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SOALAN ULANGKAJI SPM 2008

TIMES HIGHER EDUCATION

SOALAN ULANGKAJI SPM 2008ADDITIONAL MATHEMATICS

Paper 2Nov./Dis

DO NOT OPEN UNTILL INTSRUCTED TO

1. Answer all the questions

2. Think thoroughly before answering any of the questions. If you need to change your answer, erase the answer properly and thoroughly before remarking the question sheet.

This question paper contains 8 printed pages and 0 non printed pages

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Section A( 40 marks )

Answer all questions in this section.

1. Solve the simultaneous equations:

x – 2y = 5 , [ 7 marks ]763

−=−x

y

y

x

2. Diagram 1 shows a rectangle PQRS. The coordinates of P and Q are (-2,1) and (4,4) respectively.Given that the equation of PR is y – x = 3, find

(a) the coordinates of point S (b) the equation of SQ (c) the area of the rectangle PQRS [ 6 marks ]

DIAGRAM 1

3. Given that px² – x is a gradient function for a curve such that p is a constant. y = 4x – 5 is a tangent equation at point (1,-1) to the curve. Find

(a) the value of p (b) the curve equation (c) the normal equation of the curve at point (1,-1) [ 6 marks ]

4. (a) Given the functions f(x) = 3x + k and f – 1 (x) = 2hx , where h and k are constants. Find the value of h and k. q [ 3 marks ]

(b) Given the functions f(x) = 4x - 3 and g(x) = , Find

(i) f – 1

(1) (ii) g f – 1

(13) [ 4 marks ]

3

52 +hx

0,6

≠xx

P

SQ

R

0x

y

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5 (a) The sum of the first n terms of the geometric progression 64,32,16,8,4……. is 127.5 . Find (i) the common ratio (ii) the value of n [ 3 marks ]

(b) A rope with a length of 200cm is cut into 25 sections whose lengths are in arithmetic progression. Given that the sum of the lengths of 3 smallest section is 4.2 cm , find

(i) the length of the largest section (ii) the sum of the last three largest section [ 4 marks ]

6. (a) The mass of students in a school is normally distributed with mean 52.5 kg and variance 10 kg² . Find the probability that a student chosen at random has a mass of less than 45 kg.

(b) A box contains blue and green balls. 40 % of the balls are blue in colour.

(i) If 6 balls are selected at random, find the probability that at least one ball is blue in colour. (ii) The variance for blue balls is 12. Find the number of balls in the box. [ 7 marks ]

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Section B( 40 marks )

Answer four questions from this section

7. Use the graph paper to answer this question.Table 1 shows the values of two variables , x and y , obtained from an experiment. The variables of x and y are related by the

equation , where p and q are constants.12=−

x

q

y

p

x 1.5 2.0 2.5 3.0 5.0y 0.55 0.94 1.45 2.02 4.76

(a) Plot against by using a scale of 2 cm to 0.05 unit on the – axis and 2 cm to 0.2 units on the -axis. Hence,

draw the line of best fit. [ 5 marks ] (b) Use the graph from (a) to find the value of (i) p (ii) q [ 5 marks ]

y

1x²1

x²1

y

1

8. (a) Given cos x = - and 0º < x < 180º , find the value of (i) sec x + cot x (ii) tan ( x – 135º ) [ 4 marks ]

(b) (i) Sketch the graph of y = 1 – sin 2x for 0 ≤ x ≤ 2∏ [ 3 marks ] (ii) Hence, by drawing a suitable straight line on the same axes, find the number of solutions that satisfying the equation x = 2 ∏ sin 2x for 0 ≤ x ≤ 2∏ [ 3 marks ]

53

Table 2 shows the distribution of marks of 60 students in a test.

(a) Without drawing the ogive, estimate (i) median (ii) interquartile range [ 3 marks ]

(b) Compute the (i) mean (ii) standard deviation for the marks of the students. [ 7 marks ]

9. Marks Frequency41 - 45 346 - 50 851 - 55 756 - 60 1561 - 65 1366 - 70 871 - 75 6

Table 1

Table 2

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10. Diagram 2 shows two circles with centres, P and Q . AB is the common tangent to the two circles at points C and D respectively. If the radii of the two circles are 7 cm and 4 cm respectively, find (a) RQD , in radian (b) the perimeter , in cm , of the shaded region (c) the area , in cm², of the shaded region [ 10 marks ]

∠

4 x

11. Diagram 3 shows a pentagon ABEDC. Given AB = 4x , AC = 6y and CD = 8x.(a) Express in terms of x and/or y (i) CB (ii) DA [ 4 marks ]

(b) If BE = nBC and AE = mAD , express AE (i) in terms of n, x and y (ii) in terms of m , x and y hence, find the value of m and of n. [ 6 marks ]

→ → → →

→ → →

→→

→

A C D B

DIAGRAM 2P

RQ

6 y

BA

C D

E

8 x

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Section C( 20 marks )

Answer two questions from this section .

12. Use the graph paper to answer this question.

Given that x and y are two positive integres with the following conditions.

I : The maximum value of x is 40

II : The sum of x and y is not more than 100

III : The difference between y and twice the value of x is 25 or less

(a) Write the inequalities other than x > 0 , y > 0 for each of the above. [ 2 marks ]

(b) By using a scale of 2 cm to 20 unit on both axes, construct a graph and shade the region as `` F`` that satisfies all the inequalities. [ 3 marks ]

(c) Based on your graph, answer all the questions

(i) Find the maximum value of y when x = 40

(ii) Find the maximum value of k when k = x + 2y

(iii) Find the minimum value of x when y = 40 [ 5 marks ]

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SOALAN ULANGKAJI SPM 2008

14. (a) Diagram 4 shows a triangle KLM. Given KL = 6.8 cm, ∠LKM = 48º and ∠LMK = 25º. Find

(i) the length of KM (ii) the area of ∆ KLM [ 4 marks ]

(b) Diagram 5 shows a cyclic quadrilateral UVWT. Given that , ∠TUV = 140º , UV = 4 cm , UT = 8 cm , and WT = 10 cm. Find (i) the length of VT (ii) ∠TVW (iii) the area of quadrilateral UVWT [ 6 marks ]

K

DIAGRAM 4

L

M48º 25º

DIAGRAM 5

V

U

W

T

140º

13. A particle moves along a straight line and passes through a fixed point O. Its displacement, s meters, from O at time t seconds alter passing through O is given by s = 2t³ – 3 t² . Find

(a) the initial acceleration

(b) the velocity when t = 4

(c) the time when the particle is instantaneously at rest

(d) the time when the particle reaches at velocity of 12 cms–1 [ 10 marks ]

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15. (a) The price indices of a pair of shirts of a particular brand P in the years 2005 and 2003 based on the year 2001 are 156 and 144 respectively. (i) Calculate the price index of a pair of shirts of brand P for the year 2005 based on the year 2003. [ 3 marks ] (ii) If a pair of shirts of brand P is priced at RM250 in the year 2003, calculate its corresponding price in the year 2001. [ 2 marks ]

(b)

Item Price in 1998 (RM) Price in 2000(RM)

Price Index in 2000 based on 1998

Weightage

K 3.00 3.60 120 4L X 2.50 125 2M 4.00 4.40 110 1N 2.50 4.00 Y 5

Table 3 shows the prices of four commodities K, L, M and N in year 1998 and 2000, the price index in year 2000 was based on 1998. Calculate

(i) the value of x and of y [ 2 marks ]

(ii) the composite index number of the cost of the item production of the four commodities in year 2000 is based on year 1998. [ 3 marks ]

Table 1

END OF QUESTION PAPER

At the moment, the most popular courses are Physiotherapy, Pharmacy and Medical Lab Technology.

What core areas are covered by the programmes? Are courses available at different levels (i.e. certificate through to degree – what is the route)?MAHSA offer programmes in the certificates, diploma and degree levels. The general background of the programmes is science based. Students in all programmes learn areas in anatomy, physiology, pathology. Different programmes also carry individual subjects. For example students in Physiotherapy learn Musculoskeletal, Electrotherapy and Physiotherapy in Gerontology whereas students in Pharmacy learn things like Pharmaceutical Microbiology and so on.

A student after SPM has the decision of choosing to enter a diploma course directly or opt to do the A’ levels programme or an equivalent programme. A diploma programme in MAHSA is a 3 year course, followed by the student later completing their last 2 years of the degree programme in MAHSA depending on the course chosen.

How much emphasis is placed on theoretical knowledge and how much on practical skills?I would say we emphasize 60% on theory and 40% on clinical practical sessions. MAHSA emphasizes this in our Mission statement where it states we will “be committed to the delivery of education of the highest quality with emphasis on hands on training” and “to produce competent and highly skilled healthcare professionals through qualified, dedicated and experienced teachers”.

Can students complete the programme overseas or is it possible to take everything in Malaysia?The diploma and degree programmes at MAHSA are fully conducted in Malaysia. We are offering the students the chance to do an international degree at a lower rate than studying abroad. However, we do have plans to promote overseas options in time to come.

Other thoughts?At MAHSA we welcome anyone with the heart and wish to pursue a career in the Allied Health Science sector. The statistics show that the country will need more than 54,000 allied health science professionals by the year 2020. There is a market for those with skills and knowledge so I would advise you not to miss the chance of a lifetime experience. For those interested in furthering your education with us at MAHSA, please feel free to contact our marketing staff at +603-2092 9999 or 130088 0300.

Realising your Dreamsas allied

Health Sciences Professionals

Pursuing a career in Allied Health Science is becoming a choice among students. From a lab technologist to a fully trained physiotherapist, the opportunities are wide. Mr. Rafeeudeen Mohamed, Registrar of

MAHSA College talks about the careers in Allied Health Science.

What are the career options in the field of Allied Health Sciences? What are the prospects?There are many options in the field of Allied Health Sciences. Here at MAHSA we offer Nursing, Pharmacy, Physiotherapy, Medical Lab Technology, Medical Imaging (Radiography) and Environmental Health. Students will be fully trained to later pursue a career following their graduation of any of the MAHSA degree or diploma programmes. This will enable them to work in any private or government hospitals or health institutions.

What advice would you give to prospective students who are thinking about careers in Allied Health Sciences? For a student sitting for SPM, how well should he/she do to enrol in this course? Go for it! The demand for Allied Health professionals in the health care industry is high and rising not just locally but on an international scale. The chances of employment are high mixed with the opportunities to travel to various countries and undergo various working experiences. The minimum requirements at MAHSA for any of our Diploma courses are 3 credits in SPM including one science subject. This excludes the Diploma in Dental Technology which requires 5 credits in SPM.

What qualities do students need in order to succeed in the field of Allied Health Sciences? Are generic or specialist skills needed?The basic qualities required by an individual choosing any Allied Health Science profession is determination to succeed, be caring and helpful, good natured and hard working. The hours are long and taxing; so an individual should be mild tempered and able to deal with emotionally stressed patients in a smiling and polite manner at all times. The most prized skill an individual should have in any profession is the ability to provide helpful communication and assistance to another person when in need.

What are currently the most popular ‘allied health science’ courses among Malaysian students?

Career options after SPM

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