This document contains tutorial questions covering topics related to number systems, real numbers, indices, surds, logarithms and equations. It includes 27 multiple part questions testing concepts such as classifying numbers, evaluating expressions, solving equations, graphing intervals and more. An example study tip is provided at the end recommending desire, discipline and time management as keys to academic success.

1. Tutorial Questions for Accountancy Mathematics (QA016)
Mathematics Unit, Perak Matriculation College
Topic 1-1
1.1 Real Numbers
1.2 Indices, Surds and Logarithms
Concept Practice 1.1 : Real Numbers
1. State whether the following statements are True (T) or False (F).
Statements T / F Statements T / F
a. 1 is a prime number g. -2 is a whole number
b.
3
e
is a rational number h. -3 is an integer
c.
3
2
is an integer i. 0 is a rational number
d. All real numbers are rational
numbers j. 6 is a rational number
e. 0.256 is an irrational number
k. 0.12312124125…is an irrational
number
f. 0.312121212…is a rational number
l. The set of whole numbers is a
subset of rational numbers
2. Classify the following set of real numbers into rational numbers and irrational numbers :






 ...21821888.1...,23456789.1,...,46767676.0,279.0,142.3,235.3,23.1,
5
2
,6,0.1,1 
TOPIC 1 : NUMBER SYSTEM & EQUATIONS

2. Tutorial Questions for Accountancy Mathematics (QA016)
Mathematics Unit, Perak Matriculation College
Topic 1-2
3. Tick ( / ) in any appropriate box. The tick can be more than one in any row.
Number Z W Q Q R N
2
5.0

7
22
5
5.8
1.323232…
0.625
1.26287…
4. Write each of the following inequalities using interval notation, set notation and show
them on the real number line.
Inequalities
Interval
Notation
Set
Notation
Number line
a. 4x
b. 3x
c. 7x
d. 5x
e. 96  x

3. Tutorial Questions for Accountancy Mathematics (QA016)
Mathematics Unit, Perak Matriculation College
Topic 1-3
5. Graph the following intervals and write the answers in interval notation :
Question Real number line Answer
a.   3,7 0,9 
b.     ,37,
c.  7,4)5,3[ 
d. )9,6[]6,0( 
e.  7,0)7,4[ 
f. ]9,3(]6,( 
g. ),7[)7,( 
            ,)6,3);7,4);6);)5,4)[;7,3);7,0): gandfedcbaAns

4. Tutorial Questions for Accountancy Mathematics (QA016)
Mathematics Unit, Perak Matriculation College
Topic 1-4
Reinforcement Exercise 1.1 : Real Numbers
6. Given P =  5,1 , Q =  42,- and R =  73, . Find the following:
a. QP  b. QP  c. 'P R
     : ) 1,4 ; ) 2,5 ) 1,3Ans a b and c
7. Given A = (-6,0] , B = [-1,11) and  ZxxxC  ,55: . By using real number
line, find the following:
a. BA  b. BA  c. A C
     : ) 1,0 ; ) 6,11 ) 5, 4, 3, 2, 1,0Ans a b and c      
Concept Practice 1.2 : Indices, Surds and Logarithms
8. Evaluate
a.  2
3
09.0
b.
3
2
64
27





 c.   3
4
125

625
1
)
16
9
);
1000
27
): candbaAns
9. State whether the following statements are true (T) or false (F)
Statements True or False Statements True or False
a.
222
326 
d.
3
33
3 12
xx
x 

b.
xxx
3332

e.
4
4
4
3
2
3
2












c. 9333 22
 xxx
f.
33
5
6
6
5













10. Simplify
a. 18 b. 3332  c. 2218
d. )25(2  e. )25()22(  f. )23()23( 
1))25(2210);210);25);35);23): fandedcbaAns 

5. Tutorial Questions for Accountancy Mathematics (QA016)
Mathematics Unit, Perak Matriculation College
Topic 1-5
11. Evaluate
a.  2
32  b.  2
32  c.  2
34 
3819)625);625):  candbaAns
12. Given that 3010.02log and 8451.07log , find the following
a. 49log b. 560log c. 14log
1461.1)7481.2);6902.1): candbaAns
13. Simplify
a. 25log2 4 
b. 2log
32log
b
b
c.
c
c
c
c
3log
9log 2
2)5);
25
16
log): 4 candbaAns
14. Evaluate the following logarithms without using calculator.
a.
8log
2
1
b. 18log 23 c.
log27log8log125
log6log5
 

3
: ) 3 )2 )
2
Ans a b c
15. Solve the following equations.
a. 82 x
b. 813 1
x
c. 41
93 
 xx
d. 23
22
2

 xx
e. 1
24
2

 xx
f. 6
55
2

 xx
2,3);
2
1
,1);2,1);9);3);3):  fedcbaAns
16. Solve the following equations.
a. x
x
x
x




 5
3
22
43
32
8
4
2
b. 1 4
3 3
3
x x
  c.   1
3 2 2 2x x
 
d. 2
2 2 6 0x x
   e.     63432 2
 xx
f.   1323 12
 xx
           
14
: ; 0; 1; 1; 1; 1
3
Ans a b c d e f 
17. Solve each of the following equations.
a. 523 x b. xx  75 c. xx  64
8);2);2): cbaAns 

6. Tutorial Questions for Accountancy Mathematics (QA016)
Mathematics Unit, Perak Matriculation College
Topic 1-6
18. Solve each of the following equations.
a. 3loglog 1010 x b. 3log)2(log 1010 x
c. xx 10
2
10 log)12(log  d. 3log45log 77 x
5
81
);4);5);3): dcbaAns
19. Solve each of the following equations.
a. 32log 3 log 1 0x x   b. 3log log 9 3xx  
c. 512log 5 log 7 0x x   d. 22log 2 log 1x x 
1 1
: )9; )9;3 )125;625 )2;
3 4
Ans a b c d
Reinforcement Exercise 1.2 : Indices, Surds and Logarithms
20. Simplify each of the following :
a. 124
23
33
33




n
nn
b. 3
3

x
xx c.
14123
7497 
 nn
d.
nn
n 4
1
3
2
1684 
e.
nnnn 321
220105 
f. sr
sr
r
s
r
s
s
r
s
r


























11
11
sr
n
s
r
fandedcxbaAns








)5);2);1););3): 53
21. Simplify
a.
5
1
b.
32
1

c.
13
1
13
1



d.
325
3324


e.
 
   22
3535
35
5
1
3
1







 f.
31
1
31
1
1




5 31 11 6 1
: ) ; ) 3 2 ; ) 3 ; ) ; ) )1 3
5 47 47 30
Ans a b c d e and f  
22. If 2
1
2
1
2
1
yxz  , prove that   xyzyx 4
2
 . ovedAns Pr:

7. Tutorial Questions for Accountancy Mathematics (QA016)
Mathematics Unit, Perak Matriculation College
Topic 1-7
23. Prove that m
x
x
n
n
mn
log1
log
log

 . ovedAns Pr:
24. If  yx
yx
loglog
2
1
4
log 





, prove that xyyx 1422
 . ovedAns Pr:
25. Solve each of the following equations.
a.
2
3 2
1
49
7
x
x

b. 1 1
27 9x x 

c.  1
25 1 26 5x x
  d. 2
2 2 0x x
x  
1
: ) 2; ) 5 ) 1 ) ; 1
2
Ans a b c d no solution   
26. Solve each of the following equations.
a. 1215  xx b. 13627  xxx c. xxx  23352
5 1
: )2; ) ; )
3 2
Ans a b c
27. Solve the following equations.
a. 33log)3(log3  xx b. 6
3 9log 3 log 3 log 3xx   c. 103log5
10 2 0x
x x
  
d. 5log2log23 25 xx e. )187(loglog 93  xx f. xxx ln)33ln()1ln( 
: )3 )3 )2 )5,25 )9 )3Ans a b c d e f
STUDY TIP:
The keys to success are desire and discipline. You must want success and you must discipline yourself to do
what it takes to get success. There are a lot of things that you cannot do anything about, but you can learn to
be disciplined. Set your goals, make plans, and schedule your time. Before you know it, you will have the
discipline that is necessary for success.
END OF CHAPTER 1
WELL DONE ! ! !