SecondaryCode 4021
Mathematics
53 topics and 97 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 each of the following and work with it: natural numbers, integers (positive, zero and negative), prime numbers, square numbers, cube numbers, rational and irrational numbers, reciprocals, common factors and common multiples
1.2Sets1 objective
- Understand the language and notation of sets, along with Venn diagrams, and use them all to describe sets
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
- Use the right words and notation for proper fractions, improper fractions, mixed numbers, decimals and percentages, in the contexts where each one fits
- Recognise when two of these forms have the same value, and switch from one form to another
1.5Ordering1 objective
- Put quantities in order of size, and show you can read and use the symbols =, ≠, >, <, ⩾ and ⩽
1.6The four operations1 objective
- Apply addition, subtraction, multiplication and division to integers, fractions and decimals, including doing the operations in the correct order and using brackets
1.7Indices I2 objectives
- Understand, and be able to apply, indices that are positive, zero or negative integers
- Know the rules of indices and how to apply them
1.8Standard form3 objectives
- Use standard form, writing a number as A × 10n, where 1 ⩽ A < 10 and the power n is any integer, positive or negative
- Convert an ordinary number into standard form and back again
- Work out answers involving values written in standard form
1.9Estimation3 objectives
- Round a value to whatever degree of accuracy you are asked for
- Make an estimate of the answer to a calculation, whether it uses numbers, quantities or measurements
- Round each answer to an accuracy that makes sense for the problem it belongs to
1.10Limits of accuracy1 objective
- State the upper and lower bounds of a value once you know the accuracy it was rounded to
1.11Ratio and proportion1 objective
- Understand ratio and proportion and use them to: write a ratio in its simplest form, divide a quantity into parts according to a given ratio, and reason proportionally and use ratios 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
1.13Percentages4 objectives
- Work out how much a stated percentage of a quantity comes to
- Express one quantity, compared with a second one, as a percentage
- Work out percentage changes, both increases and decreases
- Work out problems on simple interest and on compound interest
1.14Using a calculator3 objectives
- Use a calculator efficiently
- Input numbers correctly into a calculator
- Interpret what a calculator's screen shows, reading it the right way
1.15Time3 objectives
- Work out problems involving time in seconds (s), minutes (min), hours (h), days, weeks, months and years, including how one unit relates to another.
- Work out times with the 24-hour clock and with the 12-hour clock.
- Read clocks and timetables.
1.16Money2 objectives
- Calculate with money.
- Convert a sum of money into a different currency.
2.1Introduction to algebra2 objectives
- Know that algebra uses letters to stand for generalised numbers.
- Put numbers in place of letters within expressions and formulas.
2.2Algebraic manipulation3 objectives
- Simplify an expression by gathering its like terms together.
- Expand brackets where algebraic expressions are multiplied together.
- Factorise an expression by taking out its common factors.
2.3Indices II2 objectives
- Understand how to apply indices, covering positive, zero and negative values.
- Understand the rules that govern indices and how to apply them.
2.4Equations4 objectives
- Construct expressions, equations and formulas that are simple in form.
- Solve linear equations that have a single unknown.
- Solve a pair of simultaneous linear equations, finding both unknowns.
- Rearrange a simple formula to make a different letter its subject.
2.5Inequalities1 objective
- Represent inequalities, including those drawn on a number line, and make sense of what they say.
2.6Sequences3 objectives
- Continue the sequence of numbers or pattern supplied.
- Recognise the patterns a sequence follows, including its term-to-term rule, and the links between different sequences.
- Find the nth term of each of these kinds of sequence, and use it: (a) linear (b) simple quadratic (c) simple cubic.
2.7Graphs in practical situations2 objectives
- Use graphs of real-life situations and interpret them, including conversion graphs and travel graphs.
- Draw a graph from a set of data you are given.
2.8Graphs of functions2 objectives
- Construct tables of values, then plot, identify and make sense of graphs of functions in these forms: ax + b, ± x² + ax + b, x/a (x ≠ 0), where a and b stand for integer constants.
- Solve the related equations from their graphs, including finding the roots on a graph and interpreting them.
2.9Sketching curves1 objective
- Recognise, sketch and interpret the graphs of (a) linear and (b) quadratic functions. You need to know about symmetry and roots, but not about turning points.
3.1Coordinates1 objective
- Use Cartesian coordinates for points in two dimensions, and interpret them.
3.2Drawing linear graphs1 objective
- Plot the graph of a straight line from a linear equation.
3.3Gradient of linear graphs1 objective
- Work out how steep a straight line is by finding its gradient.
3.4Equations of linear graphs1 objective
- Interpret the equation y = mx + c of a straight-line graph, and find that equation for a given line.
3.5Parallel lines1 objective
- Determine the gradient, along with the equation, of a straight line that is parallel to a line already provided.
4.1Geometrical terms3 objectives
- Use and interpret each of these terms in geometry: point, line, vertex, parallel, perpendicular, right angle, acute, obtuse and reflex angles, interior and exterior angles, bearing, scale factor, similar, congruent.
- Use the terms that describe triangles, special quadrilaterals, polygons, nets and simple solids, and interpret them.
- Use the terms that go with a circle, and interpret them.
4.2Geometrical constructions3 objectives
- Measure the length of a line and the size of an angle, and draw each of them.
- Construct a triangle when you know how long each side is, using only compasses and a ruler.
- 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 the directions they give.
4.4Similarity1 objective
- Work out the lengths of shapes that are similar to one another.
4.5Symmetry1 objective
- Recognise lines of symmetry and the order of rotational symmetry for two-dimensional shapes.
4.6Angles3 objectives
- Work out missing angles and give short reasons, using these facts about angles: around a point, total = 360°; on a straight line, total = 180°; vertically opposite angles are equal; in a triangle, total = 180°; in a quadrilateral, total = 360°.
- Find missing angles and justify them geometrically for the angles formed where lines are parallel: corresponding angles take the same value, alternate angles are the same size, and co-interior angles total 180° (supplementary).
- Understand and apply the angle facts belonging to regular polygons.
4.7Circle theorems1 objective
- Work out unknown angles and explain them with these facts about circles: the angle in a semicircle = 90°, and the angle between a tangent and a radius = 90°.
5.1Units of measure1 objective
- Use metric units for mass, length, area, volume and capacity in everyday problems, and change a quantity into a larger or smaller unit.
5.2Area and perimeter1 objective
- Carry out calculations of perimeter and area for rectangles, triangles, parallelograms and trapezia.
5.3Circles, arcs and sectors2 objectives
- Carry out computations that concern a circle's circumference and its area.
- Carry out calculations of arc length and sector area by treating each as a fraction of a circle's circumference or area, when the sector angle divides exactly into 360°.
5.4Surface area and volume1 objective
- Carry out calculations of surface area and volume for a cuboid, prism, cylinder, sphere, pyramid and cone, and solve problems about them.
5.5Compound shapes and parts of shapes2 objectives
- Carry out calculations of perimeter and area for compound shapes and for parts of shapes, and solve problems about them.
- Carry out calculations of surface area and volume for compound solids and for parts of solids, and solve problems about them.
6.1Pythagoras’ theorem1 objective
- Know Pythagoras’ theorem and put it to use.
6.2Right-angled triangles2 objectives
- Know what the sine, cosine and tangent of an acute angle are, and use these ratios to work out sides and angles in a right-angled triangle.
- Solve two-dimensional problems by applying Pythagoras’ theorem and trigonometry.
7.1Transformations1 objective
- Recognise, describe and draw each of these transformations of a shape: a reflection in a line that is vertical or horizontal; a rotation through a multiple of 90° about the origin, one of the shape's vertices or the midpoint of one of its edges; an enlargement by a scale factor from a given centre; a translation by a vector.
8.1Introduction to probability3 objectives
- Understand the probability scale, which goes from 0 to 1, and use it.
- Work out the probability for one event on its own.
- Understand that for any event, the probability that it does not occur = 1 – the probability that it does occur.
8.2Relative and expected frequencies2 objectives
- Understand that a relative frequency can be used to estimate a 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
- Sort statistical data into classes and set it out in a table.
9.2Interpreting statistical data3 objectives
- Read tables and statistical diagrams, interpret them, and draw inferences from them.
- Compare data sets with one another, making use of tables, graphs and statistical measures.
- Understand the limits on what conclusions can be drawn from the data provided.
9.3Averages and range1 objective
- Find the mean, median, mode and range of individual data, and distinguish between the uses that each of these measures serves.
9.4Statistical charts and diagrams1 objective
- Draw each of these and interpret it: simple frequency distributions, stem-and-leaf diagrams, pictograms, pie charts and bar charts.
9.5Scatter diagrams3 objectives
- Plot scatter diagrams and interpret them.
- Understand what it means for correlation to be positive, negative or zero.
- Sketch by eye a straight line of best fit, then interpret and use it.
Kindred builds your map from these, so you can see what you've covered and what's still to do.