SecondaryCode 4029
Mathematics
68 topics and 146 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 the following, and work with them: integers (positive, zero and negative); natural numbers; prime, square and cube numbers; reciprocals; rational and irrational numbers; common factors and common multiples
1.2Sets1 objective
- Understand set language and notation, and use them, with Venn diagrams, to describe sets and the relationships between them
1.3Powers and roots1 objective
- Work out values involving squares, square roots, cubes, cube roots, and other powers and roots of numbers
1.4Fractions, decimals and percentages2 objectives
- Apply the vocabulary and notation of proper fractions, improper fractions, mixed numbers, decimals and percentages where the context calls for them
- Recognise when two of these forms have the same value, and switch from one form to another
1.5Ordering1 objective
- Order quantities by their magnitude, and show that you can read and use the symbols =, ≠, >, <, ⩾ and ⩽
1.6The four operations1 objective
- Apply the four operations when calculating with integers, fractions and decimals, including doing operations in the correct order and using brackets
1.7Indices I2 objectives
- Understand what positive, zero, negative and fractional indices mean, and work with them
- Understand the rules of indices and put them to use
1.8Standard form3 objectives
- Use standard form, written A × 10n, in which n is any positive or negative integer and 1 ⩽ A < 10
- Convert numbers to standard form, and from standard form back to ordinary numbers
- Work out answers involving values written in standard form
1.9Estimation3 objectives
- Round a value to the degree of accuracy asked for
- Make a rough estimate of the answer to a calculation with numbers, quantities and measurements
- Round answers to whatever degree of accuracy the problem's context makes reasonable
1.10Limits of accuracy2 objectives
- Give the lower and upper bounds of data that have been rounded to a stated accuracy
- Find the lower and upper bounds of a calculated result when the data used in the calculation were rounded to a stated accuracy
1.11Ratio and proportion1 objective
- Understand ratio and proportion and use them to: divide a quantity in the ratio given, write a ratio in its simplest form, and apply proportional reasoning and ratios to problems set in context
1.12Rates3 objectives
- Use the rate measures that are most commonly encountered
- Apply the other kinds of rate measure
- Solve questions where average speed is involved
1.13Percentages5 objectives
- Determine what a particular percentage of a quantity comes to
- Express any quantity as a percentage of a second quantity
- Work out a percentage increase or a percentage decrease
- Work out problems involving simple interest 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 screen shows in a sensible way.
1.15Time3 objectives
- Work out problems involving time in seconds (s), minutes (min), hours (h), days, weeks, months, years, including how these units relate to one another.
- Work out times, expressing them in 24-hour or 12-hour clock time.
- 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 a letter can stand for a generalised number.
- Substitute numbers for the letters in an expression or formula.
2.2Algebraic manipulation5 objectives
- Simplify an expression by grouping its like terms together.
- Expand the product formed when algebraic expressions are multiplied.
- Factorise an expression by taking out its common factors.
- Factorise each expression that takes one of these forms: ax2 + bx + c, a2 + 2ab + b2, a2x2 − b2y2, ax + bx + kay + kby, ax3 + bx2 + cx.
- Complete the square on expressions written as ax2 + bx + c.
2.3Algebraic fractions2 objectives
- Manipulate algebraic fractions.
- Factorise rational expressions and write them in their simplest form.
2.4Indices II2 objectives
- Understand what positive, zero, negative and fractional indices mean, and work with them.
- Understand the rules of indices and put them to use.
2.5Equations6 objectives
- Construct equations, formulas and algebraic expressions.
- Solve a linear equation that has a single unknown.
- Solve fractional equations whose denominators are numbers or linear algebraic expressions.
- Solve a pair of simultaneous linear equations with two unknowns.
- Solve quadratic equations using each of three methods: factorising, completing the square, and 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 given region.
2.7Sequences3 objectives
- Continue a sequence of numbers or a pattern that has been provided.
- Recognise the patterns in a sequence, including its term-to-term rule, and see how different sequences relate to one another.
- 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.
- Apply what a rate of change means to simple kinematics, working with distance–time graphs, speed–time graphs, acceleration and deceleration.
- Work out the distance covered by finding the area beneath a speed–time graph.
2.10Graphs of functions4 objectives
- Construct a table of values for each function of the form axn (and sums of no more than three such terms) or abx + c, and draw, recognise and interpret its graph, where n = –2, –1, 2 1 − , 0, 2 1 , 1, 2, 3; a and c are rational; and b is a positive integer.
- Solve the related equations from their graphs, including finding the roots graphically and interpreting them.
- Draw and make sense of graphs that model situations of exponential growth and decay.
- Estimate the gradient of a curve by drawing a tangent to it.
2.11Sketching curves1 objective
- Recognise the graphs of linear, quadratic, cubic, reciprocal and exponential functions, and sketch and interpret them.
2.12Functions3 objectives
- Understand what functions are, what their domain and range mean, and how to apply function notation.
- Understand inverse functions, written f –1(x), and find them.
- 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
- Determine a straight line's gradient.
- Work out a straight line's gradient given the coordinates of any two of its points.
3.4Length and midpoint2 objectives
- Calculate how long a line segment is.
- Find a line segment's midpoint and state its coordinates.
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 both the gradient and the equation of a straight line that is perpendicular to a line you are given.
4.1Geometrical terms2 objectives
- Use each of these geometrical terms and interpret it: point, line, plane and vertex; parallel, perpendicular and perpendicular bisector; right, acute, obtuse and reflex angles; interior and exterior angles; bearing; similar, congruent and scale factor.
- Use, and interpret, the vocabulary that describes polygons, triangles, special quadrilaterals, solids and nets.
4.2Geometrical constructions3 objectives
- Measure lines and angles, and also draw them.
- Construct a triangle when you know how long each of its sides is, with a ruler and compasses only.
- 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 make sense of them.
4.4Similarity3 objectives
- Work out the lengths of shapes that are similar.
- Apply the links between length and area in similar figures, and between length, surface area and volume in similar solids.
- Solve problems and offer short explanations which involve similarity.
4.5Symmetry2 objectives
- Recognise, in two-dimensional shapes, any line symmetry and the order of rotational symmetry.
- Recognise which kinds of symmetry cones, cylinders, prisms and pyramids have.
4.6Angles3 objectives
- Work out unknown angles and give simple reasons for them, using these geometrical facts: the sum of the angles round a point = 360°; the sum of the angles at a point on one side of a straight line = 180°; angles that are vertically opposite are equal; in a triangle, the angle sum = 180°; in a quadrilateral, the angle sum = 360°.
- Work out missing angles and give geometric reasons for angles formed between parallel lines, where corresponding and alternate angles are each equal, and co-interior angles total 180° (supplementary).
- Know the angle properties of polygons, both regular and irregular, and use them. Three-letter notation for angles, e.g. angle ABC, must be understood. Reasons for answers should use correct geometrical terms. This covers interior and exterior angles and the angle sum.
4.7Circle theorems I1 objective
- Work out unknown angles and give reasons, using these circle properties: the angle in a semicircle = 90°; the angle between a tangent and a radius = 90°; the angle at the centre is double the angle at the circumference; in the same segment, the angles are equal; in a cyclic quadrilateral, opposite angles add up to 180° (supplementary); the alternate segment theorem. Reasons for answers should quote the geometrical properties set out in this course.
4.8Circle theorems II1 objective
- Use these symmetry properties of circles: chords of equal length are equidistant from the centre; a chord's perpendicular bisector goes through the centre; the two tangents drawn to a circle from an external point have equal length. Reasons for answers should quote the geometrical properties set out in this course.
5.1Units of measure1 objective
- Use metric units for mass, length, area, volume and capacity in real-life problems, and convert a quantity to a larger or a smaller unit. The units covered are: mm, cm, m, km, mm², cm², m², km², mm³, cm³, m³, ml, l, g, kg. Conversions cover changing between units of area, e.g. cm² ↔ m², and between units of volume and units of capacity, e.g. m³ ↔ litres.
5.2Area and perimeter1 objective
- Carry out calculations for the perimeter and area of rectangles, triangles, parallelograms and trapezia. Except for the area of a triangle, students are not handed any formulas.
5.3Circles, arcs and sectors2 objectives
- Carry out computations on a circle's circumference and the area it encloses.
- Carry out calculations that treat an arc length as a fraction of the circumference and a sector area as a fraction of the area of the circle. You may be asked to leave answers in terms of π. The formulas are printed in the List of formulas. Both minor and major sectors are covered.
5.4Surface area and volume1 objective
- Carry out calculations and solve problems on the surface area and volume of a cuboid, prism, cylinder, sphere, pyramid or cone. You may be asked to leave answers in terms of π. The List of formulas gives the curved surface area of a cylinder and of a cone, the surface area of a sphere, and the volume of a prism, pyramid, cylinder, cone and sphere. A prism here is any solid whose cross-section is uniform, e.g. a cylindrical sector.
5.5Compound shapes and parts of shapes2 objectives
- Carry out working to find the perimeters and areas of compound shapes and of parts of shapes, and tackle problems involving them.
- Carry out calculations and solve problems about the volume and surface area of compound solids, and of parts of solids. You may be asked to leave answers in terms of π. e.g. work out the surface area and the volume of a frustum.
6.1Pythagoras’ theorem1 objective
- Know Pythagoras’ theorem and put it to use.
6.2Right-angled triangles4 objectives
- Know the sine, cosine and tangent of an acute angle as ratios, and use them to find sides and angles in a right-angled triangle.
- Solve two-dimensional questions with the help of Pythagoras’ theorem and trigonometry.
- Know that a point's perpendicular distance to a line is the least distance between them.
- Carry out calculations with angles of elevation and of depression. Angles are stated in degrees, and answers must also be in degrees, rounded to one decimal place. A question may also call for bearings.
6.3Non-right-angled triangles2 objectives
- Apply the sine and cosine rules to find lengths and angles in triangles of any shape.
- Apply the formula area = ½ ab sinC to find the area of a triangle. Questions can involve the ambiguous case as well as obtuse angles. The List of formulas provides the sine rule, the cosine rule and this area formula.
6.4Pythagoras’ theorem and trigonometry in 3D1 objective
- Carry out working on problems set in three-dimensional space by applying 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: reflection in a straight line; rotation about a centre through a multiple of 90°; enlargement by a scale factor from a given centre; translation by a vector. A question may combine two or more transformations. Draw every straight edge with a ruler. Scale factors can be positive, negative or fractional.
7.2Vectors in two dimensions3 objectives
- Describe a translation by giving its vector, written as (x, y), AB or a.
- Add and subtract vectors.
- Work out a scalar multiple of a vector. In print, vectors appear as AB or a.
7.3Magnitude of a vector1 objective
- Find the magnitude of a vector (x, y), which equals √(x² + y²). Modulus signs mark a magnitude, e.g. |a| for vector a and |AB| for vector AB.
7.4Vector geometry4 objectives
- Represent a vector as a directed line segment.
- Use position vectors.
- Use sums and differences of two or more vectors so that a given vector can be written in terms of a pair of coplanar vectors.
- Use vectors in geometric reasoning and problem solving: for example, show that vectors are parallel or that 3 points are collinear, or solve a vector problem that involves ratio and similarity.
8.1Introduction to probability4 objectives
- Understand the probability scale, which runs from 0 to 1, and use it.
- Understand the notation of probability and work with it.
- Find the probability that a single event happens.
- Understand that the probability of an event not happening = 1 – the probability that it does happen.
8.2Relative and expected frequencies2 objectives
- Know 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 two or more data sets by means of tables, graphs and statistical measures.
- 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 distinguish what each of these measures is used for.
- Work out an estimate of the mean when discrete or continuous data have been grouped.
- Identify the modal class of grouped data presented as a frequency distribution.
9.4Statistical charts and diagrams1 objective
- Draw pictograms, bar charts, pie charts and simple frequency distributions, and interpret them.
9.5Scatter diagrams3 objectives
- Plot scatter diagrams and interpret them.
- Understand the meaning of positive, negative and zero correlation.
- Draw a line of best fit by eye, keeping it straight, then interpret it and use it.
9.6Cumulative frequency diagrams2 objectives
- Draw up cumulative frequency tables and diagrams, and interpret what they show.
- Estimate the median, quartiles, percentiles and interquartile range from a cumulative frequency diagram, and interpret these values.
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.