List of topics in Unit 3 - Foundation.

Questions and information 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 and various other websites.

 

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

1.2.1    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

1.3.1    the notation for positive integral indices

1.4.1    how to find equivalent fractions

1.4.2     the equivalences between fractions, decimals 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

1.4.8    calculate fractional and percentage changes (increase and decrease)

1.4.9  understand and use multipliers

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

1.5.3    add, subtract, multiply and divide fractions

1.5.3    add, subtract, multiply and divide negative numbers

1.5.5    use a calculator efficiently and effectively, including:

1.5.5(a)    order of operations

1.5.5(b)    addition, subtraction, multiplication and division

1.5.5(c)    square, cube and other powers

1.5.5(d)    square root and cube root

1.5.5(e)    brackets

1.5.5(f)    other appropriate functions

1.6.1    round an answer to a reasonable degree of accuracy in light of the context

1.6.5    premature rounding in problems involving multiple steps may affect the accuracy of the final answer

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

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

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

2.2.9    solve a range of cubic equations by trial and improvement methods, justifying the accuracy of the solution

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

3.2.1     measure and accurately draw:

3.2.1(a)    a straight line

3.2.1(b)    a circle or arc of a circle

3.2.1(c)    an angle of any size

3.2.2     accurately draw, using a ruler and a protractor:

3.2.2(a)    an angle bisector

3.2.2(b)    a perpendicular line bisector

3.2.2(c)      2-D shapes given side lengths and, if appropriate, angles (compasses will be required to draw triangles when three side lengths are known)

3.2.2(d)    the locus of a point which moves such that it satisfies certain conditions, including:

3.2.2(d) i.  a given distance from a fixed point or line (compasses will be required)

3.2.2(d) ii.  equidistant from two fixed points or lines

3.2.3    solve problems involving intersecting loci in two dimensions – this will include the identification of regions that satisfy certain conditions

3.3.1    read and interpret scales

3.3.2    use and interpret maps

3.3.3    interpret and produce scale drawings; scales may be written in the form 1 cm represents 5 m, or 1:500

3.3.4    understand 3-figure bearings and use this knowledge to interpret and draw bearings

3.3.5    interpret plans and elevations of 3-D shapes

3.3.6    interpret 2-D representations of 3-D shapes on isometric paper

3.3.7     interpret nets of 3-D shapes

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

3.5.1    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

3.5.4    convert between units of time

3.5.6    make sensible estimates of metric measurements in everyday situations, recognising the appropriateness of units in different contexts

3.5.8     recall and use compound measures for speed and fuel consumption. Units include: m/s, km/h, mph and mpg

3.5.9     recall and use other compound measures, including density, population density and flow rates. Units include kg/m^3, g/cm^3, population per km^2, m^3 per hour, litres per second

3.6.1     2-D shapes:

3.6.1(a)    Estimate of the area of an irregular shape drawn on a square grid

3.6.1(b)      Perimeter and area of a square, rectangle, triangle, parallelogram, trapezium, circle, semicircle and a composite shape

3.6.3     3-D shapes:

3.6.3(a)      Surface area, cross-sectional area, volume and capacity of a cube, cuboid, prism, and a composite solid

3.6.3(b)      Cross-sectional area, volume and capacity of a cylinder

3.7.1    use Pythagoras’ theorem in 2-D, including reverse problems

3.9.1    identify congruent and similar shapes

3.9.2    use the knowledge that, for two similar 2-D or 3-D shapes, one is an enlargement of the other

4.1.1     understand and use the statistical problem solving process: specify the problem/planning; collect, process and represent data; interpret and discuss results, including limitations of data and anomalies

4.1.2    specify and test hypotheses, taking account of the limitations of the data available

4.1.3    design and criticise questions for a questionnaire, including notions of fairness and bias

4.1.4    consider the effect of sample size and other factors that affect the reliability of data and conclusions drawn

4.1.5    understand and use tallying methods

4.1.6    understand and use frequency tables

4.1.7    sort, classify and tabulate qualitative (categorical) data, discrete or continuous quantitative data

4.1.8    group discrete or continuous data into class intervals of equal or unequal widths

4.2.1     construct and interpret pictograms, bar charts and pie charts for qualitative data and for discrete quantitative data

4.2.2    construct and interpret vertical line diagrams for discrete data

4.2.3    construct line graphs for the values of a variable at different points in time; understand that intermediate values in a line graph may or may not have meaning

4.2.4    construct scatter diagrams for data on paired variables

4.2.5    draw 'by eye' a line of 'best fit' and understand and interpret what this represents. In questions where the mean point has been given, calculated or plotted, candidates will be expected to draw the line of 'best fit' through that point

4.2.6    interpret and draw conclusions from scatter diagrams; use terms such as positive correlation, negative correlation, little or no correlation

4.2.7    appreciate that correlation does not imply causality

4.2.8    find the mean, median mode and range of a list of values

4.2.9    construct and interpret grouped frequency diagrams and frequency polygons

4.2.10  find the mean, median, mode and range for a discrete (ungrouped) frequency distribution

4.2.11  find an estimate for the mean of a grouped frequency distribution

4.2.13  determine the modal category for qualitative data and modal class for grouped data

4.2.14  determine the group containing the median for grouped data

4.2.15  select, calculate and estimate appropriate measures of central tendency (i.e. the mean, median or the mode)

4.2.16   compare data distributions using one measure of central tendency and/or one measure of spread

4.2.21  recognise that graphs may be misleading

4.2.22  look at data to find patterns and exceptions

4.2.23  draw inferences and conclusions from summary measures and data representations, relate results back to the original problem

 

List of topics in Unit 3 - Higher.

Questions and information linked to some topics.

Foundation content also needed for Higher.

 

 

1.3.2    the notation for zero and negative indices

1.3.6    convert ordinary numbers into and out of standard form

1.3.7    use numbers written in standard form

1.5.5     use a calculator efficiently and effectively, including:

1.5.5(g)    standard form

1.5.6    use the trigonometric functions on a calculator efficiently and effectively

1.9.4    manipulate and simplify numerical expressions involving surds

1.9.6    use pi in exact calculations

1.9.7    use surds in exact calculations

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

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

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

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

2.2.10 construct and use equations that describe direct and inverse proportion

2.5.3  construct and use tangents to curves to estimate rates of change for non-linear functions, and use appropriate compound measures to express results, including finding velocity in distance-time graphs and acceleration in velocity-time graphs

2.5.4  interpret the meaning of the area under a graph, including the area under velocity-time graphs and graphs in other practical contexts

2.5.5  use the trapezium rule to estimate the area under a curve

3.5.10 convert between units of area and volume

3.6.2    2-D shapes:

3.6.2(a)    Length of a circular arc

3.6.2(b)      Area of a sector and a segment

3.6.3     3-D shapes:

3.6.3(c)    Surface area of a cylinder

3.6.3(d)      Surface area, volume and capacity of a sphere, cone, pyramid and a compound solid

3.6.3(d)      Volume and capacity of a sphere, cone, pyramid and a compound solid

3.7.2    use Pythagoras’ theorem in 3-D, including reverse problems

3.7.3  use trigonometric relationships in right-angled triangles to solve problems, including those involving bearings and angles of elevation and depression

3.7.4    calculate a side or an angle of a right-angled triangle in 2-D and 3-D

3.7.5    extend trigonometry to angles of any size

3.7.6    apply knowledge of trigonometry with angles of any size to the solution of problems in 2-D or 3-D, including appropriate use of the sine rule and cosine rule 

3.7.7    use the formula: area of a triangle = ½absinC

3.7.8    sketch, understand the behaviour of, and use the graphs of trigonometric functions

3.9.3    use the knowledge that, in similar shapes, corresponding dimensions are in the same ratio

3.9.4    use the knowledge that, in similar and congruent shapes, corresponding angles are equal

3.9.5    use the relationships between the ratios of lengths, areas, volumes and capacities of similar shapes

3.9.6    understand and use the following conditions to prove the congruence of triangles using formal arguments:

3.9.6(a)    side-side-side (SSS)

3.9.6(b)    side-angle-side (SAS)

3.9.6(c)    angle-angle-side (AAS)

3.9.6(d)    right angle-hypotenuse-side (RHS)

4.2.12 find an estimate for the median of a grouped frequency distribution.

4.2.17 select, calculate and estimate appropriate measures of spread, including the range and interquartile range applied to discrete, grouped and continuous data

4.2.18 construct and interpret cumulative frequency tables and diagrams, including estimating the median, interquartile range and other percentages

4.2.19 interpret and use box-and-whisker diagrams to compare distributions

4.2.20 construct and interpret histograms with unequal class widths, including calculating the median and other percentages of the distribution