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1 9/ 9/ Matematik Kertas Mei 007 jam SEKTOR SEKOLH ERSRM PENUH HGIN SEKOLH KEMENTERIN PELJRN MLYSI PEPERIKSN PERTENGHN THUN TINGKTN MTEMTIK Kertas Satu jam lima belas minit JNGN UK KERTS SOLN INI SEHINGG IERITHU. Kertas soalan ini adalah dalam ahasa Inggeris.. alon dikehendaki membaca maklumat di halaman. Kertas soalan ini mengandungi halaman bercetak. 9/ 007 Hak ipta SP

2 9/ INFORMTION FOR NITES. This question paper consists of 0 questions.. nswer all questions.. nswer each question by blackening the correct space on the answer sheet.. lacken only one space for each question. 5. If you wish to change your answer, erase the blackened mark that you have done. Then blacken the space for the new answer. 6. The diagrams in the questions provided are not drawn to scale unless stated. 7. list of formulae is provided on page to. 8. You may use a non-programmable scientific calculator. 9/ 007 Hak ipta SP

3 9/ MTHEMTIL FORMULE The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELTIONS a m x a n = a m+ n a m a n = a m n ( a m ) n = a mn - = ad bc d c b a 5 P ( ) = n( ) n( S) 6 P ( ) = P() 7 istance = ( x y x ) + ( y ) x + x y + y 8 Midpoint, ( x, y ) =, 9 verage speed = distance travelled time taken 0 Mean = sum of data number of data Mean = sum of (class mark frequency) sum of frequencies Pythagoras Theorem c = a + b m = y x y x m = y-intercept x-intercept 9/ 007 Hak ipta SP

4 9/ SHPES N SPE rea of trapezium = sum of parallel sides height ircumference of circle = πd = πr rea of circle = πr urved surface area of cylinder = πrh 5 Surface area of sphere = πr 6 Volume of right prism = cross sectional area length 7 Volume of cylinder = πr h 8 Volume of cone = πr h 9 Volume of sphere = πr 0 Volume of right pyramid = base area height Sum of interior angles of a polygon = ( n ) 80 arc length = circumference of circle angle subtended at centre 60 area of sector angle subtended at centre = area of circle 60 P' Scale factor, k = P 5 rea of image = k area of object 9/ 007 Hak ipta SP

5 9/ nswer all questions Round off 0.00 correct to three significant figures = ( 0 ) = / 007 Hak ipta SP 5

6 9/ iagram shows a rectangle and three regular octagons. Given that the area of an octagon is. unit..5 unit unit IGRM Find the area of the shaded regions and give your answer correct to three significant figures. 9. unit 9.5 unit 9.00 unit unit 5 Express 5 as a number in base eight = / 007 Hak ipta SP 6

7 9/ 7 In iagram, PQRST is a regular pentagon. UTR is a straight line. U P y 0 T S x R Q IGRM The value of x + y = / 007 Hak ipta SP 7

8 9/ 8 In iagram, PQRS is a rhombus, PSTU is a trapezium and QST is a straight line. R x Q S P The value of x is T o 55 IGRM U O 55 O 60 O 70 O 75 9 iagram shows a circle with centre O. LM and LN are tangents to the circle at points M and N respectively. N 50 O L 0 x M IGRM Find the value of x / 007 Hak ipta SP 8

9 9/ 0 In iagram 5, PQRS is a cyclic quadrilateral and TS is a tangent to the circle at point S. Q 00 P x R 60 T S IGRM 5 Find the value of x / 007 Hak ipta SP 9

10 9/ iagram 6 shows points plotted on artesian plane. y 6 R x IGRM 6 etermine which of the point,,, or, is the image of point R under a 90 anticlockwise rotation about the centre (, ). 9/ 007 Hak ipta SP 0

11 9/ iagram 7 shows two quadrilaterals, PQRS and PQ R S drawn on square grids. Quadrilateral PQ R S is the image of quadrilateral PQRS under an enlargement at centre P with the scale factor k. P Q Q R S R S Find the value of k. IGRM 7 9/ 007 Hak ipta SP

12 9/ In iagram 8, O is the centre of a unit circle. y H ( 0.6, 0.906) θ - O x - IGRM 8 Find the value of sin θ iagram 9 shows the graph of y = cos x. y ( q, 0.5) x Find the value of q IGRM 9 0 9/ 007 Hak ipta SP

13 9/ 5 etermine which of the following is the graph of y = sin x for 0 x 90. y O 90 x y O 90 x 9/ 007 Hak y ipta SP

14 9/ 6 iagram 0 shows a right triangular prism. U is the midpoint of TV. T V cm U S R P 8 cm Q IGRM 0 Name the angle between the line UQ and the plane PSTV. PQU QUP QPU QUV 7 Express m 5 as a single fraction in its simplest form. m 7m 5 m 7 m + 5 m 5( m ) m 5 ( m + ) m 9/ 007 Hak ipta SP

15 9/ 8 5p p( p) p p p 6 p 6 p p 9 5 p p = ( p + )(5 p 6) ( p )(5 p + 6) ( p + )(5 p ) ( p )(5 p + ) 0 Given that p ( p ) = ( p + r) 6( r ) 5 6( r) 5 6 ( r + ) 5, express p in terms of r. ( r ) 5 Given that y + = x, express y in terms of x. x x + 8 x x + x( x) ( x ) 9/ 007 Hak ipta SP 5

16 9/ x y 5 Simplify x y ( x y ) x y x y x y 6 7 Simplify ( ). Given that k = ( k) 5, then k = 7 9/ 007 Hak ipta SP 6

17 9/ 5 List all the integers x which satisfy both of the inequalities x and x 0.,,, 0,,,, 0,,,,, 0,, 6 The solution for m < 8 and 6 + m is 5 < m 5 < m m 5 < m 5 7 Table shows the frequency of the score obtained in a game. TLE Given that the median score is, find the value of x. Score 0 Number of student x 6 9/ 007 Hak ipta SP 7

18 9/ 8 iagram shows the monthly expenditure among the students of 5 lfa and 5 eta. Number of students RM 5 lfa 5 eta IGRM alculate the mean of expenditure, in RM, of the students from the two classes. RM 5.00 RM 5.00 RM 6.8 RM / 007 Hak ipta SP 8

19 9/ 9 etermine which of the following graphs represents y = x. y O x y O x y O x y O x 9/ 007 Hak ipta SP 9

20 9/ 0 iagram shows a Venn diagram with the universal set, ξ, set P, Q, and R. The shaded region in the Venn diagram represent the set P' ( Q R) P Q R P Q R' IGRM P Q R iagram shows the number of elements in set X, Y and Z. X m Y m Z Given that n(x) = n(y), find the value of m. IGRM 9/ 007 Hak ipta SP 0

21 9/ Given that the universal set ξ = R S T. Set R = {, I,, E}, Set S = {,, R, } and Set T = {, O, I, N}. Set ( R T ') S is {, I,, E,, R, O, N} {, I,, E} {,, R, } {, } Table shows the relation between three variables g, h and f. Given that g varies directly as h and varies inversely as f. g h f x 6 0 TLE Find the value of x Given that y and y = n when n = and x =. ( x + ) Find the value of n when y = and x = / 007 Hak ipta SP

22 9/ 5 straight line PQ with gradient passes through the point (, 9). Find the y-intercept of the line straight line passes through the points K (0, t ) and L ( t, 0) and has a gradient of, find the value of t box contains red pens and blue pens. If a pen is picked randomly from the box, the probability of picking a blue pen is. 7 Find the number of red pen / 007 Hak ipta SP

23 9/ 8 two digit number is created from the digits in the set R. Given that R = { x : x, x is an integer }. Find the probability that the sum of the two digits is greater than iagram 5 shows a bar graph which represent the games played by a group of students. 0 8 Number of students 6 Football Rugby Hockey Tennis Games IGRM 5 If a student is chosen randomly from the group, state the probability that the student likes to play football / 007 Hak ipta SP

24 9/ 9/ 007 Hak ipta SP 0 0 k 6 0 = k Find the value of k. 8 7 EN OF QUESTION PPER S

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