Page 1
Formulae and Tables
for use in the State Examinations
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Draft for consultation
Observations are invited on this draft booklet of Anyone receiving this document should note its draft
Formulae and Tables, which is intended to replace status, and should not assume that content currently
the Mathematics Tables for use in the state in the draft will be included in the final version. The
examinations. final version will be circulated to all schools in
advance of its introduction in the state examinations.
In 2007, the State Examinations Commission
convened a working group to review and update the The working group recognises that the Mathematics
Mathematics Tables booklet, which is provided to Tables booklet is used by other institutions in their
candidates for use in the state examinations. The own examinations and by various individuals for
Department of Education and Science and the other purposes. Whereas the needs of such users will
National Council for Curriculum and Assessment are be noted, final decisions will be taken in the context
represented on the working group. of the booklet’s primary purpose as a reference for
candidates taking examinations conducted by the
The group has carried out some consultation and now State Examinations Commission.
presents this draft for wider consultation.
Comments should be forwarded by e-mail to
This draft is available in English only. The final before 31 May 2008.
booklet will be provided in both Irish and English.
Page 2
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Contents
Length and area ....................................................................................................................................................4
Surface area and volume.......................................................................................................................................5
Area approximations.............................................................................................................................................6
Trigonometry ........................................................................................................................................................7
Co-ordinate geometry .........................................................................................................................................10
Geometry ............................................................................................................................................................11
Algebra ...............................................................................................................................................................12
Sequences and series ..........................................................................................................................................12
Number sets – notation .......................................................................................................................................13
Calculus ..............................................................................................................................................................14
Financial mathematics ........................................................................................................................................16
Statistics and probability.....................................................................................................................................18
Units of measurement .........................................................................................................................................26
Common quantities, their symbols and units of measurement ...........................................................................28
Frequently used constants...................................................................................................................................33
Particle physics ...................................................................................................................................................34
Mechanics...........................................................................................................................................................36
Heat and temperature..........................................................................................................................................41
Waves .................................................................................................................................................................41
Electricity............................................................................................................................................................43
Modern physics...................................................................................................................................................45
Electrical circuit symbols ...................................................................................................................................46
The elements.......................................................................................................................................................51
.
Page 3
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Length and area
Parallelogram Arc / Sector Triangle
b h c
θ b
C h
a r
Perimeter = 2a + 2b C
Area = ah When θ is in radians: a
= ab sin C Length of arc = rθ Perimeter = a + b + c
1
Circle / Disc Area of sector = r 2θ 1
2 Area = ah
2
When θ is in degrees: 1
= ab sin C
r 2
⎛ θ ⎞
Length of arc = 2 π r ⎜ ⎟
⎝ 360° ⎠ = s ( s − a)( s − b)( s − c) ,
a+b+c
Length of circle = 2 π r ⎛ θ ⎞ where s = .
Area of sector = π r 2 ⎜ ⎟ 2
Area of disc = πr 2 ⎝ 360° ⎠
Page 4
Formulae and Tables
for use in the State Examinations
PDF Watermark Remover DEMO : Purchase from www.PDFWatermarkRemover.com to remove the waterma
,PDF Watermark Remover DEMO : Purchase from www.PDFWatermarkRemover.com to remove the waterma
Draft for consultation
Observations are invited on this draft booklet of Anyone receiving this document should note its draft
Formulae and Tables, which is intended to replace status, and should not assume that content currently
the Mathematics Tables for use in the state in the draft will be included in the final version. The
examinations. final version will be circulated to all schools in
advance of its introduction in the state examinations.
In 2007, the State Examinations Commission
convened a working group to review and update the The working group recognises that the Mathematics
Mathematics Tables booklet, which is provided to Tables booklet is used by other institutions in their
candidates for use in the state examinations. The own examinations and by various individuals for
Department of Education and Science and the other purposes. Whereas the needs of such users will
National Council for Curriculum and Assessment are be noted, final decisions will be taken in the context
represented on the working group. of the booklet’s primary purpose as a reference for
candidates taking examinations conducted by the
The group has carried out some consultation and now State Examinations Commission.
presents this draft for wider consultation.
Comments should be forwarded by e-mail to
This draft is available in English only. The final before 31 May 2008.
booklet will be provided in both Irish and English.
Page 2
,PDF Watermark Remover DEMO : Purchase from www.PDFWatermarkRemover.com to remove the waterma
Contents
Length and area ....................................................................................................................................................4
Surface area and volume.......................................................................................................................................5
Area approximations.............................................................................................................................................6
Trigonometry ........................................................................................................................................................7
Co-ordinate geometry .........................................................................................................................................10
Geometry ............................................................................................................................................................11
Algebra ...............................................................................................................................................................12
Sequences and series ..........................................................................................................................................12
Number sets – notation .......................................................................................................................................13
Calculus ..............................................................................................................................................................14
Financial mathematics ........................................................................................................................................16
Statistics and probability.....................................................................................................................................18
Units of measurement .........................................................................................................................................26
Common quantities, their symbols and units of measurement ...........................................................................28
Frequently used constants...................................................................................................................................33
Particle physics ...................................................................................................................................................34
Mechanics...........................................................................................................................................................36
Heat and temperature..........................................................................................................................................41
Waves .................................................................................................................................................................41
Electricity............................................................................................................................................................43
Modern physics...................................................................................................................................................45
Electrical circuit symbols ...................................................................................................................................46
The elements.......................................................................................................................................................51
.
Page 3
, PDF Watermark Remover DEMO : Purchase from www.PDFWatermarkRemover.com to remove the waterma
Length and area
Parallelogram Arc / Sector Triangle
b h c
θ b
C h
a r
Perimeter = 2a + 2b C
Area = ah When θ is in radians: a
= ab sin C Length of arc = rθ Perimeter = a + b + c
1
Circle / Disc Area of sector = r 2θ 1
2 Area = ah
2
When θ is in degrees: 1
= ab sin C
r 2
⎛ θ ⎞
Length of arc = 2 π r ⎜ ⎟
⎝ 360° ⎠ = s ( s − a)( s − b)( s − c) ,
a+b+c
Length of circle = 2 π r ⎛ θ ⎞ where s = .
Area of sector = π r 2 ⎜ ⎟ 2
Area of disc = πr 2 ⎝ 360° ⎠
Page 4
