 1 Time: Two hours

SULIT 3472/1

NAMA: _______________________________________________ TINGKATAN: ______________

SPM MODEL PAPER

[80 marks] This question paper consists of 25 questions. Answer all the questions. Give only one answer for each question. Write your answers clearly in the spaces provided. Show your working. It may help you to get marks. You may use a non-programmable scientific calculator. 1 Diagram 1 shows the linear function f.

Diagram 1 (a) State the value of x.(b) Using the function notation, express f in terms of y.

[2 marks]Answer:

2 Given that f : x and fg : x 7x – 2, find(a) g(x), (b) f –1(5).

[3 marks]Answer:

3 Given the functions f(x) = , x ≠ –2, and g(x) = kx + 4. Find (a) f (6),(b) the value of k such that gf (6) = 6.

[3 marks]Answer:

4 One of the roots of the quadratic equation x2 – 8x + (3 + 2k) = 0 is three times the other root. Find the value of k.

[3 marks]Answer:

5

Diagram 2 Diagram 2 shows the graph of the curves y = x2 – 4x – 3mx + 21 and y = –2(x – 5)2 + 2n that intersect the x-axis at two points. Find(a) the values of m and n,(b) the minimum or the maximum point of each curve.

[4 marks]Answer:

6 Find the range of the values of x for (x + 2)(2x – 1) < 5(2x – 1).

[3 marks]Answer:

7 Given 5log 4x = 125, find the value of x.[2 marks]

Answer:

8 Given that log8 4p – log2 2q = 2, express p in terms of q.[3 marks]

Answer:

9 Diagram 3 shows three circles with centres O.

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SULIT 3472/1

NAMA: _______________________________________________ TINGKATAN: ______________

SPM MODEL PAPER

[80 marks] This question paper consists of 25 questions. Answer all the questions. Give only one answer for each question. Write your answers clearly in the spaces provided. Show your working. It may help you to get marks. You may use a non-programmable scientific calculator.

Diagram 3 The perimeter of the circles form an arithmetic progression. The terms of the progression are in ascending order.(a) Write down the first three terms of the progression.(b) Find the common difference of the progression.

[3 marks]Answer:

10 The first term of a geometric progression is three times its common ratio. Given that the sum to infinity of the progression is 6, find (a) its common ratio,(b) the fifth term.

[3 marks]Answer:

11 The first three terms of an arithmetic progression are k + 5,

– 5 and 7h – 2k2. Express h in terms of k.[2 marks]

Answer:

12 The variables x and y are related by the equation y2 = 2x(m – nx), where m and n are constants. A straight line

graph is obtained by plotting against x, as shown in Diagram 4.

Diagram 4 Find the value of m and of n.

[3 marks]Answer:

13 Diagram 5 shows a straight line passing through S(6, 0) and T(0, 8).

Diagram 5 (a) Write down the equation of the straight line ST in the

form(b) A point M moves such that TM : MS = 3 : 2. Find the

coordinates of point M.[4 marks]

Answer:

14

Diagram 6

In Diagram 6, the straight line AB is perpendicular with the straight line BC. Find the value of k.

[3 marks]Answer:

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15 Given that and If

find the value of k and of t.[3 marks]

Answer:

16

Diagram 7 In Diagram 7, point M lies on the straight line PQ such that

Express in terms of and[3 marks]

Answer:

17 Solve the equation 2 sin (u + 60°) = cos (u + 60°) for 0° < u < 360°.

[4 marks]Answer:

18 Diagram 8 shows two arcs, AC and BD, of a circle with centre O. OAB and OCD are straight lines.

Diagram 8 Given that OA = OC = 8 cm and the length of arc AC = 6 cm, calculate (a) the value of u, in radian,

(b) the perimeter of ABDC, if OA : OB = 2 : 3.[3 marks]

Answer:

19 Given that g(x) = (x3 + 2)(1 – 2x)6, evaluate g'(1).[3 marks]

Answer:

20 The normal to the curve y = 2x2 + 8x – 3 at point S is

parallel to the straight line y = – x + 5. Find the equation of the tangent to the curve at point S.

[4 marks]Answer:

21

Diagram 9 Diagram 9 shows the curve y = x(x + 2)(x – 3) cutting the x-axis at x = –2, x = 0 and x = 3. Find the area of the shaded region.

[4 marks]Answer:

22 Diagram 10 shows nine letter cards.

1 M A L A Y S I A

Diagram 10 A four-letter code is to be formed using four of these cards. Find (a) the number of different four-letter codes that can be

formed,(b) the number of different four-letter codes that consist of

consonant letters and the number 1 only.[4 marks]

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SULIT 3472/1

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SPM MODEL PAPER


Answer:

23 There are 52 families in a village. 32 of them have durian trees, 29 have banana trees and k families have both. A family is selected at random from the village. Find (a) the value of k if the probability of the selected family

has both durian and banana trees is(b) the probability that the selected family has durian or

banana trees.[4 marks]

Answer:

24 A set of eight numbers has a mean of 11.(a) Find ∑x.(b) When a number 2y is added to this set, the new mean is

12. Find the value of y.[3 marks]

Answer:

25 Diagram 11 shows a standard normal distribution graph.

Diagram 11 The probability represented by the area of the shaded region is 0.156.(a) Find the value of k.(b) X is a continuous random variable which is normally

distributed with a mean of 85 and a standard deviation of 2.8.

Find the value of X when the Z-score is k.[4 marks]

Answer:

1 Solve the simultaneous equations 2x + y = 3 and y2 – 3x + 3 = 0. Give your answers correct to three decimal places.

[5 marks]

2 A curve with gradient function – 3x has a turning point at (t, 7).(a) Find the value of t. [2 marks](b) Determine whether the turning point is a maximum or a minimum point. [3 marks](c) Find the equation of the curve. [3 marks]

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PAPER 2

This question paper consists of three sections: Section A, Section B and Section C. Answer all the questions in Section A, four questions from Section B and two questions from Section C. Give only one answer/solution for each question. All the working steps must be written clearly.

Section A Answer all questions

3472/2Time: Two hours and thirty minutes


SULIT 3472/1

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3 In a race, a cyclist took 2 minutes 15 seconds to cycle the first kilometre. However, in every succeeding kilometre, he took 10 seconds more than the preceding kilometre. Calculate the time taken(a) to finish the 11th kilometre, [2 marks](b) to finish the race, if the total distance is 20 km. [3 marks]

4 Table 1 shows the mass, in kg, of 100 newborn babies.

Mass (kg) Number of newborn babies

1.1 – 1.5 3

1.6 – 2.0 13

2.1 – 2.5 15

2.6 – 3.0 20

3.1 – 3.5 27

3.6 – 4.0 16

4.1 – 4.5 4

4.6 – 5.0 2

Table 1

(a) Draw an ogive for the above data.(b) From the ogive, estimate [4 marks]

(i) the interquartile range, [2 marks](ii) the percentage of babies heavier than 2.7 kg. [2 marks]

5 (a) Prove that tan u (cos 2u + 1) = sin 2u. [2 marks](b) (i) Sketch the graph of y = –sin 2u – 1 for 0 < u < π. [2 marks]

(ii) Hence, using the same axes, sketch a suitable straight line to find the number of solutions for the equation. 1 – – tan u (cos 2u + 1) = 0 for 0 < u < π. State the number of solutions.

. [3 marks]

6 Given P(4, –1), Q(–5, 8) and R(k, 2).

(a) Find in the form of Hence, find the unit vector in the direction of [2 marks]

(b) Calculate the value(s) of k if48 SULIT


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(i) P, Q and R are collinear, [2 marks]

(ii) | | = | |. [3 marks]

7 Use the graph paper to answer this question.Table 2 shows the values of two variables, x and y, obtained from an experiment. Variable x and y are related by the equation y = abx – 1, where a and b are constant.

x 2 3 4 5 6 7

y 2.53 3.85 5.71 8.60 13.00 19.50

Table 2 (a) Plot log y against (x – 1), using a scale 2 cm to 1 unit on the (x – 1)-axis and 2 cm to 0.2 unit on the log y-axis. Hence, draw

the line of best fit. [5 marks]

(b) Use your graph from 7(a) to find the value of (i) a, (ii) b. [5 marks]

8 In Diagram 1, the straight line AB is tangent to the curve y = at A(2, 3).

Diagram 1 Find(a) the coordinates of point B, [3 marks](b) the area of the shaded region, [3 marks](c) the volume generated, in terms of π, when the shaded region is revolved through 360° about the x-axis. [4

marks]

9 Solution to this question by scale drawing will not be accepted.

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Section B[40 marks]

Answer any four questions from this section.


SULIT 3472/1

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Diagram 2 (a) Find

(i) the equation of straight line PQ,(ii) the coordinate of Q. [5 marks]

(b) The straight line PQ is extended to a point S such that PQ : QS = 3 : 2. Find the coordinates of S. [2 marks]

(c) If the coordinates of R is (6, 5) find the area, in unit2, of triangle PQR. [3 marks]

10 Diagram 3 shows an arc XRY of a circle, with centre O and a radius of 9 cm. XTYS is a semicircle, with centre T and a radius of 6 cm.

Diagram 3 Find(a) ∠XOY, [3 marks](b) the perimeter, in cm, the shaded region (use π = 3.142), [3 marks](c) the area, in cm2, of the shaded region. [4 marks]

11 The masses of papayas from a village has a normal distribution with a mean of 350 g and a standard deviation of 75 g.(a) Find the probability that a papaya chosen randomly from this village has a mass between 235 g and 375 g. [3 marks](b) A random sample of 600 papayas is chosen.

(i) Calculate the number of papayas from this sample with masses between 235 g and 375 g. [3 marks](ii) Given that 198 papayas from this sample have masses of more than n g, find the value of n. [4 marks]

50 SULIT


SULIT 3472/1

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SPM MODEL PAPER


12 A particle moves along a straight line and passes through a fixed point O. Its velocity, v m s–1, is given by v = at – bt 2, where t is the time, in seconds, after passing through O and a and b are constants. The particle stops instantaneously at t = 3s and its displacement at that time is 18 m to the right side of O.[Assume motion to the right is positive]

(a) Find the value of a and of b. [4 marks](b) Using the values of a and b that are found,

(i) find the time required by the particle to return to O,(ii) calculate the total distance, in m, travelled by the particle in the first 6 seconds, after passing through O.

[6 marks]

13 Diagram 4 shows a bar chart that represents the weekly expenses of some types of fruits for the year 2005 of a fruit seller.

Diagram 4

Table 3 shows the prices in the years 2005 and 2009 and the price index for 2009 based on 2005 for each fruit.

Fruits Price per kg in 2005 (RM)

Price per kg in 2009 (RM)

Price index for 2009 based on 2005

Banana x 2.45 125

Orange 4.00 5.20 y

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Section C[20 marks]

Answer any two questions from this section.


SULIT 3472/1

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Mango 3.00 3.75 125

Watermelon 6.50 9.10 140

Mangosteen 6.00 z 115

Table 3

(a) Find the values of(i) x, (ii) y, (ii) z. [3 marks]

(b) Calculate the composite index of the fruits for the year 2009 based on the year 2005. [4 marks](c) The total monthly expenses of the fruits in the year 2005 was RM2 050. Calculate the total monthly expenses for the year

2009. [3 marks]

14 Use a graph paper to answer this question.A factory produces two types of shirts, A and B. In a particular day, the factory produces x pieces of shirt A and y pieces of shirt B. The profit from the sales of a piece of shirt A is RM18 and the profit from a piece of shirt B is RM16.The production of the shirts per day is based on the following constraints:

I : The total number of shirt produced is at most 450.II : The number of shirt A produced is not more than three times the number of shirt B.

III : The minimum total profit for both shirts is RM3 600.(a) Write three inequalities, other than x > 0 and y > 0, which satisfy all the above constraints. [3 marks](b) Using a scale of 2 cm to 50 shirts on both axes, construct and shade the region R which satisfies all of the above constraints.(c) Use your graph in 14(b), to find [3 marks]

(i) the minimum number of shirt B if the number of shirt A produced on a particular day is 110,(ii) the maximum total profit per day. [4 marks]

15 Diagram 5 shows a quadrilateral PQRS.

Diagram 5 The area of triangle PQS is 12 cm2 and ∠SPQ is acute.Calculate(a) ∠SPQ, [2 marks](b) the length, in cm, of SQ, [2 marks](c) ∠SRQ, [3 marks](d) the area, in cm2, of quadrilateral PQRS. [3 marks]

52 SULIT

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hussenhmhuda.files.wordpress.com · Web viewIII : The minimum total profit for both shirts is RM3 600. (a) Write three inequalities, other than x > 0 and y > 0, which satisfy all