Module PMR

CHAPTER 1 : DIRECTED NUMBER

A. Complete the following multiplication table.

x -8 -6 -4 -2 0 2 4
-8
-6 36 -12
-4
-2
0 0
2 -16
4 16

B. Solving problems involving Combined Operations.

Example : 1) 3 + ( - 3) – ( - 5) 2) -18 – 3 + 5 – ( - 6 )
-1 + 2 – (- 3)
= -1 + 2 + 3
=1+3
=4

3) 12 + 34 + (- 25 ) – 15 4) -2– (- 5 )+( -4 )+(- 6 ) 5) -7 + 3 – (- 2) + ( - 2 )

6) -13 – (- 4 )+(-5) – (-3) 7) 30 + 21 – (-34 ) 8) -12 – (-4 ) + 5 +(- 6 )

9) 5+( -3 ) – ( -4 )+ (- 4 ) 10) - 8 - ( -3 ) + ( - 3 ) 11) - 3 + 2 - (-2) + (- 3)

12) 23 + 2 – (- 3 ) + (- 4) 13) 5 + 3 – (- 4 ) 14) − 20 C − (−30 C ) + 50 C

Directed Numbers 1
 Module PMR

15) 14 – (- 12) + (- 23) 16) 17) -2 – (-3) + (-4) + 5

-100 + (- 234) – ( -34)

18) -12 + (-23) – (- 3) 19) 20) -5 + (- 3 ) – ( - 4)

4 – ( -3) + (- 6 ) + ( - 2 )

21) 42 – 3(5 + 3 x 4) 22) 45 – 3( 2 + 3 x 5) 23) 45 – 4 ( 2 – 8 ÷ 4 )

24) 36 + 4(3 -2 ÷ 2) 25) -20 + 3( -3 - 4 x 5 ) 26) -45 – 2( -5 + 3 x 3 )

27) ( 4 ÷ 2 – 3) + 3 – 4 28) ( -2 -3 x 4) – 3 + 4 29) ( - 4 – 5 x 3 ) + 4

30) (3 – 2 x 3)4 + 34 31) ( 5 – 6 ÷ 3) 4 – 3 32) (-6 +3x 4)8 + 3 – 7

Directed Numbers 2
 Module PMR

Common Errors

No Errors Correct Steps

1 (-2) + (-3)- (-4) =(-5)+4

= -2-3-4 = -1
=-9

2 (-4)x 9 – (5) -36-5

=-36 +5 =-41
= -31

1 2 10 1 2 10
3 + x(- ) + x(- )
3 5 3 3 5 3
5 6 10 1 4
= + x (- ) = -
15 15 13 3 13
13 12
11 10 = -
= x (- ) 39 39
15 13 1
=
39
22
=
39

1 7 1
4 -4 + -3 +
7 7 7
4 1
=- + 6
7 7 =-3
3 7
=-
7

5 (-2.07x0.2) + 2.9 =-0.414+2.9

= - 0.414 + 2.9 =2.486
=-0.604

6 (-7) x 8 x (-4) = -56 x (-4)

=(-56) x ( -4) =224
= -224

2 5 1 5 1
7 (- ) x (- ) – (- ) +
7 6 3 21 3
5 1 5 7
=- + = +
21 3 21 21
5 7 12
=(- ) + =
21 21 21
2
=-
21
Directed Numbers 3
 Module PMR

Questions based on PMR format

1) Calculate the value 2) Calculate the value of 3) Calculate the value of

3 1 1 1 7 3 5 
of − 0.6 + (−1 − ) and -5.2 –(- + ) and ÷  − (− ) and
5 2 8 10 10  5 8 
express the answer as express the answer as express the answer as a
a decimal. a decimal. fraction in its lowest
term.

4) Calculate the value 5) Calculate the value of 6) Calculate the value of

1 1 2 5 3
of 3 + (−0.25) x 4.2 ( 3 − 2 ) ÷ 1 and 4 + (−4.2) x (-0.6) and
2 2 3 6 8
and express the express the answer as a express the answer in
answer as a decimal. fraction in its lowest decimal
terms.

Directed Numbers 4
 Module PMR

7) Calculate the value 8) Calculate the value of 9) Calculate the value of

1 2 2 3 1 2 3
of ( 2 − 1 ) x 1 1 + (−2.13) x (-0.4) and 1 x (1 − ) and
6 3 7 4 4 5 4
and express your express your answer in express your answer as
answer as a fraction in decimals. a fraction in its lowest
its lowest term. term.

10) Calculate the value 11) Calculate the value 12) Calculate the value
1  2 1  3 4 5 3  1 1
of 1 × 1 − 1  and of 1 −  ÷ 1 and of 2 ÷ 1 ×  and
4  5 3  5 7 7 4  4 2
express your answer express the answer as a express the answer as a
as a fraction in its fraction in its lowest fraction in its lowest
lowest term. term. term.

Directed Numbers 5
 Module PMR

13) Calculate the value 14) Calculate the value 15) Calculate the value
3 1 1 5  1 2  1 1
of ÷ 3 × 1 and of 1 ÷  3 − 1  and of -0.25 -  − +  and
8 8 4 12  4 3  5 8
express your answer express your answer as express the answer as a
as a fraction in its a fraction in its lowest decimal in 2 decimal
lowest terms. terms. places.

16) Evaluate 17) Calculate the value 18) Calculate the value
114 – 4 (14 + 54 ÷ 9 ) 3 1 4  1 1 2
of ÷ − (−0.027) × of  3 + 1  ÷ 1 and
64 8 9  4 3 3
and express your express your answer as
answer as a decimal in a fraction in its lowest
2 decimal places. term.

Directed Numbers 6
 Module PMR

19) Evaluate 20) Calculate the value 21) Calculate the value
3.6 - [ 0.12 X (-6)] 3 3 7 2
of 19 – (- 1.2) ÷ of 1 ×  −  and
8 5 8 3
express the answer as a
fraction in its lowest
term.

PMR past year Questions

2004

 1 2 3
1. Calculate the value of  2 −  ÷ 2 and express the answer as a
 3 5 5
fraction in its lowest term.

[2m]

 1 1
2. Calculate the value of -0.8 -  − +  and express the answer as a
 2 5
decimal.
[2m]

2005

3. Calculate the value of 96 – 3 (12 + 48 ÷ 6 )

[2m]

Directed Numbers 7
 Module PMR

 1
4. Calculate the value of 4.26 × 0.8 -  − 1  and express the answer
 2
correct to two decimal places. [2m]

2006
2
5. Calculate the value of 14 - ( − 0.6) ÷ [2m]
3

1 4 2
6. Calculate the value of 1 ×  −  and express the answer as a fraction
8 5 3
in its lowest term. [2m]

2007

7. Calculate the value of - 24 ÷ 8 - 14 [2m]

4 × 0.18
8. Calculate the value of [2m]
0.9

2008
5 3 1
9. Calculate the value of ×  −  and express the answer as a fraction
2  5 3
in its lowest term.
[2m]

Directed Numbers 8
 Module PMR

CHAPTER 1 : DIRECTED NUMBERS

ANSWERS

B. Solving problems involving Combined operations

Q A Q A Q A Q A
1 5 9 2 17 2 25 -89

2 -10 10 -8 18 -32 26 -53

3 6 11 -2 19 -1 27 -2

4 -7 12 24 20 -4 28 -13

5 -4 13 12 21 -9 29 -15

6 -11 14 6°c 22 -6 30 22

7 85 15 3 23 45 31 9

8 -9 16 -300 24 44 32 44

Questions based on PMR format

Q1 -2.7 Q8 2.602 Q15 -0.18

13
Q2 -5.175 Q9 Q16 34
16
4 1
Q3 Q10 Q17 0.39
7 12
3 3
Q4 2.45 Q11 Q18 2
5 4
5 2
Q5 Q12 4 Q19 4.32
11 5
3
Q6 6.895 Q13 Q20 22.2
20
9 17 1
Q7 Q14 Q21
14 19 3

Past year Questions

29
Q1 Q4 4.91 Q7 -17
39
Q2 -0.5 Q5 14.9 Q8 0.8
3 2
Q3 36 Q6 Q9
20 3

Directed Numbers 9