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SULIT NAMA ………………………………………………………………………. TINGKATAN …………………………………………. JABATAN PELAJARAN PERAK SOALAN LATIH TUBI BERFOKUS 1 3472 / 1 ADDITIONAL MATHEMATICS Kertas 1 April 2 jam Dua jam JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU Untuk Kegunaan Pemeriksa 1. Kertas soalan ini mengandungi 25 soalan. Kod Pemeriksa : Markah Markah 2. Answer all questions. Soalan Penuh Diperoleh 1 3 3. Write your answers in the spaces provided 2 3 in the question paper. 3 3 4 3 4. Show your working. It may help you to 5 4 get marks. 6 3 7 2 5. If you wish to change your answer, cross 8 3 out the answer that you have done. Then write down the new answer. 9 3 10 3 6. The diagrams in the questions are not 11 4 drawn to scale unless stated. 12 3 13 4 7. The marks allocated for each question are 14 4 shown in brackets. 15 3 16 3 8. You may use a scientific calculator. 17 4 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 4 Jumlah 80 Kertas soalan ini mengandungi 13 halaman bercetak. [Lihat halaman sebelah 3472/1 2011 JPN PERAK SOLAF 1 SULIT For SULIT 2 3472/1 Examiner,s Use Answer all questions 1 Diagram 1 shows an incomplete arrow diagram which represents the relationship between set X and set Y. X square of Y 2● ● p 1● ● 1 q● Diagram 1 State (a) the values of p and q, (b) the type of the relation. [ 3 marks] Answer : (a) 1 (b) 3 2 Functions f and g are such that f : x → 2x – 5 and g : x → 1 – hx. Given that g – 1(– 1 ) = 4, find (a) the value of h, (b) g (8). [ 3 marks] Answer : (a) (b) 2 3 3472/1 2011 JPN PERAK SOLAF 1 SULIT SULIT 3 3472/1 For Examiner,s Use 3 Functions f and g are such that g : x → x – 7 and gf : x → 2x – 1. Find (a) gf(3), (b) f(– 2). [3 marks] Answer : (a) (b) 3 3 4 Diagram 4 shows the graph of a quadratic function y = f(x) with an axis of symmetry x = 1. y y = f(x) x –2 O h Diagram 4 (a) Find the value of h. (b) Solve f(x) ≤ 0. [3 marks] Answer : (a) (b) 4 3 Lihat Halaman Sebelah 3472/1 2011 JPN PERAK SOLAF 1 SULIT For SULIT 4 3472/1 Examiner,s Use 5 Both the quadratic equations, px2 – 8x + 6 = 0 and 3x2 + 6x – p + 1 = 0, where p is a constant, have two different roots. Find the range of values of p. [4 marks] Answer : 5 4 6 Diagram 6 shows some information about the graph of the quadratic function y = k – a( x + h ) 2, where a , h and k are constants. y-intercept = 5 Coordinates of maximum point = ( 1 , 7 ) Diagram 6 (a) State the values of h and k. (b) Calculate the value of a. [3 marks] Answer : (a) (b) 6 3 3472/1 2011 JPN PERAK SOLAF 1 SULIT SULIT 5 3472/1 For Examiner,s Use 7 Given that 4x = N, express 8x in terms of N. [2 marks] Answer : 7 2 8 Solve the equation: 3– x ( 12 x ) = 3 [3 marks] Answer : 8 3 9 Simplify logb 8 × log4 b 2 ÷ log27 3. [3 marks] Answer : 9 3 Lihat Halaman Sebelah 3472/1 2011 JPN PERAK SOLAF 1 SULIT For SULIT 6 3472/1 Examiner,s Use 10 Solve the equation: log5 ( 4x – 1 ) = 1 + log5 ( 7 – x ) [3 marks] Answer : 10 3 11 It is given that a, 4, 11, b, ……………………. 46 is an arithmetic progression. Find (a) the value of a and of b, (b) the number of terms the progression has. [4 marks] Answer : (a) (b) 11 4 3472/1 2011 JPN PERAK SOLAF 1 SULIT SULIT 7 3472/1 For Examiner,s Use 1 12 In a geometric progression, the ratio of the fifth term to the second term is . 27 Given that the first term is 12, find (a) the common ratio, (b) the sum to infinity. [3 marks] Answer : 12 3 13 An arithmetic progression has 11 terms. The first term is – 7 and the sum of the last 7 terms is 441. Find (a) the common difference, (b) the middle term. [4 marks] Answer : (a) (b) 13 4 Lihat Halaman Sebelah 3472/1 2011 JPN PERAK SOLAF 1 SULIT For SULIT 8 3472/1 Examiner,s Use y 14 The variables x and y are related by the equation = nx2 + m, where m and n m are constants and m < 0. A straight line graph is obtained by plotting y against x 2 as shown in Diagram 14. y 9 x2 O 6 Diagram 14 Find the value of m and of n. [4 marks] Answer : 14 4 15 The variables x and y are related by the equation y = 10x3. When log10 y is plotted against log10 x, a straight line graph passing through the point ( 2 , k ) is obtained. Find the value of k. [3 marks] Answer : 15 3 3472/1 2011 JPN PERAK SOLAF 1 SULIT SULIT 9 3472/1 For Examiner,s Use 16 Point P moves such that it is equidistant from R( – 1 , 3 ) and S( 2 , q ). It is given that the equation of the locus of P is 6x + 4y = 19. (a) Express the coordinates of the midpoint of RS in terms of q. (b) Hence, find the value of q. [3 marks] Answer : (a) (b) 16 3 17 Diagram 17 shows a straight line PQR with equation y = 2x + 3. Point P lies on the y-axis. y ● R( h , 15) ● P● Q x O Diagram 17 Given that PQ : QR = 1 : 2, find (a) the value of h, (b) the coordinates of Q. [4 marks] Answer : (a) 17 (b) 4 Lihat Halaman Sebelah 3472/1 2011 JPN PERAK SOLAF 1 SULIT For SULIT 10 3472/1 Examiner,s Use 18 In Diagram 18, ABC is a sector of a circle with centre B and ADB is a semicircle with diameter AB. D C 10 cm A B Diagram 18 Given that ABC = 2.5 radians, calculate the perimeter, in cm, of the shaded region. [3 marks] Answer : 18 3 19 Diagram 19 shows a quadrant PQR with centre R and a sector QXY of a circle with centre Q. Q 6 cm X Y 2 cm P R Diagram 19 Given that XQY = radians, calculate the area, in cm 2, of the shaded region. 3 [3 marks] Answer : 19 3 3472/1 2011 JPN PERAK SOLAF 1 SULIT SULIT 11 3472/1 For Examiner,s Use 20 Diagram 20 shows part of the graph of y = f(x). y P ● R( 2 , 7 ) y = f(x) Q O x Diagram 20 [3 marks] Given that 2 0 3 f ( x) dx 12 , calculate the area of the shaded region PQR. Answer : 20 3 5 21 Given that 1 3x 2 f ( x) dx 2 , find the value 21 f ( x) dx . 2 [3 marks] Answer : 21 3 Lihat Halaman Sebelah 3472/1 2011 JPN PERAK SOLAF 1 SULIT For SULIT 12 3472/1 Examiner,s Use 22 The area of a circle is increasing at a rate of 3 cm2 s – 1. Calculate the rate at which the radius of the circle is increasing at the instant its perimeter is 9 cm. [3 marks] Answer : 22 3 23 Diagram 23 shows a graph with equation y = x 3 – 12 x + 8. y P ● x O Diagram 23 Given that point P is the maximum point of the graph, find the coordinates of P. [3 marks] Answer : 23 3 3472/1 2011 JPN PERAK SOLAF 1 SULIT SULIT 13 3472/1 For Examiner,s Use 24 The set of numbers 2, 7, 4, 11, 5, n has a mean of 6. Find (a) the value of n, (b) the median. [3 marks] Answer : (a) (b) 24 3 25 Diagram 25 shows some information about a set of numbers. Numbers : x1 , x2 , x3 , x4 , x5 ∑ x = 28 , ∑x 2 = 170 Diagram 25 Given that x2 = 8 and it is taken out from the set. Calculate the standard deviation of the remaining numbers in the set. [4 marks] Answer : 25 4 END OF QUESTION PAPER 3472/1 2011 JPN PERAK SOLAF 1 SULIT