MAKTAB SABAH KOTA KINABALU
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1 Nama :... Kelas :... MAKTAB SABAH KOTA KINABALU LATIHAN ULANG KAJI MATEMATIK TAMBAHAN TINGKATAN Disember 016
2 Answer all questions. Jawab semua soalan. 1. Diagram 1 shows the relation between set P and set Q. Rajah 1 menunjukkan hubungan antara set P dengan set Q. Set Q State Nyatakan (a) the object of, objek bagi, (b) 1 5 Set P Diagram 1 Rajah 1 the range of the above relation. Julat bagi hubungan tersebut. [ marks] [ markah] b. Diagram shows the function f : a, 0, where a and b are constants. Find the value of a and b. b Rajah menunjukkan fungsi f : a, 0, dengan keadaan a dan b adalah pemalar. Cari nilai a dan b. f b [ marks] a [ markah] 1 1 Diagram Rajah
3 . Given the functions f : 5 and g :, find Diberi fungsi f : 5 dan g :, cari (a) f 1 ( 1), (b) fg (). [ marks] [ markah]. Given the functions f : 1 and g : k 7, find Diberi fungsi f : 1 dan g : k 7, cari (a) f () (b) the value of k such that gf () = 19. nilai k dengan keadaan gf () = 19. [ marks] [ markah] 5. Given that 5 is one of the roots of the quadratic equation 8 p 0, find the value of p. Diberi bahawa 5 ialah satu daripada punca-punca persamaan kuadratik 8 p 0, cari nilai p. [ marks] [ markah] 5
4 6. (a) Solve the following quadratic equation: Selesaikan persamaan kuadratik berikut: 5 0 [ marks] [ markah] (b) The quadratic equation 1 p 0, where p is a constant, has two different roots. Find the range of values of p. Persamaan kuadratik 1 p 0, dengan p ialah pemalar, mempunyai dua punca berbeza. Cari julat nilai p. [ marks] [ markah] 6 7. The quadratic function f ( ) can be epressed in the form f ( ) ( q) r, where q and r are constants. Find the value of q and of r. Fungsi kuadratik f ( ) boleh diungkapkan dalam bentuk f ( ) ( q) r, dengan keadaan q dan r ialah pemalar. Cari nilai q dan nilai r. [ marks] [ markah] 7
5 5 8. Diagram shows the graph of a quadratic function y f ( ). The straight line y is a tangent to the curve y f ( ). Rajah menunjukkan suatu graf fungsi kuadratik y f ( ). Garis lurus y ialah tangen kepada lengkung y f ( ). y y = f() 0 6 Diagram Rajah y = (a) Write the equation of the ais of symmetry of the curve. Tulis persamaan paksi simetri lengkung itu. (b) Epress f() in the form ( b) c, where b and c are constants. Ungkapkan f() dalam bentuk pemalar. ( b) c, dengan keadaan b dan c ialah [ marks] [ markah] 8 9. Find the range of the values of for ( ) < 5. Cari julat nilai bagi ( ) < 5. [ marks] [ markah] 9
6 6 10. The quadratic function f ( ) p( q) r, where p, q and r are constants, has a minimum value of 7. The equation of the ais of symmetry is = 5. Fungsi kuadratik f ( ) p( q) r, dengan keadaan p, q dan r ialah pemalar, mempunyai nilai minimum 7. Persamaan paksi simetrinya ialah = 5. State Nyatakan (a) the range of values of p, julat nilai p, (b) the value of q, nilai q, (c) the value of r. nilai r. [ marks] [ markah] Solve the equation 9(7 ) 1 0. Selesaikan persamaan 9(7 ) 1 0. [ marks] [ markah] 11
7 7 1. Solve the equation: Selesaikan persamaan: log 5( 1) 1 log 5( 1) [ marks] [ markah] 1 1. Given log 5( 1) log 5, find the value of. Diberi log 5( 1) log 5, cari nilai. [ marks] [ markah] 1 1. Given that log a 7 m and log b 9 n, epress b log in terms of m and n. a Diberi log a 7 m dan log b 9 n, ungkapkan b log dalam sebutan m dan n. a [ marks] [ markah] 1
8 8 15. Diagram shows the straight line PQ which is perpendicular to the straight line RQ at the point Q. The equation of the straight line RQ is y. Find the coordinates of Q. Rajah menunjukkan garis lurus PQ yang berserenjang dengan garis lurus RQ pada titik Q. Persamaan garis lurus RQ ialah y. Cari koordinat Q. [ marks] y [ markah] o P(0, 7) Q R Diagram Rajah The points (, n), (5, 1) and (, 7) are the vertices of a triangle. Given that the area of the triangle is 8 units, find the values of n. Titik-titik (, n), (5, 1) dan (, 7) merupakan bucu-bucu sebuah segitiga. Diberi luas segitiga itu ialah 8 units, cari nilai-nilai n. [ marks] [ markah] 16
9 9 17. A straight line crosses the y-ais at point A(0, 8) and the -ais at point B(, 0). Satu garis lurus memotong paksi-y di titik A(0, 8) dan paksi- di titik B(, 0). y (a) Write down the equation of the straight line AB in the form 1. m n y Tulis persamaan garis lurus AB dalam bentuk 1. m n (b) A point C(, y) moves such that its distance from point A is always twice its distance from point B. Find the equation of the locus of C. Suatu titik C(, y) bergerak dengan keadaan jaraknya dari titik A adalah sentiasa dua kali jaraknya dari titik B. Cari persamaan lokus bagi C. [ marks] [ markah] P(, k) is the point dividing the line joining A(, ) and B(6, ) in the ratio m : n. Find P(, k) ialah titik yang membahagi garis lurus yang menghubungkan A(, ) dan B(6, ) mengikut nisbah m : n. Cari [ marks] [ markah] (a) m : n, (b) the value of k. nilai k. 18
10 Given that the mean of a set of four numbers is t. The sum of the square of the numbers is 00 and the variance is 5s. Epress s in terms of t. Diberi min bagi suatu set empat nombor ialah t. Hasil tambah kuasa dua setiap nombor itu ialah 00 dan variannya 5s. Nyatakan s dalam sebutan t. [ marks] [ markah] A set of seven numbers has a mean of 8 and standard deviation of. Satu set yang terdiri daripada tujuh nombor mempunyai min 8 dan sisihan piawai. (a) Find the sum of the square of the set. Cari hasil tambah kuasa dua bagi set ini. (b) When a number 1 is added to the set, the new mean is 8.5. Find the standard deviation for this new set of numbers. Apabila nombor 1 ditambah kepada set ini, min baru ialah 8.5. Cari sisihan piawai bagi set baru ini. [ marks] [ markah] 0
11 11 1. Diagram 5 shows a circle with centre O and radius cm. Rajah 5 menunjukkan sebuah bulatan berpusat O dan berjejari cm. R cm O Q 7 cm P Diagram 5 Rajah 5 Given that P, Q and R are points such that PQ 7 cm and POR is a straight line, find Diberi bahawa P, Q dan R adalah titik-titik dengan keadaan PQ = 7 cm dan POR adalah garis lurus, cari [/Guna.1 ] (a) ROQ, in radians, ROQ, dalam radian, (b) the area, in cm, of the shaded region. luas, dalam cm, kawasan berlorek. [ marks] [ markah] 1
12 1. Diagram 6 shows a sector of POQ of a circle with centre O. Rajah 6 menunjukkan sebuah sektor POQ yang berpusat O. P R O. rad. Q Diagram 6 Rajah 6 It is given that the area of sector POQ = 5.9 cm and OR RP. Diberi bahawa luas sektor POQ = 5.9 cm dan OR RP. [/Guna.1 ] Find Cari (a) the length of radius, in cm, of the sector POQ, panjang jejari, dalam cm, bagi sector POQ, (b) the area, in cm, of the shaded region. luas, dalam cm, kawasan berlorek. [ marks] [ markah]
13 1. Find the value of Cari nilai bagi (a) lim ( n) n (b) n lim n n 9 [ marks] [ markah]. Find the equation of the normal to the curve y ( ) 5 at the point (, 6). Cari persamaan normal bagi lengkung y ( ) 5 pada titik (, 6). [ marks] [ markah]
14 1 5. Given that Diberi (a) y 1, y 1, find the value of dy d when 1. cari nilai bagi dy d apabila 1. (b) Epress the approimate change in y, in term of p, when change from 1 to 1 p, where p is a small value. Ungkapkan perubahan kecil bagi y, dalam sebutan p, apabila berubah daripada 1 kepada 1 p, dengan keadaan p ialah nilai yang kecil. [ marks] [ markah] 5
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