
8Secondary 2 Standards
Top Mathematicians

Measurement and Geometry

8.MD.1
Angles, triangles and polygons
• 1.1 properties of special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon) including symmetry properties
• 1.2 classifying special quadrilaterals on the basis of their properties
• 1.3 angle sum of interior and exterior angles of any convex polygon
• 1.4 properties of perpendicular bisectors of line segments and angle bisectors
• 1.5 construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate
• 1.6 Use GSP or other dynamic geometry software to explore a given type of quadrilateral (e.g. parallelogram) to discover its properties, e.g. diagonals of a parallelogram bisect each other.
• 1.7 Investigate the sum of the interior and exterior angles of polygon and obtain the formulae for them.
• 1.8 Recognise symmetric properties (rotational and line symmetry) in some special quadrilaterals and regular polygons.
• 1.9 Justify whether a mathematical statement is true or false.
• 1.10 Use GSP or other dynamic geometry software to construct and study the properties of the perpendicular bisector of a line segment and the bisector of an angle. 

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8.MD.2
Congruence and similarity
• 2.1 congruent figures
• 2.2 similar figures
• 2.3 properties of similar triangles and polygon:
 corresponding angles are equal
 corresponding sides are proportional
• 2.4 Examine the pictures of two congruent figures and check if one figure can be mapped onto the other under translation, rotation and reflection.
• 2.5 Identify similar triangles/rectangles from cutouts of triangles/rectangles and explain why they are similar. 

8.695

8.705

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8.725

8.735

8.745


8.MD.4
Pythagoras' theorem and trigonometry
• 4.1 use of Pythagoras' theorem
• 4.2 determining whether a triangle is rightangled given the lengths of three sides
• 4.3 Either (i) use a string of length 12 units (e.g. 1 unit = 10cm) to form a rightangled triangle with sides of wholeunit lengths (e.g. 3 units, 4 units and 5 units) and find out if there is a relationship between the three sides; or (ii) use cutout pieces of two squares with sides of 3 units and 4 units respectively to form a square of sides 5 units. 

8.MD.5
Mensuration
• 5.1 volume and surface area of pyramid, cone and sphere
• 5.2 Visualise and make connections between the volumes of pyramid and cone, and the volumes of pyramid/cone and related prism/cylinder.
• 5.3 Make sense of the formulae for the volume and surface area of a sphere, e.g. by relating to the formulae for the volume and curved surface area of the related cylinder. 

8.MD.7
Problems in realworld contexts
• 7.1 solving problems in realworld contexts (including floor plans, surveying, navigation, etc) using geometry
• 7.2 interpreting the solution in the context of the problem
• 7.3 identifying the assumptions made and the limitations of the solution
• 7.4 Work on tasks that incorporate some or all elements of the mathematical modelling process. 

8.755

8.765


8.MD.1

Statistics & Probability

8.SP.1
Data analysis
• 1.1 analysis and interpretation of:
 dot diagrams
 histograms
 stemandleaf diagrams
• 1.2 purposes and uses, advantages and disadvantages of the different forms of statistical representations
• 1.3 explaining why a given statistical diagram leads to misinterpretation of data
• 1.4 mean, mode and median as measures of central tendency for a set of data
• 1.5 purposes and uses of mean, mode and median
• 1.6 calculation of the mean for grouped data
• 1.7 Construct dot diagrams, histograms (including equal and unequal class intervals) and stemandleaf diagrams from given data.
• 1.8 Predict, observe and explain how the different measures of central tendency are affected by changing data values.
• 1.9 Discuss the appropriate use of the measures of central tendency in different contexts. 

8.5420

8.555

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8.1035


8.SP.2
Probability
• 2.1 probability as a measure of chance
• 2.2 probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability)
• 2.3 Discuss the concept of probability (or chance) using everyday events, including simple experiments, e.g. tossing a coin, and use language such as "certain", "likely" and "unlikely".
• 2.4 Compare and discuss the experimental and theoretical values of probability using computer simulations. 

8.1045

8.1055

8.1065

8.1075


8.SP.1

Number and Algebra

8.NA.2
Ratio and proportion
• 2.1 map scales (distance and area)
• 2.2 direct and inverse proportion
• 2.3 Interpret the various scales used on maps, floor plans and other scale drawings, and calculate the actual distance/length and area.
• 2.4 Work in groups to make a scale drawing of an existing or dream classroom/bedroom and explain the choice of the scale used.
• 2.5 Discuss examples of direct and inverse proportion and explain the concepts using tables, equations and graphs. 
8.NA.5
Algebraic expressions and formulae
• 5.1 simplification of linear expressions with fractional coefficients such as 2x/3  3(x5)/2
• 5.2 expansion of the product of two linear expressions
• 5.3 use brackets and extract common factors
• 5.4 use of:
 (a + b)² = a² + 2ab + b²
 (a  b)² = a²  2ab + b²
 a  b² = (a + b)(ab)
• 5.5 factorisation of quadratic expressions ax² + bx + c
• 5.6 multiplication and division of simple algebraic fractions such as (3a/4b²)(5ab/3), 3a/4 ÷ 9a²/10
• 5.7 Use algebra manipulatives, e.g. algebra discs to explain the process of expanding the product of two linear expressions of the form px + q, where p and q are integers, to obtain a quadratic expression of the form ax² + bx + c.
• 5.8 Use the AlgeDisc application in AlgeTools, to factorise a quadratic expression of the form ax² +bx + c into two linear factors where a, b and c are integers.
• 5.9 Work in groups to identify and explain common errors in algebraic manipulations, such as (x + y)² = x² + y². 

8.85

8.910

8.105

8.1110


8.NA.6
Functions and graphs
• 6.1 Cartesian coordinates in two dimensions
• 6.2 graph of a set of ordered pairs as a representation of a relationship between two variables
• 6.3 linear functions y = ax + b
• 6.4 graphs of linear functions
• 6.5 the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)
• 6.6 Play games, e.g. Battleship Game, that involve the use of 2D Cartesian coordinates to specify points.
• 6.7 Use a function machine to generate input and output values to illustrate the concept of function as "only one output for every input" and represent the function in verbal, tabular, graphical and algebraic forms.
• 6.8 Use a linear function to represent the relationship between two variables (such as distance and time when the speed is constant), show the relationship graphically and identify that the rate of change is the gradient of the graph.
• 6.9 Use a spreadsheet or graphing software to study how the graph of y = ax + b changes when either a or b varies. 

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8.2015

8.2110

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8.NA.7
Equations and inequalities
• 7.1 solving linear equations in one variable (including fractional coefficients)
• 7.2 concept and properties of inequality
• 7.3 solving simple fractional equations that can be reduced to linear equations such as x/3 + (x2)/4 = 3, 3/(x2) = 6
• 7.4 graphs of linear equations in two variables (ax + by = c)
• 7.5 solving simultaneous linear equations in two variables by:
 substitution and elimination methods
 graphical method
• 7.6 formulating a linear equation in one variable or a pair of linear equations in two variables to solve problems
• 7.7 formulate inequalities from realworld contexts.
• 7.8 Use Graphmatica, applets or other software to draw the graph of ax + by = c (a straight line), check that the coordinates of a point on the straight line satisfy the equation, and explain why the solution of a pair of simultaneous linear equations is the point of intersection of two straight lines.
• 7.9 Draw the lines x = a and y = b, and describe the lines and their gradients.
• 7.10 Use the Algebar application in AlgeTools to formulate linear equations to solve problems (Students can draw models to help them formulate equations.) 

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8.NA.8
Problems in realworld contexts
• 8.1 solving problems based on realworld contexts:
 in everyday life (including travel plans, transport schedules, sports and games, recipes, etc)
 involving personal and household finance (including simple interest, taxation, installments, utilities bills, money exchange, etc)
• 8.2 interpreting and analysing data from tables and graphs
• 8.3 interpreting the solution in the context of the problem
• 8.4 identifying assumptions made and the limitations of the solution
• 8.5 Examine and make sense of data in variety of contexts (including real data presented in graphs, tables and formulae/equations).
• 8.6 Work on tasks that incorporate some or all of the elements of the mathematical modelling process. 

8.3820

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8.405

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8.5015

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8.5420

8.555

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8.6010

8.615

8.625

8.635


8.NA.2