List of topics in Unit 2 - Foundation.

Knowledge Organisers linked to some topics.

Higher topics are below these - Foundation knowledge is also needed for Higher.

Links will take you to the excellent resources on Corbett Maths.

 

1.1.1    read and write whole numbers of any magnitude expressed in figures or words

1.1.2    round whole numbers to the nearest 10, 100, 1000, etc

1.1.3    understand place value of whole numbers and those written in decimal form

1.1.4     round decimals to the nearest whole number or a given number of decimal places

1.1.5    round numbers to a given number of significant figures

1.1.6     understand, use and order directed numbers

1.1.7     decide whether to round up or down, as appropriate, in a problem

1.1.8     check methods and solutions using appropriate strategies

1.1.9     estimate solutions to numerical calculations by approximating the numbers in the calculations

1.2.1     the common properties of numbers, including knowledge of odd, even, integers, multiples, factors, primes

1.2.2     the meaning of the terms square, square root, cube and cube root.

1.2.3     the meaning of the term reciprocal

1.2.4     express numbers as the product of their prime factors in index form

1.2.5     find the least common multiple (LCM) and highest common factor (HCF) using prime factor decomposition or other appropriate methods

1.2.6     use prime factor decomposition to help solve other numerical problems, including links to square numbers

1.3.1     the notation for positive integral indices

1.3.4     use the rules of indices to perform calculations with numbers written in index form for positive integral indices

1.4.1     how to find equivalent fractions

1.4.2     the equivalences between fractions, decimals and percentages

1.4.3     convert numbers from one form into another

1.4.4     order and compare whole numbers, decimals, fractions and percentages

1.4.5     simplify fractions

1.4.6     express one number as a fraction or percentage of another

1.4.7     find a fraction or percentage of a quantity

1.5.1     understand and use number operations and the relationships between them, including inverse operations and the hierarchy of operations

1.5.2     add, subtract, multiply and divide whole numbers, including large whole numbers

1.5.3     add, subtract, multiply and divide decimals, fractions and negative numbers

1.5.4     understand and use operations written as number machines

1.7.3     use, interpret and produce Venn diagrams

1.8.1     carry out calculations involving knowledge of money; pounds (£) and pence

1.9.1     that recurring decimals are exact fractions, and that some exact fractions are recurring decimals

2.1.1     understand the basic conventions of algebra

2.1.2     substitute positive and negative whole numbers, fractions and decimals into simple formulae and expressions written in words or in symbols

2.1.3     recognise the definitions of the terms equation, expression and formula and be able to distinguish between them.

2.1.5     form and simplify expressions

2.1.6     collect like terms

2.1.7     expand expressions – single bracket

2.1.8     multiply and divide terms by applying rules of indices

2.1.9     simplify algebraic fractions, including the addition and subtraction of fractions with constant terms as the denominators

2.1.13  factorise linear or quadratic expressions that have at least one common factor

2.1.16  change the subject of a formula when the subject appears in one term

2.2.1     form, manipulate and solve linear and other simple equations with whole number and fractional coefficients

2.2.3     form, manipulate and solve simple linear inequalities with whole number and fractional coefficients

2.3.1     recognise, describe and continue patterns in number

2.3.2     describe, in words and symbols, the rule for the next term of a sequence

2.3.3     generate linear and non-linear sequences given the nth term rule

2.3.4     find the nth term of a sequence, given numerically or diagrammatically, where the rule is linear

2.4.1     use coordinates in 4 quadrants

2.4.2     draw, interpret, recognise and sketch the graphs of x = a, y = b, y = ax + b

2.4.3     know and use the form y = mx + c to represent a straight line where m is the gradient of the line, and c is the value of the y-intercept

2.4.4     draw and interpret quadratic graphs of the form y = ax^2 + bx + c, and draw the line y = k in order to solve

ax^2 + bx + c = k

3.1.1     Geometric terms, including:

3.1.1(a)      point, line and plane

3.1.1(b)      horizontal, vertical, diagonal

3.1.1(c)      midpoint

3.1.1(d)      parallel and perpendicular

3.1.1(e)      clockwise and anticlockwise turns

3.1.1(f)      acute, obtuse, reflex, right angle, straight angle, full turn

3.1.1(g)      exterior, interior angles

3.1.1(h)      faces, edges and vertices

3.1.2     Vocabulary and essential properties of 2-D shapes, including:

3.1.2(a)      triangles - scalene, isosceles, equilateral, right-angled

3.1.2(b)      quadrilaterals - square, rectangle, parallelogram, rhombus, kite, trapezium

3.1.2(c)      polygons – including pentagon, hexagon, octagon, regular and irregular

3.1.2(d)      circles - radius, diameter, tangent, circumference, chord, arc, sector, segment

3.1.3     Vocabulary and essential properties of 3-D shapes including cube, cuboid, cylinder, prism, pyramid, cone, sphere, tetrahedron

3.4.1     recall and use the following angle properties:

3.4.1(a)      sum of angles at a point

3.4.1(b)      sum of angles on a straight line

3.4.1(c)      opposite angles at a vertex

3.4.1(d)      alternate, corresponding and interior angles within parallel lines

3.4.1(e)      sum of angles in a triangle

3.4.2     recall and use the following angle properties:

3.4.2(a)      angle properties of right-angled, isosceles and equilateral triangles

3.4.2(b)      the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices

3.4.2(c)      sum of angles in a quadrilateral

3.4.2(d)      angle properties of special quadrilaterals, including rectangles, parallelograms and kites

3.4.3     Polygons:

3.4.3(a)      regular and irregular polygons

3.4.3(b)      sum of exterior angles of a polygon

3.4.3(c)      sum of an interior and exterior angle of a polygon

3.4.3(d)      sum of interior angles of a polygon

3.5.1     Time:

3.5.1(a)      Notation for 12- and 24-hour clock

3.5.1(b)      Seconds in a minute, minutes in an hour, hours in a day, days in a week and months in a year

3.5.2     Metric Units:

·      Standard metric units for length, mass and capacity and the relationships between them

3.5.3     carry out calculations involving time

3.8.1     find coordinates identified by given geometrical information including:

3.8.1(a)      the midpoint of a line

3.8.1(b)      the fourth vertex of a parallelogram

3.8.1(c)      location determined by distance from a given point and angle made with a given line

3.8.2     describe and draw shapes with line symmetry

3.8.3     draw lines of symmetry on a shape

3.8.4     understand order of rotational symmetry and describe and draw shapes with rotational symmetry

3.8.5     describe and draw the following transformations:

3.8.5(a)      reflection in a given line

3.8.5(b)      rotation of 90º or 180º, clockwise or anticlockwise, using a centre of rotation

3.8.5(c)     translation with direction and distance of horizontal and vertical movement

3.8.5(d)     enlargement with a positive integer or a positive, fractional scale factor, and a centre of enlargement

3.8.5(e)     enlargement with a negative scale factor and a centre of enlargement

4.3.1     the vocabulary of probability, including notions of uncertainty and risk

4.3.2     the meaning of the terms 'fair', 'an even chance', 'certain', 'likely', 'unlikely ' and 'impossible'

4.3.3     that the probability scale extends from 0 to 1

4.3.4     that probabilities may be expressed as fractions, decimals or percentages

4.3.5     that the total probability of all the possible outcomes of an experiment is 1

4.3.6     calculate theoretical probabilities based on equally likely outcomes

4.3.7     estimate the probability of an event as the proportion of times it has occurred – link to experimental evidence and relative frequency

4.3.8     draw and interpret a graphical representation of relative frequency against the number of trials and understand that the long-term stability of relative frequency is expected

4.3.9     compare an estimated probability from experimental results with a theoretical probability

4.3.10  understand and use the expected number of successes of an event when an experiment is repeated, and events are equally likely

4.4.1     that if A and B are mutually exclusive events, then the probability of A or B occurring is P(A) + P(B)

4.4.2     that If A and B are independent events, then the probability of A and B occurring is P(A) x P(B)

4.4.3     identify all the outcomes of a combination of experiments, including lists, sample space diagrams, tree diagrams and Venn diagrams

4.4.4     recognise when the addition of probabilities for mutually exclusive events and the multiplication of probabilities for two independent events is needed

 

 

List of topics in Unit 2 - Higher.

Knowledge Organisers linked to some topics.

Foundation content also needed for Higher.

 

1.3.2     the notation for zero and negative indices

1.3.3     the notation for fractional indices

1.3.5     use the rules of indices to perform calculations with numbers written in index form for positive, negative and fractional indices

1.3.6     convert ordinary numbers into and out of standard form

1.3.7     use numbers written in standard form

1.9.2     convert recurring decimals to fractional form

1.9.3     distinguish between rational and irrational numbers

1.9.4     manipulate and simplify numerical expressions involving surds

1.9.5     manipulate and simplify more complex numerical expressions involving surds, including multiplying expressions containing surds and simplifying fractions containing surds by division of common factors

2.1.4     recognise the definition of the term identity and be able to distinguish between identities, equations, expressions and formulae

2.1.10  simplify more complex algebraic fractions, including the addition and subtraction of fractions with linear expressions as denominators

2.1.11  expand two linear expressions in one or two variables

2.1.12  expand two expressions in one variable, where one is linear and the other is quadratic

2.1.14  factorise more complex expressions by the extraction of common factors

2.1.15  factorise quadratic expressions of the form x^2 + ax + b and ax^2 + bx + c, including the difference of two squares

2.1.17  change the subject of a formula when the subject appears in more than one term

2.2.2     form, manipulate and solve more complex linear equations, including equations with more than one fractional term

2.2.4     form, manipulate and solve linear inequalities where the variable appears on both sides of the inequality or where two separate inequalities are written as a double inequality

2.2.5     form, manipulate and solve by factorisation, quadratic equations of the form x^2 + bx + c = 0 or ax^2 + bx + c = 0

2.2.6     form, manipulate and solve two simultaneous linear equations with whole number coefficients by algebraic methods

2.2.7     solve equations involving fractions with linear denominators leading to quadratic or linear equations

2.3.5     find the nth term of a sequence, given numerically or diagrammatically, where the rule is quadratic

2.4.5     use straight line graphs to locate regions given by inequalities

2.4.6     identify the equations of lines parallel or perpendicular to a given line

2.4.7     form, manipulate and solve two simultaneous linear equations with whole number coefficients by graphical methods

2.4.8     draw, interpret, recognise and sketch the graphs of y = ax2 + b, y = (ax + b)(cx + d), y = a/x, y = ax3

2.4.9     draw and interpret graphs of the form y = ax3 + b and y = ax3 + bx2 + cx + d

2.4.10  use a graphical method to solve ax^2 + bx + c = dx + e and ax^3 + bx^2 + cx + d = ex + f

2.4.11  draw and interpret graphs when y is given implicitly in terms of x

3.4.4     Circle theorems:

3.4.4(a)      the tangent at any point on a circle is perpendicular to the radius at that point

3.4.4(b)      the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference

3.4.4(c)      The angle subtended at the circumference by a semicircle is a right angle

3.4.4(d)      angles in the same segment are equal

3.4.4(e)      opposite angles of a cyclic quadrilateral sum to 180°

3.4.4(f)      alternate segment theorem

3.4.4(g)      tangents from an external point are equal in length

3.4.5     construct geometric proofs using angle properties and facts, including circle theorems

3.8.6     describe and draw two successive transformations

4.4.5     recognise when problems involve three independent events, and be able to calculate the required probabilities

4.4.6     recognise when problems involve two or three dependent events, and be able to calculate the required probabilities, including sampling without replacement