Math IGCSE - 0580 Chapter (1) Numbers

1. SYLLABUS
Cambridge IGCSE
Mathematics
0580
Part 2
For examination in June and November 2017 and 2018
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2. Lesson (1.5)
Use the language and notation of
1- simple vulgar and decimal fractions
2- percentages in appropriate contexts.
3- Recognize equivalence and convert between these
forms.
4- Includes the conversion of recurring decimals to
fractions, e.g. change 0.7
Which fraction is proper, vulgar fraction and mixed
fraction
a) 7/8 b) 2/3 c) 6 ⅜

3. A) What is a decimal fractions? 2. 5
B) 1.23 means?
C) Change the fraction into decimal fraction
5/6? 1/3? 3/11?
D) change from decimal to fraction 0.49? , 0.9?
5) change from fraction to % 2/3? , 5/11?
6) change from decimal to % 0.45? , 0.5?
7) change from % to fraction and decimal:
36% 9%?

4. Arrange in order size (the smallest first)
a) 1/ 2 , 0.25 , 30%
b) 0.06 , 0.166, 0.66
c) ¾ , 0.166 , 0.66
4- Includes the conversion of recurring decimals
to fractions, e.g. change 0.7

5. Lesson (1.6)
Order quantities by magnitude and
demonstrate familiarity with the symbols
=, ≠, ≥, ≤, >, <.
When comparing quantities , all should be of the same unit.
a) Arrange in increasing order 8/17 , √1/4 , 0.48
b) Compare between 2/3 , 7/12
c) Arrange starting with smallest:
7/11, 5/8, ½, 11/16, ¾
d) Compare the longest distance first
1.95m, 2.5m, 2.03m, 1.91m, 0.69m, 2.17m

6. Lesson (1.6)
Order quantities by magnitude and
demonstrate familiarity with the symbols
=, ≠, ≥, ≤, >, <.
When comparing quantities , all should be
of the same unit.
a) Arrange in increasing order 8/17 , √1/4 , 0.48
b)Compare between 2/3 , 7/12

7. Lesson (1.7)
1- Understand the meaning and rules of indices.
2- Use the standard form A × 10n where n is a positive or negative
integer,
and (1≤ A < 10).
3- Convert numbers into and out of standard form.
4- Calculate with values in standard form.
Evaluate:
a) 7-2
b) 1001/2
c) 8-2/3
d) 51/2

8. Write in standard form the following:
3100 7200
Find:
(2.4 x 104) X (5 x 105) =
Arrange in descending order
3.6x10-3 , 5.2x10-5, 1x10-2, 8.35x10-2

9. Lesson (1.8)
Use the four rules for calculations with
1- whole numbers,
2- decimals and vulgar (and mixed) fractions,
3- including correct ordering of operations and use of brackets
Order of operation
B D M A S

10. Lesson (1.9)
Make Estimates of numbers, quantities and
lengths, give approximations to specified
numbers of significant figures and decimal
places and Round off answers to
reasonable
accuracy in the context of a given problem.

11. Round off
Write the number 23643 nearest to 10, 100, 1000
33.5602 nearest to 1d.p, 2d.p, 3d.p

12. Round off
Round off the following:
1. 528 g to nearest 10 g
2. 31.75 cm to nearest cm
3. 1.26 k.g to nearest .01 kg
4. 5.01 to nearest tenth

13. Significant Figures
Write the number 3529 nearest to
1 S.F. =
2 S.F.= 3 S.F.=
30.06052 correct to
1 S.F. =
2 S.F.= 3 S.F.=

14. Significant Figures
Notice Zero:
403 40.7
0.000407
0.408
0.003824 correct to 1 S.F =
3.0057 correct 4 S.F. =

15. Estimates
By writing each number in the calculation correct to 2
S.F. estimate the value of:
478 X 49.82
0.1248

16. Lesson (1.10)
Give appropriate upper and lower bounds for
data given to a specified accuracy.
Obtain appropriate upper and lower bounds
to solutions of simple problems given data to
a specified accuracy.

17. Limits of Accuracy
If the length of square is 4 cm nearest to meter.
Find the limit of this length?
If L = 4.3 m to nearest 0.1 m
L = 4.30 m to nearest cm
Height = 240 m to nearest 10 m
Radius = 65 cm to nearest 5 cm

18. Limits of Accuracy
Given diameter of a circle equal 8.6 cm to nearest
0.1cm. Find the limits of accuracy of the radius.
Given a rectangle measured to the nearest meter as
length 8 cm and width 5 cm then the limits of the length
L is 7.5 ≤ L < 8.5 and Width 4.5 ≤ L < 5.5
Find the limits of its perimeter P and limits of its area A?

19. Limits of Accuracy
A girl’s height is given as 162 cm to the nearest cm.
1- work out the lower and upper bounds within her
height lie?
2- Represent this range of numbers on number line.
3- If the girl’s height is x cm, express this range as an
inequality?

20. Upper and Lower bounds
Rules
Mulitip.
Upper= Upper x Upper
Lower = Lower x Lower
If 7 ≤ x < 8
5 ≤ Y < 4
Then upper x . y = lower x . Y =
Division:
Lower = Lower/upper
Upper = upper / lower

21. Upper and Lower bounds
Rules
Calculate the upper and lower bound to 33.5/22.0 given
that each of numbers is accurate to 1 d.p?

22. Upper and Lower bounds
Rules
Add:
L = L + L
U = U + U
Sub.
L = L – U
U = U - L

23. Upper and Lower bounds
Rules
Absolute error of measurement:
It is the difference between the measured value of
quantity and its true value.
The measurements of a rectangle are given as 4.6 cm
and 2.8cm, correct to the nearest 0.1cm. Find the
greatest and least possible values of the area of the
rectangle and the largest possible error in area?

24. Upper and Lower bounds
Rules
Absolute error of measurement:
H.W
The measurement of rectangle are given as 5.6 cm
and 4.8 cm, correct to the nearest tenth cm. find the
greatest and the smallest possible areas of the
rectangle?

25. Lesson (1.13)
Use a calculator efficiently.
Apply appropriate checks of accuracy.