SOALAN ULANGKAJI SPM 2012

Analysis

[3472/1] [3472/2]

Additional Mathematics

2007 1,2,3 4 5,6 7,8 13,14 22 18 19,20 9,10,11 12 21 17 22 24 25 25 2008 1,2,3 4 5,6 7,8 13,14 22 18 19,20 9,10,11 12 21 17 23 24 25 25 PAPER 1 2009 1,2,3 4 5,6 7,8 15 24 12 19,20 9,10,11 12 18,20,21 16,17 22 23 25 25 2010 1,2,3 5 4,6 7,8 13,14 22 17 20,21 9,10,11 12 19 18 23 24 25 25 2011 1,2,3 4 5,6 7,8 13,14 24 17 19,20,21 9,10,11 12 15 16 18 22 23 25 25 3 11 12 14 15 4 11 12 15 15 4 11 15 14 15 2 10 12 14 15 2 10 12 15 15 2007 1 2 5 9 4a,4b 15 13 6 7 4c,10 2008 2 1 10 5 9 7a 14 13 3 8 7b,7c PAPER 2 2009 2a,2c 2b 1 9 10 3a,7a 12 13 6 8 3b,7 2010 1 5 6 11 8 13 15 3 7 4 2011 1 4 7 6 11 8 13 14 3 9 5

NO TOPICS 1 2 3 4 5 6 7 8 9 10 Functions Quadratic Equations Quadratic Functions Simultaneous Equation Indices and Logarithms Coordinate Geometry Statistics Circular Measures Differentiation Solution of Triangles

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11 Index Number 12 Progressions 13 Linear Law 14 integration 15 Vectors 16 Trigonometric Functions

Permutations 17 And Combinations 18 Probability 19 20 21 Probability Distributions Motion Along A Straight Line Linear Programming TOTAL

SOALAN ULANGKAJI SPM 2012

71

Additional Mathematic

1

Paper 1

[3472/1]

Diagram 1 shows part of the relation f(x). Rajah 1 menunjukkan sebahagian daripada hubungan f(x).

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!

− 4

State/Nyatakan The type of the relation / Jenis hubungan The range / Julatnya

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Answer/Jawapan (a) …………………………………………..………… (b) …………………………………..………………… 2 Given the function f:x→3-x, g:x→px2-q and gf:x→3x2-18x+5, Find Diberi fungsi f:x→3-x, g:x→px2-q dan gf:x→3x2-18x+5, Cari (a) gf(-2) (b) The value of p and q / Nilai p dan q Answer/Jawapan (a) …………………………………………..………… (b) …………………………………..………………… 3 The function g is defined as g:x → 7x - 4. Find / Fungsi g ditakrifkan sebagai g:x → 7x - 4. Cari (a) g-1(x) (b) The value of h if g-1 (h) =2 / Nilai h jika g-1 (h) =2 Answer/Jawapan (a) …………………………………………..………… (b) …………………………………..………………… 4

[4M]

[4M]

[4M]

The quadratic equation with roots a and b is x2 + kx + k = 0, where a, b and k are constants. Express a in terms of b. Persamaan kudratik dengan punca-punca a dan b ialah x2 + kx + k = 0, dimana a, b dan k adalah pemalar. Ungkapkan a dalam sebutan b. [3M] Answer/Jawapan (a) …………………………………………..…………

72

SOALAN ULANGKAJI SPM 2012

5

Find the range of value of x for 4x2 ≥ 3 - 4x. Cari julat nilai-nilai x bagi 4x2 ≥ 3 - 4x. Answer/Jawapan (a) …………………………………………..…………

[3M]

6

Diagram 2 shows the graph of quadratic function of y = f(x). The straight line y = -16 is a tangent of the curve y = f(x). Diagram 2 menunjukkan graf fungsi kudratik bagi y = f(x). Garis lurus y = -16 adalah tangent kepada lengkung y = f(x).

y

������������ = ������������(������������)

-2

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y=-‐16

Diagram 2/ Rajah 2

x

6

(a) Write the equation of the axis of symmetry of the curve. Tulis persamaan paksi simetri bagi lengkung tersebut. (b) Express f(x) in the form (x+a)2+b. Where a and b are constant. Ungkapkan f(x) dlam sebutan (x+a)2+b. Di mana a dan b adalah pemalar. Answer/Jawapan (a) …………………………………………..………… (b) …………………………………..………………… 7 [4M]

2 16 1-x 2 Selesaikan persamaan 8x= 1-x 16

Solve the equation of 8x= Answer/Jawapan (a) …………………………………………..…………

[2M]

8

Solve the equation 2 lnx 4 + lnx 8 = -7 Selesaikan persamaan 2 lnx 4 + lnx 8 = -7 Answer/Jawapan (a) …………………………………………..…………

[3M]

9

The nth terms of an arithmetic progression is given by Tn = 11 - 3n. Find the common difference of progression. Di beri sebutan ke-n bagi satu janjang arimetik ialah Tn = 11 - 3n. Cari beza sepunya bagi janjang ini. Answer/Jawapan (a) …………………………………………..…………...