SecondaryCode 4024
Mathematics
68 topics and 153 objectives, each one something you should be able to do.
Written by Kindred in its own plain words. Your syllabus is still the official list, so check it for anything exact.
What this subject asks you to be able to do
1.1Types of number1 objective
- Identify and work with these kinds of number: natural numbers; integers, whether positive, zero or negative; prime, square and cube numbers; rational and irrational numbers; reciprocals; and common factors and common multiples.
1.2Sets1 objective
- Understand and use set language and notation, alongside Venn diagrams, to describe sets and show how they relate to one another.
1.3Powers and roots1 objective
- Work out results involving squaring, taking square roots, cubing, taking cube roots, and any further powers and roots of any number.
1.4Fractions, decimals and percentages4 objectives
- Use the mathematical language and notation that go with proper fractions, improper fractions, mixed numbers, decimals and percentages, in contexts where they are appropriate.
- Recognise when two of these forms are equivalent, and convert from any one form to another.
- Write each fraction so that it is in simplest form.
- Convert from recurring decimals to fractions and back again.
1.5Ordering1 objective
- Order quantities by magnitude, and show a good working knowledge of the symbols =, ≠, >, <, ⩾ and ⩽.
1.6The four operations1 objective
- Apply addition, subtraction, multiplication and division when calculating with integers, fractions and decimals, including doing the operations in the right order and using brackets properly.
1.7Indices I2 objectives
- Know how to work with indices, covering positive, zero, negative and fractional powers.
- Know the rules of indices and how to apply them.
1.8Standard form3 objectives
- Apply the standard form A × 10n, where n is an integer that can be positive or negative and 1 ⩽ A < 10.
- Convert ordinary numbers into standard form, and numbers in standard form back into ordinary ones.
- Work out results involving values written in standard form.
1.9Estimation3 objectives
- Apply rounding to values so they match a stated level of accuracy.
- Make estimates when carrying out calculations that involve numbers, quantities and measurements.
- Give answers rounded to a sensible level of accuracy for the situation described in a given problem.
1.10Limits of accuracy2 objectives
- Give the upper and lower bounds of figures that have been rounded to a given level of accuracy.
- Work out the upper and lower bounds for the outcomes of calculations in which the input data were rounded to a given accuracy.
1.11Ratio and proportion1 objective
- Understand ratio and proportion and make use of them to express ratios in their lowest terms, split a quantity according to a given ratio, apply proportional reasoning, and work with ratios in practical contexts.
1.12Rates3 objectives
- Use the common ways of measuring a rate.
- Apply rate measures other than the common ones.
- Solve questions in which average speed features.
1.13Percentages5 objectives
- Find what a specified percentage of a quantity is.
- Express how large one quantity is, as a percentage, compared with another.
- Find the percentage by which a quantity increases or decreases.
- Work out answers to problems involving simple and compound interest.
- Calculate using reverse percentages.
1.14Using a calculator3 objectives
- Use a calculator efficiently.
- Input numbers correctly into a calculator.
- Interpret what a calculator's display shows, in a sensible way.
1.15Time3 objectives
- Work out answers involving time given in seconds (s), minutes (min), hours (h), days, weeks, months and years, including how each unit relates to the others.
- Work out times using the 24-hour clock and the 12-hour clock.
- Read clocks and timetables.
1.16Money2 objectives
- Calculate with money.
- Convert an amount of money from one currency into another.
1.17Exponential growth and decay1 objective
- Apply exponential models to situations involving growth and decay.
1.18Surds2 objectives
- Understand surds and how to employ them, including the simplification of expressions.
- Rationalise the denominator.
2.1Introduction to algebra2 objectives
- know that letters may stand in for generalised numbers
- Put numbers in place of letters within expressions and formulas.
2.2Algebraic manipulation5 objectives
- Simplify an expression by grouping its like terms together.
- Expand the product formed when algebraic expressions are multiplied.
- Factorise by finding the common factors of the terms and taking them out.
- Factorise expressions in any of these forms: ax + bx + kay + kby, or a2x2 − b2y2, or a2 + 2ab + b2, or ax2 + bx + c, or ax3 + bx2 + cx.
- Complete the square on expressions written as ax2 + bx + c.
2.3Algebraic fractions2 objectives
- Manipulate algebraic fractions.
- Factorise rational expressions, then cancel them down to their simplest form.
2.4Indices II2 objectives
- Know how to work with indices, covering positive, zero, negative and fractional powers.
- Know the rules of indices and how to apply them.
2.5Equations6 objectives
- Construct an expression, an equation or a formula.
- Solve a linear equation that has a single unknown.
- Solve fractional equations whose denominators are numbers or linear algebraic expressions.
- Solve a pair of linear simultaneous equations to find both unknowns.
- Solve a quadratic equation in each of three ways: by factorising, by completing the square, and with the quadratic formula.
- Rearrange formulas to make a different variable the subject.
2.6Inequalities4 objectives
- Represent inequalities and make sense of them, including when drawn on a number line.
- Construct linear inequalities, then solve them and make sense of the answers.
- Represent linear inequalities with two variables by graphing them, and interpret the results.
- State the inequalities that together mark out a region you are given.
2.7Sequences3 objectives
- Continue a sequence of numbers or a pattern that has been provided.
- Recognise the patterns a sequence follows, including its term-to-term rule, as well as how separate sequences relate to each other.
- Determine the nth term of sequences and make use of it.
2.8Proportion1 objective
- Express direct and inverse proportion as algebraic relationships, then use that algebraic form to work out unknown quantities.
2.9Graphs in practical situations4 objectives
- Use real-life graphs, including travel graphs and conversion graphs, to read and interpret what they show.
- Draw a graph using the data supplied.
- Use rate of change when working on simple problems in kinematics involving a distance–time or speed–time graph, and acceleration or deceleration.
- Work out the distance covered by finding the area beneath a speed–time graph.
2.10Graphs of functions4 objectives
- Construct tables of values for functions of these forms, then draw, recognise and interpret their graphs: axn (also sums made of no more than three such terms) and abx + c, with n = −2, −1, 2 − 1, 0, 2 1, 1, 2, 3, where a and c may be any rational numbers and b any positive integer.
- Solve related equations using graphs, including finding roots from a graph and interpreting them.
- Draw graphs that model problems of exponential growth and decay, and interpret them.
- Estimate the gradient of a curve by drawing a tangent to it.
2.11Sketching curves5 objectives
- Recognise and interpret, as well as sketch, graphs for functions of these types: (a) linear (b) quadratic (c) cubic (d) reciprocal (e) exponential.
- The functions covered take the forms ax + by = c, y = ax² + bx + c, y = ax³ + b, y = ax³ + bx² + cx, y = a/x + b and y = arx + b, with a, b and c rational numbers and r a positive rational number.
- Students must know about turning points, roots and symmetry.
- Students must know about vertical and horizontal asymptotes.
- Students must locate the turning points of quadratic functions by completing the square.
2.12Functions3 objectives
- Understand what functions are, what their domain and range mean, and how to apply function notation.
- Understand how to determine inverse functions, written f –1(x).
- Put together composite functions according to the definition gf(x) = g(f(x)).
3.1Coordinates1 objective
- Apply and make sense of Cartesian coordinates in two dimensions.
3.2Drawing linear graphs1 objective
- Plot the graph of a straight line from a linear equation.
3.3Gradient of linear graphs2 objectives
- Work out the gradient of any straight line.
- Work out a straight line's gradient given the coordinates of any two points it passes through.
3.4Length and midpoint2 objectives
- Work out, for a line segment, its length.
- Work out, for a line segment, the coordinates of its midpoint.
3.5Equations of linear graphs1 objective
- Interpret a straight-line graph, then find the equation that describes it.
3.6Parallel lines1 objective
- Determine the gradient, along with the equation, of a straight line that is parallel to a line already provided.
3.7Perpendicular lines1 objective
- Work out the gradient and the equation of a straight line that meets a stated line at right angles.
4.1Geometrical terms3 objectives
- Use and interpret each of these geometrical terms: right, acute, obtuse and reflex angles; interior and exterior angles; bearing; point, vertex, line and plane; parallel and perpendicular lines, and the perpendicular bisector; similar, congruent and scale factor.
- Apply and make sense of the language relating to triangles, special quadrilaterals, polygons, nets and solids.
- Use and interpret the terms that describe a circle.
4.2Geometrical constructions3 objectives
- Measure lines and angles, and also draw them.
- Construct a triangle from the lengths of its three sides, with only a ruler and a pair of compasses.
- Draw nets, put them to use, and interpret them.
4.3Scale drawings2 objectives
- Draw scale drawings and then interpret them.
- Use three-figure bearings and interpret them.
4.4Similarity3 objectives
- Work out unknown lengths in similar shapes.
- Apply the links between length and area in similar figures, and between length, surface area and volume in similar solids.
- Solve problems where similarity is involved, and explain the reasoning in simple terms.
4.5Symmetry2 objectives
- Recognise line symmetry in a two-dimensional shape, and the order of its rotational symmetry.
- Recognise the ways in which prisms, cylinders, pyramids and cones are symmetrical.
4.6Angles3 objectives
- Work out unknown angles and give simple reasons for them, using these geometrical facts: angles around a point, sum = 360°; angles at one point on a straight line, sum = 180°; vertically opposite angles are equal; a triangle's angle sum = 180°; a quadrilateral's angle sum = 360°.
- Work out unknown angles between parallel lines and justify them geometrically, using the facts that corresponding angles are equal, that alternate angles are also equal, and that co-interior angles add up to 180° (supplementary).
- Know and apply the angle rules that hold for regular and irregular polygons.
4.7Circle theorems I1 objective
- Work out unknown angles and give reasons, using these circle facts: angle in a semicircle = 90°; angle between a tangent and a radius = 90°; the angle at the centre is double that at the circumference; any two angles in the same segment of the circle are equal; a cyclic quadrilateral has opposite angles that total 180° (they are supplementary); and the alternate segment theorem.
4.8Circle theorems II1 objective
- use these symmetry properties of circles: any chords of identical length are equidistant from the centre, a chord's perpendicular bisector runs through the centre, and tangents drawn from an external point have equal lengths
5.1Units of measure1 objective
- Apply metric units of mass, length, area, volume and capacity to real-world problems and change quantities into bigger or smaller units
5.2Area and perimeter1 objective
- Carry out the working needed to find the perimeter and area of rectangles, triangles, parallelograms and trapezia
5.3Circles, arcs and sectors2 objectives
- Carry out the working needed to find a circle's circumference and area
- Carry out the working needed to find arc lengths and sector areas as fractions of a circle's circumference and area
5.4Surface area and volume1 objective
- Carry out computations and tackle questions in which surface area and volume must be found for a cuboid, prism, cylinder, sphere, pyramid, cone
5.5Compound shapes and parts of shapes2 objectives
- Carry out the working and solve problems for the perimeter and area of compound shapes and of parts of shapes
- Carry out the working and solve problems for the surface area and volume of compound solids and of parts of solids
6.1Pythagoras’ theorem1 objective
- Understand and apply Pythagoras’ theorem
6.2Right-angled triangles4 objectives
- Know the sine, cosine and tangent ratios of acute angles, and apply them when calculating the lengths of sides and the sizes of angles in a right-angled triangle
- Solve two-dimensional problems by means of Pythagoras’ theorem and trigonometry
- Know that a point is closest to a line when the distance is measured along the perpendicular to that line
- Carry out the working for problems with angles of elevation and angles of depression
6.3Non-right-angled triangles2 objectives
- apply the sine rule and the cosine rule when working with side lengths and angles in any triangle
- apply the formula for a triangle's area: area of triangle = 2 1 ab sinC
6.4Pythagoras’ theorem and trigonometry in 3D1 objective
- Carry out the working and solve problems in three-dimensional settings with Pythagoras’ theorem and trigonometry, including finding the angle a line makes with a plane
7.1Transformations1 objective
- Recognise, describe and draw these transformations of a shape: a reflection in a straight line; a rotation through a multiple of 90° about a centre; an enlargement with a given centre and scale factor; and a translation by a vector.
7.2Vectors in two dimensions3 objectives
- describe a translation by means of a vector denoted by x y J L K K N P O O, AB or a
- Add and subtract vectors
- Work out scalar multiples of a vector
7.3Magnitude of a vector1 objective
- Work out the magnitude of a vector x y J L K K N P O O, using the expression xy 22 +
7.4Vector geometry4 objectives
- Represent a vector by drawing it as a directed line segment
- Use position vectors
- Apply vector sums and differences, involving two or more vectors, to write given vectors using two coplanar vectors as building blocks
- Use vectors for reasoning and for solving problems in geometry
8.1Introduction to probability4 objectives
- Understand and apply the scale of probabilities that runs from 0 to 1
- Understand and apply the conventions of notation used in probability
- Work out the probability of one individual event
- Understand that, for any event, the probability that it does not happen = 1 – the probability that it does happen
8.2Relative and expected frequencies2 objectives
- Appreciate that relative frequency can be used as an estimate of probability
- Calculate expected frequencies
8.3Probability of combined events1 objective
- Work out probabilities for combined events, making use of sample space diagrams, Venn diagrams and tree diagrams as suitable.
9.1Classifying statistical data1 objective
- Classify statistical data and tabulate it.
9.2Interpreting statistical data3 objectives
- Read tables and statistical diagrams, interpret them, and draw inferences from them.
- Compare data sets with one another by means of statistical measures, tables and graphs.
- Understand the limits on what conclusions can be drawn from the data provided.
9.3Averages and measures of spread3 objectives
- Find the mean, median, mode and range of individual data, and tell apart the different purposes these measures are used for.
- Work out an estimated mean for data that are grouped, whether discrete or continuous.
- Identify, in a grouped frequency distribution, which class is the modal class.
9.4Statistical charts and diagrams1 objective
- Draw pictograms, bar charts, pie charts and simple frequency distributions, and interpret what each one shows.
9.5Scatter diagrams3 objectives
- Plot scatter diagrams and interpret them.
- Understand the meaning of positive, negative and zero correlation.
- Sketch by eye a straight line of best fit, then interpret and use it.
9.6Cumulative frequency diagrams2 objectives
- Draw up cumulative frequency tables and diagrams, and interpret what they show.
- Estimate, from a cumulative frequency diagram, the median, quartiles, percentiles and interquartile range, and interpret each of them.
9.7Histograms2 objectives
- Draw and interpret histograms.
- Calculate with frequency density.
Kindred builds your map from these, so you can see what you've covered and what's still to do.