Maths 0607 — specification explorer

1. Types of number Notes and examples

• C1.1.1

  Identify and use:

  • natural numbers (0, 1, 2, …)
  • integers (positive, zero and negative)
  • prime numbers
  • square numbers
  • cube numbers
  • triangle numbers
  • common factors
  • common multiples
  • rational and irrational numbers
  • reciprocals.

2. Sets Notes and examples

• C1.2.1Understand and use set language, notation and Venn diagrams to describe sets.

3. Powers and roots Notes and examples

• C1.3.1

  Calculate with the following:

  • squares
  • square roots
  • cubes
  • cube roots
  • other powers and roots of numbers.

4. Fractions, decimals and percentages Notes and examples

• C1.4.1

  Use the language and notation of the following in Candidates are expected to be able to write appropriate contexts: fractions in their simplest form.:

  • proper fractions
  • improper fractions
  • mixed numbers
  • decimals
  • percentages.
• C1.4.2Recognise equivalence and convert between these forms.

5. Ordering Notes and examples

• C1.5.1Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ⩾ and ⩽ .

6. The four operations Notes and examples

• C1.6.1

  Use the four operations for calculations with Includes: integers, fractions and decimals, including correct

  • ordering of operations and use of brackets.

7. Indices I Notes and examples

• C1.7.1Understand and use indices (positive, zero and e.g. find the value of negative integers).
• C1.7.2Understand and use the rules of indices. e.g. find the value of

8. Standard form Notes and examples

• C1.8.1Use the standard form A × 10 where n is a positive or negative integer and 1 ⩽ A < 10 .
• C1.8.2Convert numbers into and out of standard form.
• C1.8.3Calculate with values in standard form. Core candidates are expected to calculate with standard form only on papers where calculators are allowed.

9. Estimation Notes and examples

• C1.9.1Round values to a specified degree of accuracy. Includes decimal places and significant figures. e.g. Write 5764 correct to the nearest thousand.
• C1.9.2Make estimates for calculations involving e.g. By writing each number correct to 1 significant numbers, quantities and measurements. figure, estimate the value of
• C1.9.3Round answers to a reasonable degree of accuracy in the context of a given problem.

10. Ratio and proportion Notes and examples

• C1.10.1

  Understand and use ratio and proportion to: context. value.:

  • give ratios in their simplest form e.g. 20 : 30 : 40 in its simplest form is 2 : 3 : 4.
  • divide a quantity in a given ratio
  • use proportional reasoning and ratios in e.g. adapt recipes; use map scales; determine best

11. Rates Notes and examples

• C1.11.1Use common measures of rate. e.g. calculate with:
• C1.11.2Solve problems involving average speed. Knowledge of speed/distance/time formula is required. e.g. A cyclist travels 45 km in 3 hours 45 minutes. What is their average speed?
• C1.11.3Notation used will be e.g. m/s (metres per second),

12. Percentages Notes and examples

• C1.12.1Calculate a given percentage of a quantity.
• C1.12.2Express one quantity as a percentage of another.
• C1.12.3Calculate percentage increase or decrease.
• C1.12.4Calculate with simple and compound interest.

13. Using a calculator Notes and examples

• C1.13.1Use a calculator efficiently.
• C1.13.2Enter values appropriately on a calculator.
• C1.13.3Interpret the calculator display appropriately.

14. Time Notes and examples

• C1.14.1Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units.
• C1.14.2Calculate times in terms of the 24-hour and 12-hour clock.
• C1.14.3Read clocks and timetables.

15. Money Notes and examples

• C1.15.1Calculate with money.
• C1.15.2Convert from one currency to another.

1. Introduction to algebra Notes and examples

• C2.1.1Know that letters can be used to represent generalised numbers.
• C2.1.2Substitute numbers into expressions and formulas.

2. Algebraic manipulation Notes and examples

• C2.2.1Simplify expressions by collecting like terms. Simplify means give the answer in its simplest form, e.g.
• C2.2.2Expand products of algebraic expressions. e.g. expand
• C2.2.3Includes products of two brackets involving one variable, e.g. expand 3 Factorise by extracting common factors. Factorise means factorise fully, e.g.

3. Algebraic fractions Notes and examples

• C2.3.1Simplify algebraic fractions. Only one step required. e.g. e.g

4. Indices II Notes and examples

• C2.4.1Understand and use indices (positive, zero and e.g. negative integers).
• C2.4.2Understand and use the rules of indices. e.g. simplify:
• C2.4.3Knowledge of logarithms is

5. Equations Notes and examples

• C2.5.1Construct simple expressions, equations and e.g. write an expression for a number that is 2 more formulas. than
• C2.5.2Includes constructing linear simultaneous equations. 2 Solve linear equations in one unknown. Examples include:
• C2.5.3Solve simultaneous linear equations in two unknowns.
• C2.5.4Use a graphic display calculator to solve e.g. equations, including those which may be unfamiliar.
• C2.5.5Change the subject of simple formulas. e.g. change the subject of formulas where:

6. Inequalities Notes and examples

• C2.6.1Represent and interpret inequalities, including on a When representing and interpreting inequalities on number line. a number line: e.g.

7. Sequences Notes and examples

• C2.7.1Continue a given number sequence or pattern.
• C2.7.2Recognise patterns in sequences, including the term-to-term rule, and relationships between different sequences.
• C2.7.3

  Find and use the n th term of the following sequences:

  • (a) linear
  • (b) simple quadratic
  • (c) simple cubic.

1. Graphs of functions Notes and examples

• C3.1.1Recognise the following function types from the e.g. identify from different sketch graphs which one shape of their graphs: is the graph of (a) linear f( x ) = ax + b (b) quadratic f( x ) = ax + bx + c .

2. Sketching graphs on a calculator Notes and examples

• C3.2.1

  Use a graphic display calculator to: Includes unfamiliar functions not mentioned explicitly in this syllabus.

  • (a) sketch the graph of a function
  • (b) produce a table of values
  • (c) plot points
  • (d) find zeros, local maxima or local minima
  • (e) find the intersection of the graphs of functions
  • (f) find the vertex of a quadratic.

3. Functions Notes and examples

• C3.3.1Understand and use function notation. Examples may include:
• C3.3.2This topic may include mapping diagrams.

1. Coordinates Notes and examples

• C4.1.1Use and interpret Cartesian coordinates in two dimensions.

2. Gradient of linear graphs Notes and examples

• C4.2.1Find the gradient of a straight line. From a grid only.

3. Length and midpoint Notes and examples

• C4.3.1Calculate the length of a line segment from the coordinates of its end points.
• C4.3.2Find the coordinates of the midpoint of a line segment from the coordinates of its end points.

4. Equations of linear graphs Notes and examples

• C4.4.1Interpret and obtain the equation of a straight-line Questions may: graph in the form y = mx + c .
• C4.4.2Candidates are expected to give equations of a line in a fully simplified form.

5. Parallel lines Notes and examples

• C4.5.1Find the gradient and equation of a straight line e.g. find the equation of the line parallel to parallel to a given line. y

1. Geometrical terms Notes and examples

• C5.1.1

  Use and interpret the following geometrical Candidates are terms: shapes are congruent.:

  • point
  • vertex
  • line
  • parallel
  • perpendicular
  • bearing
  • right angle
  • acute, obtuse and reflex angles
  • interior and exterior angles
  • similar
  • congruent
  • scale factor.
• C5.1.2

  Use and interpret the vocabulary of: Includes the following terms:

  • triangles Triangles:
  • special quadrilaterals
  • polygons
  • simple solids.
• C5.1.3Quadrilaterals:
• C5.1.3aUse and interpret the vocabulary of a circle.
• C5.1.4Polygons:

2. Angle measurement in degrees Notes and examples

• C5.2.1Measure and draw lines and angles.
• C5.2.2Use and interpret three-figure bearings.

3. Similarity Notes and examples

• C5.3.1Calculate lengths of similar shapes.

4. Symmetry Notes and examples

• C5.4.1Recognise line symmetry and order of rotational Includes properties of triangles, quadrilaterals and symmetry in two dimensions. polygons directly related to their symmetries.

5. Angles Notes and examples

• C5.5.1

  Calculate unknown angles and give simple Knowledge of three-letter notation for angles is explanations using the following geometrical required, e.g. angle properties: to use the correct geometrical terminology when of a quadrilateral = 360°.:

  • sum of angles at a point = 360° giving reasons for answers.
  • sum of angles at a point on a straight line = 180°
  • vertically opposite angles are equal
  • angle sum of a triangle = 180° and angle sum
• C5.5.2

  Calculate unknown angles and give geometric explanations for angles formed within parallel lines:

  • corresponding angles are equal
  • alternate angles are equal
  • co-interior angles sum to 180° (supplementary).
• C5.5.3Know and use angle properties of regular Includes exterior and interior angles, and angle polygons. sum.

6. Circle theorems I Notes and examples

• C5.6.1

  Calculate unknown angles and give explanations Candidates are expected to use the geometrical using the following geometrical properties of circles: properties listed in the syllabus when giving:

  • angle in a semicircle = 90° reasons for answers.
  • angle between tangent and radius = 90°.

7. Circle theorems II Notes and examples

• C5.7.1Use the symmetry property of circles that tangents from an external point are equal in length.

1. Units of measure Notes and examples

• C6.1.1Use metric units of mass, length, area, volume and capacity in practical situations and convert quantities into larger or smaller units.

2. Area and perimeter Notes and examples

• C6.2.1Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium.

3. Circles, arcs and sectors Notes and examples

• C6.3.1Carry out calculations involving the circumference and area of a circle.
• C6.3.2Carry out calculations involving arc length and sector area as fractions of the circumference and area of a circle, where the sector angle is a factor of 360°.

4. Surface area and volume Notes and examples

• C6.4.1

  Carry out calculations and solve problems involving the surface area and volume of a:

  • cuboid
  • prism
  • cylinder
  • sphere
  • pyramid
  • cone.

5. Compound shapes and parts of shapes Notes and examples

• C6.5.1

  Carry out calculations and solve problems Answers may be asked for in terms of involving perimeters and areas of:

  • compound shapes
  • parts of shapes.
• C6.5.2

  Carry out calculations and solve problems involving surface areas and volumes of:

  • compound solids
  • parts of solids. e.g. find the volume of half of a sphere.

1. Pythagoras’ theorem Notes and examples

• C7.1.1Know and use Pythagoras’ theorem. Includes finding:

2. Right-angled triangles

• C7.2.1Know and use the sine, cosine and tangent Angles will be given in degrees and answers should ratios for acute angles in calculations involving be written in degrees, with decimals correct to one sides and angles of a right-angled triangle. decimal place.
• C7.2.2Solve problems in two dimensions using Knowledge of bearings may be required. Pythagoras’ theorem and trigonometry.

1. Transformations Notes and examples

• C8.1.1Recognise, describe and draw the following transformations:
• C8.1.1aReflection of a shape in a vertical or horizontal line.
• C8.1.2Rotation of a shape about the origin, vertices or midpoints of edges of the shape, through multiples of 90°.
• C8.1.3Enlargement of a shape from a centre by a scale factor. KK x OO
• C8.1.4Translation of a shape by a vector .

1. Introduction to probability Notes and examples

• C9.1.1Understand and use the probability scale from 0 to 1.
• C9.1.2Calculate the probability of a single event. Probability notation is
• C9.1.3Probabilities should be given as a fraction, decimal or percentage. Problems may require using information from tables, graphs or Venn diagrams (limited to two sets). 3 Understand that the probability of an event e.g. The probability that a counter is blue is 0.8. not occurring = 1 – the probability of the event What is the probability that it is not blue? occurring.

2. Relative and expected frequencies Notes and examples

• C9.2.1Understand relative frequency as an estimate of e.g. use results of experiments with a spinner to probability. estimate the probability of a given outcome.
• C9.2.2Calculate expected frequencies. e.g. use probability to estimate an expected value from a population.
• C9.2.3Includes understanding what is meant by fair, bias and random.

3. Probability of combined events Notes and examples

• C9.3.1

  Calculate the probability of combined events using, Combined events will only be with replacement. where appropriate: end of the branches and probabilities by the side of the branches.:

  • sample space diagrams
  • Venn diagrams Venn diagrams will be limited to two sets.
  • tree diagrams. In tree diagrams, outcomes will be written at the

1. Classifying statistical data Notes and examples

• C10.1.1Classify and tabulate statistical data. e.g. tally tables, two-way tables.

2. Interpreting statistical data Notes and examples

• C10.2.1Read, interpret and draw inferences from tables and statistical diagrams.
• C10.2.2Compare sets of data using tables, graphs and e.g. compare averages and ranges between two statistical measures. data sets.
• C10.2.3Appreciate restrictions on drawing conclusions from given data.

3. Discrete and continuous data Notes and examples

• C10.3.1Distinguish between discrete and continuous data.

4. Averages and range Notes and examples

• C10.4.1Calculate the mean, median, mode, quartiles, Data may be in a list or frequency table, but will not range and interquartile range for individual data and be grouped. distinguish between the purposes for which these are used.

5. Averages on a calculator Notes and examples

• C10.5.1Use a graphic display calculator to calculate:
• C10.5.1amean, median and quartiles for discrete data
• C10.5.2mean for grouped data.

6. Statistical charts and diagrams Notes and examples

• C10.6.1

  Draw and interpret:

  • (a) bar charts Includes composite (stacked) and dual (side-by-
  • (b) pie charts side) bar charts.
  • (c) pictograms
  • (d) stem-and-leaf diagrams Stem-and-leaf diagrams should have ordered data with a key.
  • (e) simple frequency distributions.

7. Scatter diagrams Notes and examples

• C10.7.1Draw and interpret scatter diagrams. Plotted points should be clearly marked, for example as small crosses (×).
• C10.7.2Understand what is meant by positive, negative The coefficient of correlation is and zero correlation.
• C10.7.3Draw by eye, interpret and use a straight line of A line of best fit: best fit.