N.3
investigate situations involving proportionality so that they can:
a. b.
use absolute and relative comparison where appropriate
solve problems involving proportionality including those involving currency conversion and those involving average speed, distance, and time
N.4 analyse numerical patterns in diff erent ways, including making out tables and graphs, and continue such patterns
N.5
explore the concept of a set so that they can: a.
understand the concept of a set as a well-defi ned collection of elements, and that set equality is a relationship where two sets have the same elements
b. defi ne sets by listing their elements, if fi nite (including in a 2-set or 3-set Venn diagram), or by generating rules that define them
c.
use and understand suitable set notation and terminology, including null set, Ø , subset, ⊂ complement, element, ∊, universal set, cardinal number, #, intersection, ∩ , union, ∪ , set diff erence, \ , ℕ , ℤ , ℚ , ℝ and ℝ \ ℚ
d.
perform the operations of intersection and union on 2 sets and on 3 sets, set diff erence, and complement, including the use of brackets to defi ne the order of operations
e.
investigate whether the set operations of intersection, union, and diff erence are commutative and/or associative
Geometry and
trigonometry strand Students should be able to: GT.1
c.
calculate, interpret, and apply units of measure and time
GT.2 investigate 2D shapes and 3D solids so that they can: a. b.
draw and interpret scaled diagrams
draw and interpret nets of rectangular solids, prisms (polygonal bases), cylinders
c.
fi nd the perimeter and area of plane fi gures made from combinations of discs, triangles, and rectangles, including relevant operations involving pi
d. fi nd the volume of rectangular solids, cylinders, triangular-based prisms, spheres, and combinations of these, including relevant operations involving pi
e.
fi nd the surface area and curved surface area (as appropriate) of rectangular solids, cylinders, triangular-based prisms, spheres, and combinations of these
GT.3 investigate the concept of proof through their engagement with geometry so that they can:
a.
perform constructions 1 to 15 in Geometry for Post-Primary School Mathematics (constructions 3 and 7 at HL only)
d. e.
b.
recall and use the concepts, axioms, theorems, corollaries and converses, specifi ed in Geometry for Post-Primary School Mathematics (section 9 for OL and section 10 for HL) I.
axioms 1, 2, 3, 4 and 5 II.
theorems 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 15 and 11, 12, 19, and appropriate converses, including relevant operations involving square roots
III. corollaries 3, 4 and 1, 2, 5 and appropriate converses
c. use and explain the terms: theorem, proof, axiom, corollary, converse, and implies
create and evaluate proofs of geometrical propositions
display understanding of the proofs of theorems 1, 2, 3, 4, 5, 6, 9, 10, 14, 15, and 13, 19; and of corollaries 3, 4, and 1, 2, 5 (full formal proofs are not examinable)
GT.4 evaluate and use trigonometric ratios (sin, cos, and tan, defi ned in terms of right-angled triangles) and their inverses, involving angles between 0° and 90° at integer values and in decimal form
GT.5 investigate properties of points, lines and line segments in the co-ordinate plane so that they can:
a. b.
fi nd and interpret: distance, midpoint, slope, point of intersection, and slopes of parallel and perpendicular lines
draw graphs of line segments and interpret such graphs in context, including discussing the rate of change (slope) and the y intercept
fi nd and interpret the equation of a line in the form y = mx + c ; y − y1
ax + by + c = 0 (for a, b, c, m, x1 , y1 = m(x − x1) ; and ∊ℚ ); including
fi nding the slope, the y-intercept, and other points on the line
GT.6 investigate transformations of simple objects so that they can:
a. b.
recognise and draw the image of points and objects under translation, central symmetry, axial symmetry, and rotation
draw the axes of symmetry in shapes Algebra and
functions strand Students should be able to: AF.1
investigate patterns and relationships (linear, quadratic, doubling and tripling) in number, spatial patterns and real-world phenomena involving change so that they can:
a. represent these patterns and relationships in tables and graphs
b.
generate a generalised expression for linear (and quadratic) patterns in words and algebraic expressions and fluently convert between each representation
c.
categorise patterns as linear, non-linear, quadratic, and exponential (doubling and tripling) using their defining characteristics as they appear in the different representations
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