|
INORGANIC
Part 6 Period 4 survey & group trends page
sub-index: 6.1
Survey of Period 4 elements * 6.2
Period 4 trends in physical properties * 6.3
Period 4 trends in bonding, formulae and
oxidation state * 6.4
Important element trends down a Group
Advanced
Level Inorganic Chemistry Periodic Table Index *
Part 1
Periodic Table history
* Part 2
Electron configurations, spectroscopy,
hydrogen spectrum, ionisation energies *
Part 3
Period 1 survey H to He *
Part 4
Period 2 survey Li to Ne *
Part 5 Period 3 survey Na to Ar *
Part 6
Period 4 survey K to Kr and important trends
down a group *
Part 7
s-block Groups 1/2 Alkali Metals/Alkaline Earth
Metals *
Part 8
p-block Groups 3/13 to 0/18 *
Part 9
Group 7/17 The Halogens *
Part 10
3d block elements & Transition Metal Series
*
Part 11
Group & Series data & periodicity plots
6.4 A summary of important physical and chemical
trends down a
Group
GROUP DATA TABLES -
data aligned down the group
z = at. no., cond'y =
conductivity, config. = configuration, oxidation states are numerically equal to
valencies
M = metal, SM
= semi-metal (metalloid), NM = non-metallic element
Group 1 Alkali Metals
|
ZElement |
|
Electron configuration |
Melting Point |
Boiling Point |
Pauling electro-negativity |
Atomic metallic radius pm |
1st ionisation energy
kJ/mol |
Density g/cm3 |
Relative electrical cond'y |
ox. state |
oxide formulae |
chloride formulae |
|
oC |
K |
oC |
K |
|
3Li lithium |
M |
[He]2s1 |
181 |
454 |
1347 |
1620 |
0.98 |
152 |
513 |
0.5 |
0.108 |
+1 |
Li2O |
LiCl |
|
11Na sodium |
M |
[Ne]3s1 |
98 |
371 |
883 |
1156 |
0.93 |
186 |
496 |
1.0 |
0.218 |
+1 |
Na2O, Na2O2 |
NaCl |
|
19K potassium |
M |
[Ar]4s1 |
64 |
337 |
774 |
1047 |
0.82 |
231 |
419 |
0.8 |
0.143 |
+1 |
K2O, K2O2,
KO2 |
KCl |
|
37Rb rubidium |
M |
[Kr]5s1 |
39 |
312 |
688 |
961 |
0.82 |
244 |
403 |
1.5 |
0.080 |
+1 |
Rb2O, Rb2O2,
RbO2 |
RbCl |
|
55Cs caesium |
M |
[Xe]6s1 |
29 |
302 |
679 |
952 |
0.79 |
265 |
376 |
1.9 |
0.053 |
+1 |
Cs2O, Cs2O2,
CsO2 |
CsCl |
|
87Fr francium |
M |
[Rn]7s1 |
27 |
300 |
677 |
950 |
0.70 |
270 |
400 |
2.0 |
0.014 |
+1 |
assumed Fr2O, Fr2O2,
FrO2 |
assumed FrCl |
-
One of the most
consistent sets of data for any group of the periodic table, helped
by the fact they are all metals.
-
The melting/boiling
points, electronegativity, 1st ionisation energy and electrical
conductivity decrease down the group.
-
The atomic radius and
density increase down the group.
-
The formulae are
perfectly consistent with what you might expect from the principles
of the Periodic Table e.g. the chlorides, the metal having the only
possible oxidation state of +1 (valency 1).
-
Down the group the
peroxide (M2O2) and the 'superoxide' (MO2)
become more stable with respect to the expected oxide formula (M2O).
-
7
Detailed advanced level chemistry notes s-block Group 1 Alkali
Metals
-
Explanation of general group trends down the groups of the periodic
table (end of this page)

Group 2 Alkaline Earth Metals
|
ZElement |
|
Electron configuration |
Melting Point |
Boiling Point |
Pauling electro-negativity |
Atomic metallic radius pm |
1st ionisation energy kJ/mol |
Density g/cm3 |
Relative electrical conductivity |
ox. state |
oxide formulae |
chloride formulae |
|
oC |
K |
oC |
K |
|
4Be beryllium |
M |
[He]2s2 |
1278 |
1551 |
2970 |
3243 |
1.57 |
111 |
900 |
1.8 |
0.250 |
+2 |
BeO |
BeCl2 |
|
12Mg magnesium |
M |
[Ne]3s2 |
649 |
922 |
1090 |
1363 |
1.31 |
160 |
738 |
1.7 |
0.224 |
+2 |
MgO, MgO2 |
MgCl2 |
|
20Ca calcium |
M |
[Ar]4s2 |
839 |
1112 |
1484 |
1757 |
1.00 |
197 |
590 |
1.6 |
0.218 |
+2 |
CaO, CaO2 |
CaCl2 |
|
38Sr strontium |
M |
[Kr]5s2 |
769 |
1042 |
1384 |
1657 |
0.95 |
215 |
550 |
2.5 |
0.043 |
+2 |
SrO, SrO2 |
SrCl2 |
|
56Ba barium |
M |
[Xe]6s2 |
729 |
1002 |
1637 |
1910 |
0.89 |
215 |
503 |
3.6 |
0.016 |
+2 |
BaO, BaO2 |
BaCl2 |
|
88Ra radium |
M |
[Rn]7s2 |
700 |
973 |
1140 |
1413 |
0.89 |
223 |
509 |
5.0 |
0.010 |
+2 |
assumed RaO, RaO2 |
assumed RaCl2 |

Group 3/13
|
ZElement |
|
Electron configuration |
Melting Point |
Boiling Point |
Pauling electro-negativity |
Atomic metallic radius pm |
1st ionisation energy kJ/mol |
Density g/cm3 |
Relative electrical conductivity |
ox. states |
oxide formulae |
chloride formulae |
|
oC |
K |
oC |
K |
|
5B boron |
NM |
[He]2s22p1 |
2300 |
2573 |
3659 |
3932 |
2.04 |
90 (cov) |
801 |
2.3 |
<0.001 |
+3 |
B2O3 |
BCl3 |
|
13Al aluminium |
M |
[Ne]3s23p1 |
661 |
934 |
2467 |
2740 |
1.61 |
143 |
577 |
2.7 |
0.382 |
+3 |
Al2O3 |
AlCl3 |
|
31Ga gallium |
M |
[Ar]3d104s24p1 |
30 |
303 |
2400 |
2673 |
1.81 |
153 |
579 |
5.9 |
0.058 |
+1, +3 |
Ga2O3 |
GaCl3 |
|
49In indium |
M |
[Kr]4d105s25p1 |
156 |
429 |
2080 |
2353 |
1.78 |
163 |
558 |
7.3 |
0.111 |
+1, +3 |
In2O3 |
InCl3 |
|
81Tl thallium |
M |
[Xe]4f145d106s26p1 |
304 |
577 |
1457 |
1730 |
1.80 |
170 |
589 |
11.9 |
0.055 |
+1, +3 |
Tl2O3 |
TlCl3 |

Group 4/14
|
ZElement |
|
Electron configuration |
Melting Point |
Boiling Point |
Pauling electro-negativity |
Atomic covalent or metallic radius pm |
1st ionisation energy kJ/mol |
Density g/cm3 |
Relative electrical conductivity |
ox. states |
oxide formulae |
chloride formulae |
|
oC |
K |
oC |
K |
|
6C carbon |
NM |
[He]2s22p2 |
3547 |
3820 |
4827 |
5100 |
2.55 |
77
(cov) |
1086 |
2.3 |
0.001 |
+2, +4 |
CO, CO2 |
CCl4 |
|
14Si silicon |
NM |
[Ne]3s23p2 |
1410 |
1683 |
2355 |
2628 |
1.90 |
117
(cov) |
786 |
2.3 |
<0.001 |
+4 |
SiO2 |
SiCl4 |
|
32Ge germanium |
SM |
[Ar]3d104s24p2 |
937 |
1210 |
2830 |
3103 |
2.01 |
139
(met) |
762 |
5.3 |
<0.001 |
+2, +4 |
GeO, GeO2 |
GeCl2, GeCl4 |
|
50Sn tin |
M |
[Kr]4d105s25p2 |
232 |
505 |
2270 |
2543 |
1.96 |
158
(met) |
709 |
5.8 |
0.088 |
+2, +4 |
SnO, SnO2 |
SnCl2, SnCl4 |
|
82Pb lead |
M |
[Xe]4f145d106s26p2 |
328 |
601 |
1740 |
2013 |
2.33 |
175
(met) |
716 |
11.4 |
0.046 |
+2, +4 |
PbO, Pb3O4,
PbO2 |
PbCl2, PbCl4 |

Group 5/15
|
ZElement |
|
Electron configuration |
Melting Point |
Boiling Point |
Pauling electro-negativity |
Atomic covalent or metallic radius pm |
1st ionisation energy kJ/mol |
Density g/cm3 |
Relative electrical conductivity |
Ox. states |
oxide formulae |
chloride formulae |
|
oC |
K |
oC |
K |
|
7N nitrogen |
NM |
[He]2s22p3 |
-210 |
63 |
-196 |
77 |
3.04 |
75
(cov) |
1402 |
<0.1 |
<0.001 |
-3 to +5 |
N2O, NO, N2O3,
NO2, N2O5 |
NCl3 |
|
15P phosphorus |
NM |
[Ne]3s23p3 |
44 |
317 |
280 |
553 |
2.19 |
110
(cov) |
1060 |
1.8 |
<0.001 |
+3, +5 |
P4O6,
P4O10 |
PCl3,
PCl5 |
|
33As arsenic |
SM |
[Ar]3d104s24p3 |
sub |
sub |
sub |
sub |
2.18 |
122
(cov) |
947 |
5.8 |
0.029 |
+3, +5 |
As4O6,
As4O10 |
AsCl3 |
|
51Sb antimony |
SM |
[Kr]4d105s25p3 |
631 |
904 |
1635 |
1908 |
2.05 |
143
(cov), 161 (met) |
834 |
6.7 |
0.026 |
+3, +5 |
Sb2O3 |
SbCl3 |
|
83Bi bismuth |
M |
[Xe]4f145d106s26p3 |
272 |
545 |
1560 |
1833 |
2.02 |
182
(met) |
703 |
9.7 |
0.009 |
+3, +5 |
Bi2O3 |
BiCl3 |

Group 6/16
|
ZElement |
|
Electron configuration |
Melting Point |
Boiling Point |
Pauling electro-negativity |
Atomic covalent or metallic radius pm |
1st ionisation energy kJ/mol |
Density g/cm3 |
Relative electrical conductivity |
Ox. state |
oxide formulae |
chloride formulae |
|
oC |
K |
oC |
K |
|
8O oxygen |
NM |
[He]2s22p4 |
-218 |
55 |
-183 |
90 |
3.44 |
73 (cov) |
1314 |
<0.1 |
<0.001 |
-1, -2 |
O2 |
OCl2 |
|
16S sulphur |
NM |
[Ne]3s23p4 |
117 |
390 |
445 |
718 |
2.58 |
102
(cov) |
1000 |
2.1 |
<0.001 |
-2,
+2, +4, +6 |
SO2, SO3 |
S2Cl2,
SCl2, SCl4 |
|
34Se selenium |
SM |
[Ar]3d104s24p4 |
217 |
490 |
685 |
958 |
2.55 |
117
(cov), 190 (met) |
941 |
4.8 |
0.080 |
+2, +4, +6 |
SeO2, SeO3 |
Se2Cl2, SeCl4 |
|
52Te tellurium |
SM |
[Kr]4d105s25p4 |
450 |
723 |
990 |
1263 |
2.10 |
135
(cov), 210 (met) |
869 |
6.2 |
<0.001 |
+4, +6 |
TeO, TeO2, TeO3 |
TeCl2, TeCl4 |
|
84Po polonium |
M |
[Xe]4f145d106s26p4 |
254 |
527 |
962 |
1235 |
2.00 |
167 |
812 |
9.3 |
0.020 |
+2, +4, +6 |
PoO, PoO2 |
PoCl2, PoCl4 |

Group 7/17 The Halogens
|
ZElement |
|
Electron configuration |
Melting Point |
Boiling Point |
Pauling electro-negativity |
Atomic covalent radius pm |
1st ionisation energy kJ/mol |
Density g/cm3 |
Relative electrical conductivity |
ox. formulae |
oxide formula |
chloride formulae |
|
oC |
K |
oC |
K |
|
9F fluorine |
NM |
[He]2s22p5 |
-219 |
54 |
-188 |
85 |
3.98 |
64 |
1681 |
<0.1 |
<0.001 |
-1 |
F2O |
FCl |
|
17Cl chlorine |
NM |
[Ne]3s23p5 |
-101 |
172 |
-34 |
239 |
3.16 |
99 |
1251 |
<0.1 |
<0.001 |
-1, +1, +3, +4, +5, +7 |
Cl2O, ClO2,
Cl2O6,
Cl2O7 |
Cl2 |
|
35Br bromine |
NM |
[Ar]3d104s24p5 |
-7 |
266 |
59 |
332 |
2.96 |
114 |
1140 |
3.1 |
<0.001 |
-1, +1, +3, +4, +5, +7 |
Br2O, BrO2, BrO3 |
BrCl |
|
53I iodine |
NM |
[Kr]4d105s25p5 |
114 |
387 |
184 |
457 |
2.66 |
133 |
1010 |
4.9 |
<0.001 |
-1, +1, +3, +5, +7 |
I2O4, I2O5,
I2O7 |
ICl |
|
85At astatine |
NM |
[Xe]4f145d106s26p5 |
302 |
575 |
337 |
610 |
2.20 |
140 |
930 |
7.5 |
<0.001 |
-1, +1, +3, +5, +7
??? |
na |
na |

Group 0/18 The Noble Gases
|
ZElement |
|
Electron configuration |
Melting Point |
Boiling Point |
Pauling electro-negativity |
Atomic covalent radius pm |
1st ionisation energy kJ/mol |
Density g/cm3 |
Relative electrical conductivity |
Ox. state |
oxide formulae |
chloride formulae |
|
oC |
K |
oC |
K |
|
2He helium |
NM |
1s2 |
-272 |
1 |
-269 |
4 |
5.50 |
49 |
2372 |
<0.1 |
<0.001 |
- |
na |
na |
|
10Ne neon |
NM |
[He]2s22p6 |
-249 |
24 |
-246 |
27 |
4.84 |
51 |
2081 |
<0.1 |
<0.001 |
- |
na |
na |
|
18Ar argon |
NM |
[Ne]3s23p6 |
-189 |
84 |
-186 |
87 |
3.20 |
94 |
1520 |
<0.1 |
<0.001 |
- |
na |
na |
|
36Kr krypton |
NM |
[Ar]3d104s24p6 |
-157 |
116 |
-152 |
121 |
3.20 |
109 |
1520 |
<0.1 |
<0.001 |
+2 |
na |
na |
|
54Xe xenon |
NM |
[Kr]4d105s25p6 |
-112 |
161 |
-105 |
168 |
2.40 |
130 |
1170 |
<0.1 |
<0.001 |
+2, +4, +6, +8 |
XeO3,
XeO4 |
na |
|
86Rn radon |
NM |
[Xe]4f145d106s26p6 |
-71 |
202 |
-62 |
211 |
2.10 |
136 |
1037 |
<0.1 |
<0.001 |
- |
na |
na |

Summary and general arguments for group
trends
-
1st Ionisation
enthalpy of an element:
ΔH
for the process X(g)
==> X+(g) + e-
-
The 1st
ionisation energy decreases down a group as the outer electrons
are increasingly less strongly held.
-
As you go down the
group from one element down to the next, the outer electron is
further and further from the nucleus because of the extra full
shell of electrons due to the change in period. The outer
electrons are also shielded by this
extra full shell of negative charge from the effect of the
positive nucleus. The effective nuclear charge can be considered
to be equal to the number of outer electrons and this is
effectively the same for all the elements in a group.
-
However, it
is spread over an increasingly larger 'outer surface', down the
group, so steadily reducing the electric field effect of the
positive nucleus attracting the outer negative electrons. Therefore the outer electron
is less and less strongly held by the nucleus and this combination of factors
means the outer electron is increasingly more easily lost, (e.g. the M+
ion more easily formed), and so less energy is needed remove it.
-
The 'diluting effect' of the increasing outer surface area on the
strength of the electron attracting electric field effect,
outweighs the increase in atomic/proton number down the group.
Atomic radius
of an element
-
Can
be defined as volume within which 95% of the electron charge exists
on a time averaged basis.
-
Atomic
radius increases down the
group as an extra inner shell of electrons is added per period.
-
The argument
is almost identical to that for ionisation energy above.
-
As you go from one
period to another an extra full inner shell of electrons is
added and
the outer electrons are increasingly further away, increasingly
shielded by more filled inner shells and hence less strongly attracted to
the nucleus
-
Therefore the volume occupied by the electrons expands as you
go down the group.
-
Ionic radii
-
The ionic
radius increases down the
group as an extra inner shell of electrons is added per period.
-
For the trend we assume
all the ions have the same charge for the same group e.g. Gp1/2 form M+/M2+
ions or Gp7 form X- ions and the argument is identical to
that for the atomic radius increase.
-
The reasons are
identical to the argument set out for atomic radius.
-
Metallic or
non-metallic character of an element:
-
Elements tend to get
more metallic down a group.
-
The trend doesn't show up strongly in
Gps 1, 2 (both all metals) and 7 Halogens (all non-metals), but in Gp 4 you start with non-metallic carbon at
the top and very metallic lead at the bottom.
-
The principal reason
is the lowering of ionisation energies as you descend the group.
-
Electronegativity
of an element
(usually
the Pauling scale)
-
The power (electric field effect) of an atom to
attract electron charge towards it, in the context of the electrons of
a covalent bond linking it to another atom.
-
Electronegativity
decreases down a group.
-
The reason are essentially
the same as the lowering of the 1st ionisation energy due to increase in
atomic radius and the outer electrons being less strongly held, even in
the context of a bonding situation.
-
So, in
this case, the arguments support the notion that the nucleus has a
lesser and lesser effect in attracting the outer electrons including a
pair of bonding electrons.
-
This weakens the bond and
less thermal energy is required effect a change of state melting or
boiling.
-
Melting points and
boiling points of elements:
-
Trends can be a bit
complicated due to significant structural changes from one
element to another in the same group.
-
However for Groups 1
and 2 the general trend is for melting points and boiling points
to decrease down the group.
-
As the atomic radii
increase down the group, the positive nucleus to delocalised
distance increases.
-
This decreases the
electrical attractive force between the immobile ions in the metal lattice and the free mobile delocalised electrons.
-
For Groups 7/17
Halogens and Group 0/18 Noble Gases the melting points and
boiling points steadily increase down the group.
-
As the molecule gets
bigger with more electrons, the Van der Waals forces (transient
dipole - induced dipole) increase in strength so more energy is
required to overcome them i.e. a higher thermal energy -
increased temperature.
-
Relative electrical
conductivity:
-
Density
-
Generally increases
as the metallic character increases, which can, as in the case of
Group 5,
-
However, even if they
are all metals (Groups 1& 2) or all non-metals (Groups 7/17 &
0/18) generally speaking density does increase down a group.
-
Oxidation states
-
In terms of the general
principles of the Periodic Table i.e. group similarity, you would expect
all the elements to exhibit the same oxidation states in their
compounds, and generally this is true except for oxygen in Group 6/16
and fluorine in Group 7/17.
-
However, down a group you
can get a significant change in the relative stabilities of different
oxidation states.
-
The character of the
chlorides
-
For Groups 1 and 2 the
halides become more ionic as the difference in electronegativity
increases and the steadily decreasing polarising power of the cation as
its radius increases down the group.
-
Trends become complicated if
two different oxidation states are involved.
-
The character of the
oxides
-
For Groups 1 and 2 the
halides become more ionic as the difference in electronegativity
increases and the steadily decreasing polarising power of the cation as
its radius increases down the group.
-
Trends become complicated if
two different oxidation states are involved.
-
The acid-base
character of oxides:
-
-

Diagrammatic summary of three
important Periodic Table Trends
and the so-called 'diagonal
relationship of some elements'

-
In the periodic
table
-
Down a group of
the Periodic Table:
-
1st ionisation
energy decreases
-
atomic radius
increases
-
electronegativity decreases
-
increase in
metallic character
-
oxide becomes
more basic
-
ease of
formation of positive ion increases
-
As you can see,
the trends across a period are the opposite of the trends down a
group.
-
These two trends
tend to cancel each other out so that elements which are
diagonal with respect to each other (top left to bottom right)
sometimes show some similarities when considering some of the
elements of periods 1 and 2.
-
This phenomenon
is explained in terms of the horizontal and vertical
relationships described above.
-
From left to right
the decrease in size of the atom or positive ion is accompanied
by an increase in electronegativity.
-
On descending a
group the increase in size of the atom or positive ion is
accompanied by a decrease in electronegativity
-
Examples of the
so-called diagonal relationship
-
Lithium and
magnesium
-
Atomic radii: Li 152
pm, Mg 160 pm
-
Ionic radii: Li+
78 pm, Mg2+ 78pm
-
Boiling point: Li
1347oC, Mg 1090oC, other group 1 metals
much lower
-
Electronegativity:
Li 1.0, Mg 1.3
-
Lithium is much
harder than the other alkali metals, more like magnesium
-
Lithium does not
form a peroxide, unlike other alkali metals, neither does
magnesium
-
Lithium carbonate
readily thermally decomposes to give the oxide, as does
magnesium oxide, but the other alkali metal carbonates do not
readily decompose on heating.
-
Lithium hydroxide is
sparingly soluble, as is magnesium hydroxide, but sodium
hydroxide etc. are very soluble in water.
-
Lithium carbonate is
sparingly soluble, as is magnesium carbonate, but sodium
carbonate etc. are quite soluble.
-
Lithium nitrate(V)
thermally decompose to give the oxide, as does magnesium
nitrate(V), but the other group 1 nitrates leave a residue of
the nitrate(III) salt (nitrite salt) on strong heating.
-
Lithium forms a
nitride (Li3N) as does magnesium (Mg3N2),
but the other group 1 alkali metals do not.
-
Beryllium and
aluminium
-
Atomic radii: Be 111
pm, Al 143 pm
-
Ionic radii: Be2+
31pm, Al3+ 50 pm
-
Boiling point: Be
2477oC, Al 2467oC
-
Oxides: BeO and Al2O3
are both amphoteric, rest of Group 2 oxides are only basic.
-
Reaction with dilute
acids: Be and Al are fairly resistant unless amalgamated or very
finely divided, other Group 2 metals readily react.
-
Reaction with conc.
nitric(V) acid: Be and Al are rendered passive, rest of Group 2
metals readily form salts.
-
Boron and silicon
-
Atomic radii: B 88
pm, Si 117 pm
-
Both elements exist
as a non-metallic giant covalent 3D lattice.
-
Both form a weakly
acidic oxide.
-
---
-
However, it should
be noted that these diagonal similarities are 'weaker' than
their similarities to the other elements in their respective
groups.

WHAT NEXT?
See also
4.1 Period 2 Survey of the
individual elements, 4.2 Period
2 element trends and explanations of physical properties *
4.3 Period 2 element trends in bonding,
structure, oxidation state, formulae & reactions,
5.1
Period 3 survey of elements,
5.2 Period 3 element trends
& explanations of physical properties, 5.3
Period 3 element trends in bonding, structure, oxidation
state, formulae & reactions, 6.1
Survey of
Period 4 elements, 6.2 Period 4 trends in physical properties, 6.3
Period 4 trends in bonding, formulae and
oxidation state
INORGANIC
Part 6 Period 4 survey & group trends page
sub-index: 6.1
Survey of Period 4 elements * 6.2
Period 4 trends in physical properties * 6.3
Period 4 trends in bonding, formulae and
oxidation state * 6.4
Important element trends down a Group
Advanced
Level Inorganic Chemistry Periodic Table Index *
Part 1
Periodic Table history
* Part 2
Electron configurations, spectroscopy,
hydrogen spectrum, ionisation energies *
Part 3
Period 1 survey H to He *
Part 4
Period 2 survey Li to Ne *
Part 5 Period 3 survey Na to Ar *
Part 6
Period 4 survey K to Kr and important trends
down a group *
Part 7
s-block Groups 1/2 Alkali Metals/Alkaline Earth
Metals *
Part 8
p-block Groups 3/13 to 0/18 *
Part 9
Group 7/17 The Halogens *
Part 10
3d block elements & Transition Metal Series
*
Part 11
Group & Series data & periodicity plots
Revising for A level Revision notes for GCE Advanced
Subsidiary Level AS Advanced Level A2 IB
Revise AQA GCE Chemistry OCR GCE Chemistry Edexcel GCE Chemistry Salters
Chemistry CIE Chemistry, WJEC GCE AS A2 Chemistry, CCEA/CEA GCE AS A2 Chemistry revising courses for pre-university students
(equal to US grade 11 and grade 12 and AP Honours/honors level courses)


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