Mathematics – 0580 – binhayyan Academy

Students study the following topics

1. Number

2. Algebra and graphs

3. Coordinate geometry

4. Geometry

5. Mensuration

6. Trigonometry

7. Transformations and vectors

8. Probability

9. Statistics

Course Content

Number

Identify and use: • natural numbers • integers (positive, zero and negative) • prime numbers • square numbers • cube numbers • common factors • common multiples • rational and irrational numbers • reciprocals.
Example tasks include: • convert between numbers and words, e.g. six billion is 6000000000 10007 is ten thousand and seven • express 72 as a product of its prime factors
• find the highest common factor (HCF) of two numbers • find the lowest common multiple (LCM) of two numbers.
Understand and use set language, notation and Venn diagrams to describe sets and represent relationships between sets.
Venn diagrams are limited to two or three sets. The following set notation will be used: • n(A) Number of elements in set A • ∈ “… is an element of …” • ∉ “… is not an element of …” • A′ Complement of set A
• ∅ The empty set • Universal set • A ⊆ B A is a subset of B • A ⊈ B A is not a subset of B • A ∪ B Union of A and B • A ∩ B Intersection of A and B.
Example definition of sets: A = {x: x is a natural number} B = {(x, y): y = mx + c} C = {x: a ⩽ x ⩽ b}
Calculate with the following: • squares • square roots • cubes • cube roots • other powers and roots of numbers.
Includes recall of squares and their corresponding roots from 1 to 15, and recall of cubes and their corresponding roots of 1, 2, 3, 4, 5 and 10, e.g.: • Write down the value of (169)^1/2 • Work out 5^2x^3(8)^1/3 .
1 Use the language and notation of the following in appropriate contexts: • proper fractions • improper fractions • mixed numbers • decimals • percentages.
2 Recognise equivalence and convert between these forms.
Candidates are expected to be able to write fractions in their simplest form. Recurring decimal notation is required, e.g. • 0.1 7 = 1777…. • 0.123 =0.1232323…• 0.123 =0.123123…
Includes converting between recurring decimals and fractions and vice versa, e.g. write 0.17 as a fraction.
Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ⩾ and ⩽.
Use the four operations for calculations with integers, fractions and decimals, including correct ordering of operations and use of brackets.
Includes: • negative numbers • improper fractions • mixed numbers • practical situations, e.g. temperature changes.
Understand and use indices (positive, zero, negative, and fractional).
Understand and use the rules of indices.
• find the value of 7^ –2, e.g. find the value of 2^–3 × 2^4 , (2^3 )^2 , 2^3 ÷ 2^4
Use the standard form A × 10n where n is a positive or negative integer and 1 ⩽ A < 10.
Convert numbers into and out of standard form.
Calculate with values in standard form.
Round values to a specified degree of accuracy
Make estimates for calculations involving numbers, quantities and measurements.
Round answers to a reasonable degree of accuracy in the context of a given problem.
Includes decimal places and significant figures. e.g. write 5764 correct to the nearest thousand. e.g. by writing each number correct to 1 significant figure, estimate the value of 41.3/9.79*0.765
Give upper and lower bounds for data rounded to a specified accuracy.
Find upper and lower bounds of the results of calculations which have used data rounded to a specified accuracy
e.g. write down the upper bound of a length measured correct to the nearest metre. Example calculations include:
• calculate the upper bound of the perimeter or the area of a rectangle given dimensions measured to the nearest centimetre • find the lower bound of the speed given rounded values of distance and time
Understand and use ratio and proportion to: • give ratios in their simplest form • divide a quantity in a given ratio • use proportional reasoning and ratios in context.
e.g. 20:30:40 in its simplest form is 2:3:4. e.g. adapt recipes; use map scales; determine best value.
Use common measures of rate.
e.g. calculate with: • hourly rates of pay • exchange rates between currencies • flow rates • fuel consumption
Apply other measures of rate.
e.g. calculate with: • pressure • density • population density. Required formulas will be given in the question.
Solve problems involving average speed.
Knowledge of speed/distance/time formula is required. e.g. A cyclist travels 45km in 3 hours 45 minutes. What is their average speed? Notation used will be, e.g. m/s (metres per second), g/cm3 (grams per cubic centimetre).
Calculate a given percentage of a quantity
Express one quantity as a percentage of another
Calculate percentage increase or decrease.
Calculate with simple and compound interest.
Problems may include repeated percentage change. Formulas are not given.
Calculate using reverse percentages.
e.g. find the cost price given the selling price and the percentage profit. Percentage calculations may include: • deposit • discount • profit and loss (as an amount or a percentage) • earnings • percentages over 100%.
Use a calculator efficiently
e.g. know not to round values within a calculation and to only round the final answer.
Enter values appropriately on a calculator.
e.g. enter 2 hours 30 minutes as 2.5 hours or 2° 30’ 0’’.
Interpret the calculator display appropriately.
e.g. in money 4.8 means $4.80; in time 3.25 means 3 hours 15 minutes.
Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units.
1 year = 365 days
Calculate times in terms of the 24-hour and 12-hour clock
In the 24-hour clock, for example, 3.15 a.m. will be denoted by 0315 and 3.15 p.m. by 1515
Includes problems involving time zones, local times and time differences.
Calculate with money.
Convert from one currency to another.
Use exponential growth and decay.
e.g. depreciation, population change. Knowledge of e is not required.

Algebra and graphs

Know that letters can be used to represent generalised numbers.
Substitute numbers into expressions and formulas.
Simplify expressions by collecting like terms.
Simplify means give the answer in its simplest form, e.g. 2a + 3b + 5a – 9b = 7a – 6b
Expand products of algebraic expressions.
e.g. expand 3x(2x – 4y). Includes products of two brackets involving one variable, e.g. expand (2x + 1)(x – 4).
Factorise by extracting common factors
Factorise means factorise fully, e.g. 9x 2 + 15xy = 3x(3x + 5y).
Understand and use indices (positive, zero and negative).
e.g. write an expression for a number that is 2 more than n. Includes constructing linear simultaneous equations.
Solve linear equations in one unknown
Solve simultaneous linear equations in two unknowns.
Examples include: • 3x + 4 = 10 • 5 – 2x = 3(x + 7).
Change the subject of simple formulas.
e.g. change the subject of formulas where: • the subject only appears once • there is not a power or root of the subject.
Represent and interpret inequalities, including on a number line.
When representing and interpreting inequalities on a number line: • open circles should be used to represent strict inequalities () • closed circles should be used to represent inclusive inequalities (⩽, ⩾) e.g. – 3 ⩽ x < 1
Continue a given number sequence or pattern.
e.g. write the next two terms in this sequence: 1, 3, 6, 10, 15, … , …
Recognise patterns in sequences, including the term-to-term rule, and relationships between different sequences.
Find and use the nth term of the following sequences: (a) linear (b) simple quadratic (c) simple cubic.
e.g. find the nth term of 2, 5, 10, 17
Use and interpret graphs in practical situations including travel graphs and conversion graphs.
e.g. interpret the gradient of a straight-line graph as a rate of change
Draw graphs from given data.
e.g. draw a distance–time graph to represent a journey
Construct tables of values, and draw, recognise and interpret graphs for functions of the following forms: • ax + b • ± x^2 + ax + b • x/a (x ≠ 0) where a and b are integer constants
Solve associated equations graphically, including finding and interpreting roots by graphical methods
e.g. find the intersection of a line and a curve.
Recognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic.
Knowledge of symmetry and roots is required. Knowledge of turning points is not required

Coordinate geometry

Use and interpret Cartesian coordinates in two dimensions.
Draw straight-line graphs for linear equations.
Equations will be given in the form y = mx + c (e.g. y = –2x + 5), unless a table of values is given.
Find the gradient of a straight line. From a grid only.
Interpret and obtain the equation of a straight-line graph in the form y = mx + c.
Questions may: • use and request lines in the forms y = mx + c x = k • involve finding the equation when the graph is given
• ask for the gradient or y-intercept of a graph from an equation, e.g. find the gradient and y-intercept of the graph with the equation y = 6x + 3.Candidates are expected to give equations of a line in a fully simplified form.
Find the gradient and equation of a straight line parallel to a given line.
e.g. find the equation of the line parallel to y = 4x – 1 that passes through (1, –3).

Geometry

Use and interpret the following geometrical terms: • point • vertex • line • parallel • perpendicular • bearing • right angle • acute, obtuse and reflex angles • interior and exterior angles • similar • congruent • scale factor.
Candidates are not expected to show that two shapes are congruent
Use and interpret the vocabulary of: • triangles • special quadrilaterals • polygons • nets • simple solids.
Includes the following terms: Triangles: • equilateral • isosceles • scalene • right-angled. Quadrilaterals: • square • rectangle • kite • rhombus • parallelogram • trapezium.
Polygons: • regular and irregular polygons • pentagon • hexagon • octagon • decagon.Simple solids: • cube • cuboid • prism • cylinder • pyramid • cone • sphere (term ‘hemisphere’ not required) • face • surface • edge
Use and interpret the vocabulary of a circle.Includes the following terms: • centre • radius (plural radii) • diameter • circumference • semicircle • chord • tangent • arc • sector • segment.
Measure and draw lines and anglesA ruler should be used for all straight edges. Constructions of perpendicular bisectors and angle bisectors are not required
Construct a triangle, given the lengths of all sides, using a ruler and pair of compasses only.e.g. construct a rhombus by drawing two triangles. Construction arcs must be shown.
Draw, use and interpret nets.Examples include: • draw nets of cubes, cuboids, prisms and pyramids • use measurements from nets to calculate volumes and surface areas
Draw and interpret scale drawings.A ruler must be used for all straight edges.
Use and interpret three-figure bearings.Bearings are measured clockwise from north (000° to 360°). e.g. find the bearing of A from B if the bearing of B from A is 025°.
Includes an understanding of the terms north, east, south and west. e.g. point D is due east of point C.
Calculate lengths of similar shapes.
Recognise line symmetry and order of rotational symmetry in two dimensions.Includes properties of triangles, quadrilaterals and polygons directly related to their symmetries.
Calculate unknown angles and give simple explanations using the following geometrical properties: • sum of angles at a point = 360° • sum of angles at a point on a straight line = 180° • vertically opposite angles are equal
• angle sum of a triangle = 180° and angle sum of a quadrilateral = 360°.Knowledge of three-letter notation for angles is required, e.g. angle ABC. Candidates are expected to use the correct geometrical terminology when giving reasons for answers.
Calculate unknown angles and give geometric explanations for angles formed within parallel lines: • corresponding angles are equal • alternate angles are equal • co-interior angles sum to 180° (supplementary).
Know and use angle properties of regular polygons. Includes exterior and interior angles, and angle sum.
Calculate unknown angles and give explanations using the following geometrical properties of circles: • angle in a semicircle = 90° • angle between tangent and radius = 90°.
Candidates will be expected to use the geometrical properties listed in the syllabus when giving reasons for answers.

Mensuration

Use metric units of mass, length, area, volume and capacity in practical situations and convert quantities into larger or smaller units
Units include: • mm, cm, m, km • mm^2 , cm^2 , m^2 , km^2 • mm^3 , cm^3 , m^3 • ml, l • g, kg. Conversion between units includes: • between different units of area, e.g. cm^2 ↔ m^2 • between units of volume and capacity, e.g. m^3 ↔ litres.
Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium. Except for area of a triangle, formulas are not given.
Carry out calculations involving the circumference and area of a circle.Answers may be asked for in terms of π. Formulas are given in the List of formulas
Carry out calculations involving arc length and sector area as fractions of the circumference and area of a circle, where the sector angle is a factor of 360°
Carry out calculations and solve problems involving the surface area and volume of a: • cuboid • prism • cylinder • sphere • pyramid • cone.
The following formulas are given in the List : • curved surface area of a cylinder • curved surface area of a cone • surface area of a sphere • volume of a prism • volume of a pyramid • volume of a cylinder • volume of a cone • volume of a sphere.
Carry out calculations and solve problems involving perimeters and areas of: • compound shapes • parts of shapes. Answers may be asked for in terms of π.
Carry out calculations and solve problems involving surface areas and volumes of: • compound solids • parts of solids.e.g. find the volume of half of a sphere.

Trigonometry

Transformations and vectors

Probability

Understand and use the probability scale from 0 to 1.Probability notation is not required
Probabilities should be given as a fraction, decimal or percentage. Problems may require using information from tables, graphs or Venn diagrams (limited to two sets).
Calculate the probability of a single event
Understand that the probability of an event not occurring = 1 – the probability of the event occurring. e.g. The probability that a counter is blue is 0.8. What is the probability that it is not blue?
Understand relative frequency as an estimate of probability. e.g. use results of experiments with a spinner to estimate the probability of a given outcome.
Calculate expected frequencies. e.g. use probability to estimate an expected value from a population. Includes understanding what is meant by fair, bias and random.
Calculate the probability of combined events using, where appropriate: • sample space diagrams • Venn diagrams • tree diagrams. Combined events will only be with replacement.
Venn diagrams will be limited to two sets. In tree diagrams, outcomes will be written at the end of the branches and probabilities by the side of the branches.

Statistics

Classify and tabulate statistical data. e.g. tally tables, two-way tables.
Read, interpret and draw inferences from tables and statistical diagrams.
Compare sets of data using tables, graphs and statistical measures.e.g. compare averages and ranges between two data sets.
Appreciate restrictions on drawing conclusions from given data.
Calculate the mean, median, mode and range for individual data and distinguish between the purposes for which these are used. Data may be in a list or frequency table, but will not be grouped.
Draw and interpret: (a) bar charts (b) pie charts (c) pictograms (d) stem-and-leaf diagrams (e) simple frequency distributions. Includes composite (stacked) and dual (side-byside) bar charts. Stem-and-leaf diagrams should have ordered data with a key
Draw and interpret scatter diagrams. Plotted points should be clearly marked, for example as small crosses (×).
Understand what is meant by positive, negative and zero correlation.
Draw by eye, interpret and use a straight line of best fit. A line of best fit: • should be a single ruled line drawn by inspection
• should extend across the full data set • does not need to coincide exactly with any of the points but there should be a roughly even distribution of points either side of the line over its entire length

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Fee:Free
Lessons:155
Level:All Levels
Last Updated:20/08/2025

Mathematics – 0580

Students study the following topics

1. Number

2. Algebra and graphs

3. Coordinate geometry

4. Geometry

5. Mensuration

6. Trigonometry

7. Transformations and vectors

8. Probability

9. Statistics

Course Content

Number

Identify and use: • natural numbers • integers (positive, zero and negative) • prime numbers • square numbers • cube numbers • common factors • common multiples • rational and irrational numbers • reciprocals.

Example tasks include: • convert between numbers and words, e.g. six billion is 6000000000 10007 is ten thousand and seven • express 72 as a product of its prime factors

• find the highest common factor (HCF) of two numbers • find the lowest common multiple (LCM) of two numbers.

Understand and use set language, notation and Venn diagrams to describe sets and represent relationships between sets.

Venn diagrams are limited to two or three sets. The following set notation will be used: • n(A) Number of elements in set A • ∈ “… is an element of …” • ∉ “… is not an element of …” • A′ Complement of set A

• ∅ The empty set • Universal set • A ⊆ B A is a subset of B • A ⊈ B A is not a subset of B • A ∪ B Union of A and B • A ∩ B Intersection of A and B.

Example definition of sets: A = {x: x is a natural number} B = {(x, y): y = mx + c} C = {x: a ⩽ x ⩽ b}

Calculate with the following: • squares • square roots • cubes • cube roots • other powers and roots of numbers.

Includes recall of squares and their corresponding roots from 1 to 15, and recall of cubes and their corresponding roots of 1, 2, 3, 4, 5 and 10, e.g.: • Write down the value of (169)^1/2 • Work out 5^2x^3(8)^1/3 .

1 Use the language and notation of the following in appropriate contexts: • proper fractions • improper fractions • mixed numbers • decimals • percentages.

2 Recognise equivalence and convert between these forms.

Candidates are expected to be able to write fractions in their simplest form. Recurring decimal notation is required, e.g. • 0.1 7 = 1777…. • 0.123 =0.1232323…• 0.123 =0.123123…

Includes converting between recurring decimals and fractions and vice versa, e.g. write 0.17 as a fraction.

Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ⩾ and ⩽.

Use the four operations for calculations with integers, fractions and decimals, including correct ordering of operations and use of brackets.

Includes: • negative numbers • improper fractions • mixed numbers • practical situations, e.g. temperature changes.

Understand and use indices (positive, zero, negative, and fractional).

Understand and use the rules of indices.

• find the value of 7^ –2, e.g. find the value of 2^–3 × 2^4 , (2^3 )^2 , 2^3 ÷ 2^4

Use the standard form A × 10n where n is a positive or negative integer and 1 ⩽ A < 10.

Convert numbers into and out of standard form.

Calculate with values in standard form.

Round values to a specified degree of accuracy

Make estimates for calculations involving numbers, quantities and measurements.

Round answers to a reasonable degree of accuracy in the context of a given problem.

Includes decimal places and significant figures. e.g. write 5764 correct to the nearest thousand. e.g. by writing each number correct to 1 significant figure, estimate the value of 41.3/9.79*0.765

Give upper and lower bounds for data rounded to a specified accuracy.

Find upper and lower bounds of the results of calculations which have used data rounded to a specified accuracy

e.g. write down the upper bound of a length measured correct to the nearest metre. Example calculations include:

• calculate the upper bound of the perimeter or the area of a rectangle given dimensions measured to the nearest centimetre • find the lower bound of the speed given rounded values of distance and time

Understand and use ratio and proportion to: • give ratios in their simplest form • divide a quantity in a given ratio • use proportional reasoning and ratios in context.

e.g. 20:30:40 in its simplest form is 2:3:4. e.g. adapt recipes; use map scales; determine best value.

Use common measures of rate.

e.g. calculate with: • hourly rates of pay • exchange rates between currencies • flow rates • fuel consumption

Apply other measures of rate.

e.g. calculate with: • pressure • density • population density. Required formulas will be given in the question.

Solve problems involving average speed.

Knowledge of speed/distance/time formula is required. e.g. A cyclist travels 45km in 3 hours 45 minutes. What is their average speed? Notation used will be, e.g. m/s (metres per second), g/cm3 (grams per cubic centimetre).

Calculate a given percentage of a quantity

Express one quantity as a percentage of another

Calculate percentage increase or decrease.

Calculate with simple and compound interest.

Problems may include repeated percentage change. Formulas are not given.

Calculate using reverse percentages.

e.g. find the cost price given the selling price and the percentage profit. Percentage calculations may include: • deposit • discount • profit and loss (as an amount or a percentage) • earnings • percentages over 100%.

Use a calculator efficiently

e.g. know not to round values within a calculation and to only round the final answer.

Enter values appropriately on a calculator.

e.g. enter 2 hours 30 minutes as 2.5 hours or 2° 30’ 0’’.

Interpret the calculator display appropriately.

e.g. in money 4.8 means $4.80; in time 3.25 means 3 hours 15 minutes.

Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units.

1 year = 365 days

Calculate times in terms of the 24-hour and 12-hour clock

In the 24-hour clock, for example, 3.15 a.m. will be denoted by 0315 and 3.15 p.m. by 1515

Includes problems involving time zones, local times and time differences.

Calculate with money.

Convert from one currency to another.

Use exponential growth and decay.

e.g. depreciation, population change. Knowledge of e is not required.

Algebra and graphs

Know that letters can be used to represent generalised numbers.

Substitute numbers into expressions and formulas.

Simplify expressions by collecting like terms.

Simplify means give the answer in its simplest form, e.g. 2a + 3b + 5a – 9b = 7a – 6b

Expand products of algebraic expressions.

e.g. expand 3x(2x – 4y). Includes products of two brackets involving one variable, e.g. expand (2x + 1)(x – 4).