by Mr Teh DEC 2010

topic 5:Indices Surds Logarithms “A stupid question is the one not asked”

E: maths.w.mr.teh@gmail.com ~ 1 ~ If you find this useful, CALL

+65-9832 2013 and ask for MORE

Question 1:

Solve, for x and y, the simultaneous equations.

27193

428

2 =÷

=

+xy

y

x

Question 2:

Evaluate 212

2

273)3(819++ ×

×xx

xx.

Question 3:

Solve )5(54 3323

++÷= xxx

.

Question 4:

Given that cba xxx 32)216()36( 32

323

4 =÷−− , find the values of a, b and

c.

Question 5:

Show that if n is a positive integer, 3221 3)3(6)9(7 ++ +− nnn is exactly

divisible by 14.

Question 6:

Given that baxxx )3(27814

41

343

37

23

=

÷

, find the value of a and of

b.

Question 7:

The equation 8)2(23)2(722 −=− ++ ababa has a solution 1=a .

(a) Find the value of b (b) Hence, find the other solution of a.

Question 8:

Solve 17 42

=−x .

by Mr Teh DEC 2010

topic 5:Indices Surds Logarithms “A stupid question is the one not asked”

E: maths.w.mr.teh@gmail.com ~ 2 ~ If you find this useful, CALL

+65-9832 2013 and ask for MORE

Question 9:

Solve 84)3(93 1 =+− xx .

Question 10:

Solve 342 21 =+ −+ xx .

Question 11:

A cuboid has a square base of side ( )cm 57 − . The volume of the

cuboid is ( ) 3cm 776590 − . Find the height of the cuboid,

expressing your answer in the form ( )cm 75 ba + , where a and b

are constants.

Question 12:

The diagram shows a cylinder with a base area of ( ) 2m 852 − .

Given that the volume of the cylinder is ( ) 3m 5287 − , find the

height of the cylinder in the form ( )m 10qp + where p and q are

integers.

Question 13:

Solve 1103 −= xx .

Question 14:

A rectangle has a length of ( )m 22 − and an area of ( ) 2m 232 + .

Find the breadth of the rectangle in the form ( )m 2ba + , where a and b are integers.

Cross sectional area

= ( ) 2m 852 −

height

by Mr Teh DEC 2010

topic 5:Indices Surds Logarithms “A stupid question is the one not asked”

E: maths.w.mr.teh@gmail.com ~ 3 ~ If you find this useful, CALL

+65-9832 2013 and ask for MORE

Question 15:

Express 347

1−

in the form 3ba + .

Question 16:

Given that m = 2x and n = 2y, express

16

log2

2nm

in terms of x and y.

Question 17:

Given that mx =5log and ny =5log , express the following in terms

of m and n.

(a) xy

(b)

25

25log

yx

Question 18:

Given that xm 3= and yn 3= , express the following in terms of x and y.

(a) mn27log3

(b) nm 819 loglog +

Question 19:

Given that log7 x = p and log7 y = q, express the following in terms of p and q

(i) 3

2

749log

yx

(ii) xy

Question 20:

Solve ( ) ( ) 2log4212log23log 555 −=−−+ xx .

Question 21:

Solve the equation 26)(710 2 += xx ee .

by Mr Teh DEC 2010

topic 5:Indices Surds Logarithms “A stupid question is the one not asked”

E: maths.w.mr.teh@gmail.com ~ 4 ~ If you find this useful, CALL

+65-9832 2013 and ask for MORE

Question 22:

Solve 0763 =+− xx

ee .

Question 23:

Solve 03)2(134 1 =+−+ xx .

Question 24:

Solve the simultaneous equations.

2lg33lg)36lg(5255 1

+=+×=+

yx

yx

Question 25:

Solve 2523 x−= , giving your answer correct to 2 decimal places where

necessary.

Question 26:

Solve 3log1)1(log1log 2739 +=−+− xx .

Question 27:

Solve 2)4(loglog 42 −=+ xx .

Question 28:

Solve 116loglog4 =− xx .

Question 29:

Solve 35log2log5 =+ xx .

Question 30:

Evaluate the value of p, without using a calculator. 23log8log3 =− pp