G2 Mathematics
Lessons in g2 mathematics. This course is still being developed; independent practice and assessment coverage is incomplete.
More
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Lesson progress unavailable
Number and proportion
Your saved work does not identify a current lesson. Choose where to continue.
About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
Find this activity in your course
Topics
G2 Mathematics
- Number and proportionSuggested next · 14 lessonsG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020 · Normal (Academic) Secondary 2 Mathematics 2021 · Normal (Academic) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in number and proportion.
- Algebra and equationsSuggested next · 19 lessonsG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020 · Normal (Academic) Secondary 2 Mathematics 2021 · Normal (Academic) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in algebra and equations.
- Functions and graphsSuggested next · 4 lessonsG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021 · Normal (Academic) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in functions and graphs.
- Geometry and reasoningSuggested next · 9 lessonsG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020 · Normal (Academic) Secondary 2 Mathematics 2021 · Normal (Academic) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in geometry and reasoning.
- Coordinates and vectorsSuggested next · 1 lessonG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in coordinates and vectors.
- Area, volume and mensurationSuggested next · 7 lessonsG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020 · Normal (Academic) Secondary 2 Mathematics 2021 · Normal (Academic) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in area, volume and mensuration.
- TrigonometrySuggested next · 4 lessonsG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021 · Normal (Academic) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in trigonometry.
- Statistics and probabilitySuggested next · 9 lessonsG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020 · Normal (Academic) Secondary 2 Mathematics 2021 · Normal (Academic) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in statistics and probability.
No topics match your search. Try a shorter phrase, or show all topics.
Practise and check
Other Science combinations
Choose the syllabus edition you are studying.
Normal (Academic) Secondary 1 Mathematics 2020
Mixed practice
Practise a mix of topics from this course.
About 10 minutes
Time is up and your answers could not be submitted; check your connection and try again.
Paper instructions
This is for practice only and doesn’t count towards your course progress.
- Question count is checked before you start.
- Feedback appears after you finish and submit.
Your work
Without an account, unfinished answers stay in this tab. Signed in, they are saved on this device until the deadline shown when you start.
Review settings
Checking saved course progress…
Getting your questions…
Recent attempts
History is stored only in this browser.
No completed attempts are saved yet.
Beyond the syllabus: optional enrichment that does not count towards your progress.
Normal (Academic) Secondary 2 Mathematics 2021
Mixed practice
Practise a mix of topics from this course.
About 10 minutes
Time is up and your answers could not be submitted; check your connection and try again.
Paper instructions
This is for practice only and doesn’t count towards your course progress.
- Question count is checked before you start.
- Feedback appears after you finish and submit.
Your work
Without an account, unfinished answers stay in this tab. Signed in, they are saved on this device until the deadline shown when you start.
Review settings
Checking saved course progress…
Getting your questions…
Recent attempts
History is stored only in this browser.
No completed attempts are saved yet.
Beyond the syllabus: optional enrichment that does not count towards your progress.
Normal (Academic) Secondary 3–4 Mathematics 2022
Mixed practice
Practise a mix of topics from this course.
About 10 minutes
Time is up and your answers could not be submitted; check your connection and try again.
Paper instructions
This is for practice only and doesn’t count towards your course progress.
- Question count is checked before you start.
- Feedback appears after you finish and submit.
Your work
Without an account, unfinished answers stay in this tab. Signed in, they are saved on this device until the deadline shown when you start.
Review settings
Checking saved course progress…
Getting your questions…
Recent attempts
History is stored only in this browser.
No completed attempts are saved yet.
Beyond the syllabus: optional enrichment that does not count towards your progress.
G2 Mathematics 2027
Mixed practice
Practise a mix of topics from this course.
About 10 minutes
Time is up and your answers could not be submitted; check your connection and try again.
Paper instructions
This is for practice only and doesn’t count towards your course progress.
- Question count is checked before you start.
- Feedback appears after you finish and submit.
Your work
Without an account, unfinished answers stay in this tab. Signed in, they are saved on this device until the deadline shown when you start.
Review settings
Checking saved course progress…
Getting your questions…
Recent attempts
History is stored only in this browser.
No completed attempts are saved yet.
Beyond the syllabus: optional enrichment that does not count towards your progress.
Course info
Course guidance
Lessons in g2 mathematics. This course is still being developed; independent practice and assessment coverage is incomplete.
Learning goals
- Identify primes, factors and multiples
- Use prime factorisation to find HCF and LCM
- Calculate with integers and rational numbers
- Compare and order numbers and representations
- Round, estimate and judge numerical accuracy
- Use integer, zero, negative and fractional indices appropriately
- Represent and simplify ratios of quantities
- Share a quantity in a specified ratio
- Relate part-to-part ratios to part-to-whole fractions
- Model and solve direct or inverse proportional relationships
- Interpret a percentage relative to its base
- Calculate percentage changes and contextual amounts
- Recover a whole or original amount from a percentage part
- Use rate, speed, distance and time relationships
- Convert compatible measurement units
- Interpret algebraic notation and represented operations
- Evaluate an algebraic expression by substitution
- Represent a situation with algebraic expressions
- Express and use the general term of a sequence
- Simplify linear expressions by combining like terms
- Expand and factorise algebraic expressions
- Calculate and simplify algebraic fractions with restrictions
- Change the subject of a formula
- Solve linear equations and check the solution
- Solve simultaneous equations by justified methods
- Solve quadratic equations by suitable methods
- Solve inequalities and represent their solution sets
- Formulate, use and interpret a mathematical model
- Multiply and divide algebraic fractions with domain restrictions
- Interpret and draw graphs of functions
- Add and subtract algebraic fractions with domain restrictions
- Read and plot ordered coordinate pairs
- Find and interpret a graph gradient
- Classify shapes by their properties
- Deduce unknown angles from geometric relationships
- Construct geometric figures from stated conditions
- Reason about congruence, similarity and scale factors
- Classify angles by their size
- Reason and calculate using coordinate geometry
- Calculate and justify area and perimeter
- Calculate and justify volume and surface area
- Calculate circle, arc, sector and segment measures
- Use and justify Pythagoras’ theorem
- Use trigonometric ratios in right-angled triangles
- Use sine and cosine rules for general triangles
- Read and interpret data displays
- Organise data and construct a suitable display
- Evaluate the purposes and limitations of data displays
- Calculate and interpret the arithmetic mean
- Find and interpret the mode and median
- Estimate the mean from grouped data
- Calculate measures of spread
- Compare variability using appropriate measures
- Calculate event probabilities from an explicit sample space
- Distinguish independence from mutual exclusivity
Syllabus statements covered
- primes and prime factorisation • finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation • negative numbers, integers, rational numbers, real numbers and their four operations • calculations with calculator • representation and ordering of numbers on the number line • use of <, >, ⩽, ⩾ • approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures and estimating the results of computation) • use of standard form A × 10^n, where n is an integer, and 1 ⩽ A < 10 • positive, negative, zero and fractional indices • laws of indices
- comparison between two or more quantities by ratio • relationship between ratio and fraction • dividing a quantity in a given ratio • ratios involving rational numbers • equivalent ratios • writing a ratio in its simplest form • map scales (distance and area) • direct and inverse proportion
- expressing percentage as a fraction or decimal • expressing one quantity as a percentage of another • comparing two quantities by percentage • percentages greater than 100% • increasing/decreasing a quantity by a given percentage • finding percentage increase/decrease • reverse percentages
- relationships between distance, time and speed • writing speed in different units (e.g. km/h, m/min, m/s and cm/s) • calculation of speed, distance or time given the other two quantities • average rate and average speed • conversion of units (e.g. km/h to m/s)
- using letters to represent numbers • interpreting notations: ab as a × b; a/b as a ÷ b or a × (1/b); a² as a × a, a³ as a × a × a, a²b as a × a × b, …; 3y as y + y + y or 3 × y; 3(x + y) as 3 × (x + y); (3 + y)/5 as (3 + y) ÷ 5 or (1/5) × (3 + y) • evaluation of algebraic expressions and formulae • translation of simple real-world situations into algebraic expressions • recognising and representing patterns/relationships by finding an algebraic expression for the nth term • addition and subtraction of linear expressions • simplification of linear expressions such as −2(3x − 5) + 4x and 2x/3 − 3(x − 5)/2 • use brackets and extract common factors • factorisation of linear expressions ax + bx + kay + kby • expansion of the product of algebraic expressions • changing the subject of a formula • finding the value of an unknown quantity in a given formula • use of (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b², a² − b² = (a + b)(a − b) • factorisation of quadratic expressions ax² + bx + c • multiplication and division of simple algebraic fractions such as (3a/(4b²))(5ab/3); (3a/4) ÷ (9a²/10) • addition and subtraction of algebraic fractions with linear or quadratic denominator such as 1/(x − 2) + 2/(x − 3); 1/(x² − 9) + 2/(x − 3); 1/(x − 3) + 2/(x − 3)²
- solving linear equations in one variable • solving simple fractional equations that reduce to linear equations, such as x/3 + (x − 2)/4 = 3 and 3/(x − 2) = 6 • solving simultaneous linear equations in two variables by substitution and elimination or graphically • solving quadratic equations in one variable by factorisation, formula, completing the square for y = x² + px + q, or graphically • solving fractional equations that reduce to quadratics, such as 6/(x + 4) = x + 3 and 1/(x − 2) + 2/(x − 3) = 5 • formulating equations to solve problems • solving simple inequalities ax ≤ b, ax ≥ b, ax < b, ax > b where a and b are integers
- Cartesian coordinates in two dimensions • graph of a set of ordered pairs as a representation of a relationship between two variables • linear functions (y = ax + b) and quadratic functions (y = ax² + bx + c) • graphs of linear functions • the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients) • graphs of quadratic functions and their properties: ∗ positive or negative coefficient of x^2 ∗ maximum and minimum points ∗ symmetry • graphs of power functions of the form y = ax^n, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these • graphs of exponential functions y = ka^x, where a is a positive integer • estimation of the gradient of a curve by drawing a tangent
- right, acute, obtuse and reflex angles • vertically opposite angles, angles on a straight line and angles at a point • angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles • properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon) including symmetry properties • classifying special quadrilaterals on the basis of their properties • angle sum of interior and exterior angles of any convex polygon • construction of simple geometrical figures from given data using compasses, ruler, set squares and protractor, where appropriate
- congruent and similar figures • properties of similar triangles and polygons: ∗ corresponding angles are equal ∗ corresponding sides are proportional • enlargement and reduction of a plane figure • scale drawings • properties and construction of perpendicular bisectors of line segments and angle bisectors • solving simple problems involving similarity and congruence
- symmetry properties of circles: ∗ equal chords are equidistant from the centre ∗ the perpendicular bisector of a chord passes through the centre ∗ tangents from an external point are equal in length ∗ the line joining an external point to the centre of the circle bisects the angle between the tangents • angle properties of circles: ∗ angle in a semicircle is a right angle ∗ angle between tangent and radius of a circle is a right angle ∗ angle at the centre is twice the angle at the circumference ∗ angles in the same segment are equal ∗ angles in opposite segments are supplementary All circle properties in this row are tested only in Paper 2 Section B.
- finding the gradient of a straight line given the coordinates of two points on it • finding the length of a line segment given the coordinates of its end points • interpreting and finding the equation of a straight line graph in the form y = mx + c • geometric problems involving the use of coordinates
- area of parallelogram and trapezium • problems involving perimeter and area of composite plane figures • volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere • conversion between cm^2 and m^2, and between cm^3 and m^3 • problems involving volume and surface area of composite solids • arc length as fraction of the circumference and sector area as fraction of the area of a circle • area of a segment • use of radian measure of angle (including conversion between radians and degrees) • problems involving the arc length, sector area of a circle and area of a segment Radian measure and problems involving arc length, sector area and segment area are tested only in Paper 2 Section B.
- use of Pythagoras’ theorem • determining whether a triangle is right-angled given the lengths of three sides • use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles • extending sine and cosine to obtuse angles • use of the formula ½ab sin C for the area of a triangle • use of sine rule and cosine rule for any triangle • problems in two and three dimensions including those involving angles of elevation and depression and bearings Sine/cosine rules and two-/three-dimensional problems (including elevation, depression and bearings) are tested only in Paper 2 Section B.
- simple concepts in collecting, classifying and tabulating data • analysis and interpretation of: ∗ tables ∗ bar graphs ∗ pictograms ∗ line graphs ∗ pie charts ∗ dot diagrams ∗ histograms with equal class intervals ∗ stem-and-leaf diagrams ∗ cumulative frequency diagrams ∗ box-and-whisker plots • purposes and uses, advantages and disadvantages of the different forms of statistical representations • drawing simple inference from statistical diagrams • explaining why a given statistical diagram leads to misinterpretation of data • mean, mode and median as measures of central tendency for a set of data • purposes and use of mean, mode and median • calculation of the mean for grouped data • quartiles and percentiles • range, interquartile range and standard deviation as measures of spread for a set of data • calculation of the standard deviation for a set of data (grouped and ungrouped) • using the mean and standard deviation to compare two sets of data Cumulative frequency diagrams, box-and-whisker plots, quartiles/percentiles, spread (range, interquartile range and standard deviation), calculating standard deviation and comparing data by mean/standard deviation are tested only in Paper 2 Section B.
- probability as a measure of chance • probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability) • probability of simple combined events (including using possibility diagrams and tree diagrams, where appropriate) • addition and multiplication of probabilities (mutually exclusive events and independent events) Combined events and addition/multiplication of probabilities are tested only in Paper 2 Section B.
- primes and prime factorisation
- finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation
- negative numbers, integers, rational numbers, real numbers and their four operations
- calculations with calculator
- representation and ordering of numbers on the number line
- use of <, >, ≤, ≥
- approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, and estimating the results of computation)
- comparison between two or more quantities by ratio
- relationship between ratio and fraction
- dividing a quantity in a given ratio
- ratios involving rational numbers
- equivalent ratios
- writing a ratio in its simplest form
- problems involving ratio
- expressing percentage as a fraction or decimal
- expressing one quantity as a percentage of another
- comparing two quantities by percentage
- percentages greater than 100%
- increasing/decreasing a quantity by a given percentage (including concept of percentage point)
- finding percentage increase/decrease
- reverse percentages
- problems involving percentages
- relationships between distance, time and speed
- writing speed in different units (e.g. km/h, m/min, m/s and cm/s)
- concepts of average rate, speed, constant speed and average speed
- conversion of units (e.g. km/h to m/s)
- calculation of speed, distance or time given the other two quantities
- problems involving rate and speed
- using letters to represent numbers
- interpreting notations: ab as a × b; a/b as a ÷ b or a × (1/b); a² as a × a, a³ as a × a × a, a²b as a × a × b, …; 3y as y + y + y or 3 × y; 3(x + y) as 3 × (x + y); (3 + y)/5 as (3 + y) ÷ 5 or (1/5) × (3 + y)
- evaluation of algebraic expressions and formulae
- translation of simple real-world situations into algebraic expressions
- recognising and representing patterns/relationships by finding an algebraic expression for the nth term
- addition and subtraction of linear expressions
- simplification of linear expressions with integral coefficients such as 2(x − 3y); 4x − 2(3x − 5); 3(x − y) − (2y + x) − y
- concepts of equation
- solving linear equations with integral coefficients in one variable
- formulating a linear equation in one variable to solve problems
- right, acute, obtuse and reflex angles
- vertically opposite angles, angles on a straight line, angles at a point
- angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
- properties of triangles
- area of parallelogram and trapezium
- problems involving perimeter and area of composite plane figures
- volume and surface area of prism and cylinder
- conversion between cm² and m² , and between cm³ and m³
- problems involving volume and surface area of composite solids
- simple concepts in collecting, classifying and tabulating data
- analysis and interpretation of: • tables • bar graphs • pictograms • line graphs • pie charts
- purposes and uses, advantages and disadvantages of the different forms of statistical representations
- explaining why a given statistical diagram leads to misinterpretation of data
- map scales (distance and area)
- direct and inverse proportion
- simplification of linear expressions with fractional coefficients such as 2x/3 − 3(x − 5)/2
- expansion of the product of two linear expressions
- use brackets and extract common factors
- use of: • (a + b) 2 = a^2 + 2ab + b^2 • (a − b) 2 = a^2 − 2ab + b^2 • a^2 − b^2 = (a + b)(a − b)
- factorisation of quadratic expressions ax^2 + bx + c
- multiplication and division of simple algebraic fractions such as (3a/(4b²))(5ab/3); (3a/4) ÷ (9a²/10)
- solving linear equations in one variable (including fractional coefficients)
- concept and properties of inequality
- solving simple inequalities in the form ax ≤ b, ax ≥ b , ax < b and ax > b, where a and b are integers.
- solving simple fractional equations that can be reduced to linear equations such as x/3 + (x − 2)/4 = 3; 3/(x − 2) = 6
- graphs of linear equations in two variables(ax + by = c)
- solving simultaneous linear equations in two variables by: • substitution and elimination methods • graphical method
- formulating a linear equation in one variable or a pair of linear equations in two variables to solve problems
- Cartesian coordinates in two dimensions
- graph of a set of ordered pairs as a representation of a relationship between two variables
- linear functions y = ax + b
- graphs of linear functions
- the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)
- properties of special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon) including symmetry properties
- classifying special quadrilaterals on the basis of their properties
- angle sum of interior and exterior angles of any convex polygon
- construction of simple geometrical figures from given data using compasses, ruler, set squares and protractors, where appropriate
- congruent figures
- similar figures
- properties of similar triangles and polygons: • corresponding angles are equal • corresponding sides are proportional
- volume and surface area of pyramid, cone and sphere
- use of Pythagoras’ theorem
- determining whether a triangle is right-angled given the lengths of three sides.
- analysis and interpretation of: • dot diagrams • histograms • stem-and-leaf diagrams
- purposes and uses, advantages and disadvantages of the different forms of statistical representations
- explaining why a given statistical diagram leads to misinterpretation of data
- mean, mode and median as measures of central tendency for a set of data
- purposes and uses of mean, mode and median
- calculation of the mean for grouped data
- probability as a measure of chance
- probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability)
- use of standard form A×10^n , where n is an integer, and 1 ≤ A < 10
- positive, negative, zero and fractional indices
- laws of indices
- factorisation of linear expressions of the form ax + bx + kay + kby
- expansion of the product of algebraic expressions
- changing the subject of a formula
- finding the value of an unknown quantity in a given formula
- addition and subtraction of algebraic fractions with linear or quadratic denominator such as 1/(x − 2) + 2/(x − 3); 1/(x² − 9) + 2/(x − 3); 1/(x − 3) + 2/(x − 3)²
- solving quadratic equations in one variable by: • factorisation • use of formula • completing the square for y = x^2 + px + q • graphical method
- solving fractional equations that can be reduced to quadratic equations such as 6/(x + 4) = x + 3; 1/(x − 2) + 2/(x − 3) = 5
- formulating a quadratic equation in one variable to solve problems
- quadratic functions y = ax^2 + bx + c
- graphs of quadratic functions and their properties: • positive or negative coefficient of x² • maximum and minimum points • symmetry
- graphs of power functions y = ax^n, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these
- graphs of exponential functions y = ka^x, where a is a positive integer, a > 1
- estimation of the gradient of a curve by drawing a tangent
- enlargement and reduction of a plane figure
- scale drawings
- properties and construction of perpendicular bisectors of line segments and angle bisectors
- solving simple problems involving congruence and similarity
- symmetry properties of circles: • equal chords are equidistant from the centre • the perpendicular bisector of a chord passes through the centre • tangents from an external point are equal in length • the line joining an external point to the centre of the circle bisects the angle between the tangents
- angle properties of circles: • angle in a semicircle is a right angle • angle between tangent and radius of a circle is a right angle • angle at the centre is twice the angle at the circumference • angles in the same segment are equal • angles in opposite segments are supplementary
- finding the gradient of a straight line given the coordinates of two points on it
- finding the length of a line segment given the coordinates of its end points
- interpreting and finding the equation of a straight line in the form y = mx + c
- geometric problems involving the use of coordinates
- arc length as fraction of the circumference and sector area as fraction of the area of a circle
- area of a segment
- use of radian measure of angle (including conversion between radians and degrees)
- problems involving the arc length, sector area of a circle and area of a segment
- use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles
- extending sine and cosine to obtuse angles
- use of the formula ½ab sin C for the area of a triangle
- use of sine rule and cosine rule for any triangle
- problems in two and three dimensions including those involving angles of elevation and depression and bearings
- quartiles and percentiles
- range, interquartile range and standard deviation as measures of spread for a set of data
- analysis and interpretation of: • cumulative frequency diagrams • box-and-whisker plots
- purposes and uses, advantages and disadvantages of the different forms of statistical representations
- calculation of the standard deviation for a set of data (grouped and ungrouped)
- using the mean and standard deviation to compare two sets of data
- probability of simple combined events (including using possibility diagrams and tree diagrams, where appropriate)
- addition and multiplication of probabilities (mutually exclusive events and independent events)