1 FHMM1014 Mathematics I UNIVERSITI TUNKU ABDUL RAHMAN ACADEMIC YEAR 2013/2014 (TRIMESTER 1) FHMM1014 MATHEMATICS I FOUNDATION IN SCIENCE EXTRA QUESTION Real Number 1. Evaluate each of the following expressions. (i) (ii) (iii) (iv) (v) 2.
2  3 4 2  3  4 1  2  5  3 1 2 2  3 4 3  2  35  2

Draw the region for the following statements. (i) (ii) (iii) (iv)
3 x  5 1  x  3 5  x  2 2 x 6

Exponents and Logarithms 3. Simplify the expressions. (i)
 4 xy  3x 
3 1



y



1 2

   

(ii)

3x

y 3 27 x 4
1

2



3

(iii) (iv) (v)

xx  1 2  x  1 x2



1 2

5n1 10 n  20 2n  23n

9

1  n 2

3

n 3

 32



1 5

4.

Solve the following equations: (i) (ii) (iii)
2 2 x  64 x 1 32x+ 2 – 28 (3x) + 3 = 0

2(4 x )  (2 x )  3  0

2 FHMM1014 Mathematics I (iv) (v) 5.

5 2 x 1  6(5 x )  1  0
3 x 1  4 2 x 1

Solve the following equations: (i) (ii) (iii) (iv) (v)

2(log 9 x  log x 9)  5 log2 x + 3logx 2 = 4 log 4 x  12 log x 4  7 log 4 x  4 log x 4 2 log( x  1)  log( x  2)  log( 2 x  1)

6.

Solve the following equations. (i) 2ln x  ln 9  5 e4x  6 (ii) (iii) e 3 x1  e 5 x4 (iv) 3ln x  3x (v) ln x  1  ln 3x  1  ln x Solve the following simultaneous equations: (i)

7.

log 8 ( xy )  3,

(log 2 x)(log 2 y)  18.
(ii)

log 4 ( xy ) 

1 , 2

(log 2 x)(log 2 y)  2.
(iii)

x  5 y  0,
(1  log 5 y) log x 5  1.

8.

(a) (b)

If 10 x  10  x  4 , prove that x  log10 (2  3 ) . Given

1  , solve for x. 2e x  e  x 5

e x  2e  x

Answers: 1. (i) (iv) 2. (i) 14 (ii) (v) (ii) 20 14 (iii) 6

3 14

3 FHMM1014 Mathematics I (iii) 3. (i) (iv) 4. (i) (iv) 5. (i) (iii) (v) 6. (i) (iv) (iv)

12 y
5



1 2

(ii) (v)

x 10 y 9
13 1 2

(iii)

x2  x 1 x2 x 1

x

3 2

(ii) (v)

x  2, x  1 x  1.484

(iii)

x  0.585

x  1, x  0 x  3, x  81 x  64, x  256 x  1.3028

(ii) (iv)

x  2, x  8

x  16, x 

1 16

x  1.3536 ln 3

(ii) (v)

x

ln 6 4

(iii)

x

3 2

x  e ln 31

x  1 2

7.

(i) (ii) (iii)

x  8, y  64; x  64, y  8

x

1 1 , y  4; x  4, y  2 2

x  5, y  1

8.

(b)

x  0.6496