449/ 449/ Matematik Kertas Oktober 007 4 jam SEKTOR SEKOLAH ERASRAMA PENUH AHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN IAGNOSTIK TINGKATAN 4 007 MATEMATIK Kertas Satu jam lima belas minit JANGAN UKA KERTAS SOALAN INI SEHINGGA IERITAHU. Kertas soalan ini adalah dalam ahasa Inggeris.. alon dikehendaki membaca maklumat di halaman. Kertas soalan ini mengandungi 3 halaman bercetak. 449/ 007 Hak ipta Sektor SP
449/ INFORMATION FOR ANIATES. This question paper consists of 40 questions.. Answer all questions. 3. Answer each question by blackening the correct space on the answer sheet. 4. 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. A list of formulae is provided on page 3 to 4. 8. You may use a non-programmable scientific calculator. 449/ 007 Hak ipta Sektor SP
449/ MATHEMATIAL FORMULAE The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS a m x a n = a m+ n a m a n = a m n 3 ( a m ) n = a mn 4 A - = ad bc d c b a 5 P ( A ) = n( A) n( S) 6 P ( A ) = P(A) 7 istance = ( x y x ) + ( y ) x + x y + y 8 Midpoint, ( x, y ) =, 9 Average 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 3 m = y x y x 449/ 007 Hak ipta Sektor SP 3
449/ 4 m = y-intercept x-intercept SHAPES AN SPAE Area of trapezium = sum of parallel sides height ircumference of circle = πd = πr 3 Area of circle = πr 4 urved surface area of cylinder = πrh 5 Surface area of sphere = 4πr 6 Volume of right prism = cross sectional area length 7 Volume of cylinder = πr h 8 Volume of cone = 3 πr h 9 Volume of sphere = 3 4 πr 3 0 Volume of right pyramid = 3 base area height Sum of interior angles of a polygon = ( n ) 80 arc length = circumference of circle angle subtended at centre 360 o 3 area of sector angle subtended at centre = area of circle 360 o 4 PA' Scale factor, k = PA 5 Area of image = k area of object 449/ 007 Hak ipta Sektor SP 4
449/ Answer all questions. Round off 0.0907 correct to three significant figures. A 0.0900 0.09 0.090 0.09 7.6 0 6 7 5.3 0 = 3 A.96 0 6.96 0 3 6.73 0 6 6.73 0 3.8 0 3 ( 4 0 ) 5 = A 0 3.07 0 3.07 0 9 7.675 0 0 7.675 0 449/ 007 Hak ipta Sektor SP 5
449/ 4 A motorcycle moved at a speed of 0km h -. Find the distance, in m, travelled by the motorcycle in 90 minutes. A 3 3.0 0 5.8 0 4.08 0 7.08 0 5 Given that 3 = 7 4( 3 + ) x x, calculate the value of x. A 3 3 6 Given that s = r r, then r = A + s s 3s + s 449/ 007 Hak ipta Sektor SP 6
449/ 7 Given that p + 3 = q, express p in terms of q. A ( ) p = q + 6 ( ) p = q 3 p = ( q) 6 ( ) p = q 6 8 Express t 3 4t 3 as a single fraction in its simplest form. t A t 4 4t 4 t 4t 9 ( x y ) 4 x( 3 x )= A 6 x + y + 4 xy 4 x 6 x y 4 xy 4 x 6 x + 4 xy 6 x xy 449/ 007 Hak ipta Sektor SP 7
449/ 0 Which of the following statement is true? a A = or ac + ad = a(c + d) a + b b 3 ( x + ) = x + 6 or 4 = 3 + = 3 and 3 = 5 ( m+ )( m ) = m 4 and ma+ am= a m iagram shows that FGH is a tangent to the circle and EG = EK. K x H E G 8 º IAGRAM F Find the value of x. A 6º 59º 46º 45º 449/ 007 Hak ipta Sektor SP 8
449/ In iagram, UTV is a tangent to the circle PQST at T. PQR and RST are straight lines. P Q yº 30º R S U T IAGRAM 50º V alculate the value of y. A 5 0 30 35 3 Table shows the scores obtained by a group of participants in a competition. Score 3 4 5 Frequency 5 5 8 0 TALE Find the difference between the mode and the median of the data. A 0 4 449/ 007 Hak ipta Sektor SP 9
449/ 4 iagram 3 is a pictograph showing the number of three types of stationary sold by a shop in a particular week. The ratio of the number of pens to the number of erasers is 3:. Pen Θ Θ Θ Θ Θ Θ Ruler Θ Θ Θ Eraser Θ represents dozen of stationary IAGRAM 3 Find the total number of rulers and erasers sold in that week. A 48 7 84 00 5 iagram 4 shows five triangles drawn on a square grid. A T IAGRAM 4 Which of the triangles, A,, or is the image of triangle T under an enlargement with a scale factor of? 449/ 007 Hak ipta Sektor SP 0
449/ 6 In iagram 5, MLK is a straight line. N x º y º M L K IAGRAM 5 Given that sin xº = 3 5, then tan y º = A 5 5 5 5 7 Given that cos x = 0.650. alculate the possible values of x if 0º x 360º. A 30 4 and 9 8 30 4 and 0 4 39 8 and 0 4 39 8 and 9 8 449/ 007 Hak ipta Sektor SP
449/ 8 iagram 6 shows a Venn diagram with the universal set, ξ = K L M. K M L A IAGRAM 6 Which of the region, A,, or, represents the set (K L ) M? 9 iagram 7 shows a Venn diagram with the universal set ξ = { Form Five students }, set F = {Students who can speak French} and set J = {Students who can speak Japanese}. ξ F J IAGRAM 7 Given that n(f) = 44, n(j) = 36, n(ξ) = 80 and the number of students who can only speak Japanese is 8, find the number of students who can not speak French or Japanese. A 8 4 8 34 449/ 007 Hak ipta Sektor SP
449/ 0 iagram 8 shows two straight lines JL and ON on a artesian plane where O is the origin. y N (5,0) J K O L x The two straight lines intersect at point K. Given that the equation of JL is 3y + x = 4. Find the coordinates of K. A (, 4) IAGRAM 8, 3, 3, 3 449/ 007 Hak ipta Sektor SP 3
449/ In iagram 9, JKL is a straight line and JM = KM. y J (4, 3) O K M x L (-, h) IAGRAM 9 Find the value of h. A 3 4 Table is a frequency table which shows the masses of students in a class. Mass (kg) Frequency 5 53 3 54 56 5 57 59 6 60 6 4 63 65 TALE alculate the mean mass, in kg, of the students. A 56.55 57.55 58.55 60.05 449/ 007 Hak ipta Sektor SP 4
449/ 3 iagram 0 shows triangles V and W drawn on a square grid. V A W IAGRAM 0 Triangle W is the image of triangle V under clockwise rotation of 90 0. Which of the points, A,, or, is the centre of rotation? 4 3 3 5 64 43 8 = A 4 8 4 5 Simplify 3 5 7 ( x y) x y. 4 A xy 3 4 x y 0 x y 3 0 x y 449/ 007 Hak ipta Sektor SP 5
449/ 6 iagram shows a regular pentagon JKLMN. FGH is a straight line. K L F 6 o G J 3 o y o x o N 77 o M IAGRAM H alculate the value of y x. A 6 08 80 8 7 A number is chosen at random from set P = {x:x is an integer and < x }. Find the probability that the number chosen is a prime factor of 6. A 0 5 3 0 5 449/ 007 Hak ipta Sektor SP 6
449/ 8 iagram shows a pentagon KLMNP. Given that KL and NP are straight lines and parallel to each other. M L x o 00 o y o N P 70 o K IAGRAM Find the value of x + y. A 6 50 60 9 If m< m m, then the integers m that satisfy the inequalities are A,, 3, 4 0,,, 3, 4,, 3, 3, 4 449/ 007 Hak ipta Sektor SP 7
449/ 30 The number line that represents the solution for 3x < 6 is A 6 8 6 8 449/ 007 Hak ipta Sektor SP 8
449/ 3 iagram 3 is a Venn diagram showing the elements of sets ξ, P, Q and R. ξ P Q R g b a h d c e f i j k Find n[ ( P Q) Q '] A 3 5 6 IAGRAM 3 3 In iagram 4, O is the origin. The straight line JK is parallel to the straight line OL. y J ( 3,0) O K L (,4) x alculate the coordinates of K. IAGRAM 4 A (0, -) (0, ) (0, 6) (0, 9) 449/ 007 Hak ipta Sektor SP 9
449/ 33 In iagram 5, QST is a straight line. R 5 cm T 6 cm S P Q IAGRAM 5 5 Given tan PQT = and A 3 4 5 3 sin SQR =. alculate, in cm, the length of TS. 5 34 Table 3 shows the marks obtained by 50 students in a mathematics test. etermine the median class. A 0 9 30 39 40 49 50 59 Marks Frequency 0 9 0 30 39 6 40 49 4 50 59 5 60 69 5 TALE 3 449/ 007 Hak ipta Sektor SP 0
449/ 35 Table 4 shows the results of a study conducted on a group of 60 students and the food they bought at the canteen. Type of food Number of students Fried noodles n Nasi lemak 4 read p Roti canai 0 TALE 4 If a student, chosen at random from the group, had a probability of 4 in buying fried noodles, calculate the value of p. A 3 5 6 36 iagram 6 shows the circle STQ with centre O. PQR and RS are tangents to the circle at Q and S respectively. S R 36 y O T IAGRAM 6 Q P Find the value of y. A 7 36 54 7 449/ 007 Hak ipta Sektor SP
449/ 37 In iagram 7 below, JK and LM are two vertical poles on a horizontal plane. J 45 m K 50 m IAGRAM 7 M L 0 m alculate the angle of depression of peak L from peak J. A 4 40 6 34 56 35 63 6 38 iagram 8 shows a steel frame placed on a horizontal plane. PQ and RST are vertical while PS is horizontal. Given that the angle of elevation of point R from point Q is 68. 0 m R P S Q 8 m IAGRAM 8 T The height of PQ is A 8 8.9 0 3.8 449/ 007 Hak ipta Sektor SP
449/ 39 iagram 9 shows a cuboid with a horizontal rectangular base KLMN. S R P Q 0 cm The angle between the line KR and the base KLMN is o A 6 34 o 53 8 o 63 6 o 68 K N 4 cm M 3 cm L IAGRAM 9 40 iagram 0 shows a cuboid with a horizontal base TUVW. M is the midpoint of TU. S R P W Q V T M U IAGRAM 0 etermine the angle between the plane PSM and the horizontal base TUVW. A PMT TMS SMW MPQ EN OF QUESTION PAPER 449/ 007 Hak ipta Sektor SP 3
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