SOAL MATEMATIKA SEMESTER GENAPDisusun oleh :

Vito Adrian (XI IPA 2 / 35)

1. Hasil bagi dan sisa dari 2x2-5x2+2x-4 dibagi x+2 adalah….a. 2x2-9x+20 sisa -44 b. 2x2-9x+20 sisa -24c. 2x2-9x+20 sisa -14d. 2x2-9x+20 sisa -14 e. 2x2-9x+20 sisa -14 Pembahasan:Maka:

-2 2 -5 2 -4-4 18 -40 +

2 -9 20 -44Jadi hasil baginya 2x2-9x+20 Sisa -44

2. A polynomial if divided by x + 2,the rest is -13, divided by x – 3,the rest is 7. The polynomial if divided by x2 – x - 6 gives rest….Answer :S(x) = ax + b, P(x): (x + 2) Þ S(-2) = -13 ® -2a + b = -13P(x): (x – 3) Þ S(3) = 7 ® 3a + b = 7 _

-5a = -20® a = 4 a = 4 is substituted to -2a + b = -13

® -8 + b = -13® b = -5

So the rest is ax + b = 4x - 5

3. Nilai dari Lim x 2 – 4 adalah…. x→2 x2 + x - 6

Pembahasan: Lim x 2 – 4 = Lim (x – 2) ( x + 2 )

x→2 x2 + x – 6 x→2 (x – 2) ( x + 3) = Lim (x + 2) x→2 (x + 3) = 2 + 2 2 + 3 = 4 5

4. The amount from Lim 4x 2 + 3x - 6 is …. x→~ 2x2 – 8x -1

Answer :Pay attention that both equation above have the same rank/order, so p = q (p divided by q)

Lim 4x 2 + 3x - 6 = 4 = 2x→~ 2x2 – 8x -1 2

5. Diketahui f(x) = x2 – 6x + 4, tentukan f–1 (x)!Pembahasan :y = x2 – 6x + 4y – 4 = x2 – 6xy – 4 = (x – 3) 2 – 9y + 5 = (x – 3) 2

x – 3 = √ y+5x = 3 √ y+5f – 1 (x) = 3 √ x+5

6. Known that f(x) = 52x, decide the number of f – 1 (x)!Answer :

y = 52x (remember the logarhytm way : a n = b ® n = a log b )

2x = 5 log y

x = 125 log y

f – 1 (x) = 125 log x

7. Diketahui f(x) = 2x -1 dan (g o f)(x) =

2x−512 x−6 , tentukan rumus fungsi g(x)!

Pembahasan :

(g o f)(x) =

2x−512 x−6

g(f(x)) =

2x−512 x−6

g(2x-1) =

2x−512 x−6

g(2x-1) =

(2 x−1)−46(2 x−1)

g(x) =

x−46 x

8. A function is known as f(x) = 2x – 3 and g(x) = 1

3x+1, x≠−1

3 . Decide the number of (f o g) - 1(x)!Answer :

(f o g)(x) = 2(1

3x+1 ) – 3 = 2−3(3 x+1)3x+1

=−9 x−13 x+1

If y = (f o g)(x)

y = −9 x−13 x+1

y(3x+1) = -9x – 13xy + y = -9x – 13xy + 9x = -y – 1x (3y + 9) = -(y + 1)

x = −( y+1 )3 y+9

(f o g) - 1(x) = − x+13x+9

9. Nilai turunan pertama dari: f(x) = 2(x)2 + 12x2 – 8x + 4 adalah …Pembahasan :f(x) = 2x3 + 12x2 – 8x + 4f1(x) = 2.3x2 + 12.2x – 8

= 6x2 + 24x -8

10. Decide the derivatives from f(x) = tan x !Answer :

f(x) = tan x =

sin xcos x

If : u = sin x → u’ = cos x v = cos x → v’ = - sin x

f’ (x) =

u' v−uv 'v2

=

cos x . cos x−sin x .(−sin x )cos2 x

=

cos2 x+sin2 xcos2 x

=

1

cos2 x

= sec2 x