Maths — Higher, Unit 1

Maths 4XMAF/4XMAH — specification explorer

All 99 specification statements from the official Pearson Edexcel specification, as printed — filter by paper, unit or tier exactly as Pearson Edexcel assesses them.

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Assessment homes come from the parsed Pearson specification (content summaries & assessment overviews). Hover a chip for the printed rule. Filters appear only where the qualification has that structure — a linear IGCSE has no unit scope, and only Maths A splits Foundation / Higher tiers.

1. Numbers and the number system

1.1Aunderstand and use integers (positive, negative and zero)Unit 1 (Foundation)
1.1Bunderstand place valueUnit 1 (Foundation)
1.1Cuse directed numbers in practical situationsUnit 1 (Foundation)
1.1Dorder integersUnit 1 (Foundation)
1.1Euse the four rules of addition, subtraction, multiplication and divisionUnit 1 (Foundation)
1.1Fuse brackets and the hierarchy of operationsUnit 1 (Foundation)
1.1Guse the terms ‛odd’, ‛even’, ‛prime numbers’, ‛factors’ and ‛multiples’Unit 1 (Foundation)
1.1Hidentify prime factors, common factors and common multiplesUnit 1 (Foundation)

2. Numbers and the number system (1.2)

1.2Aunderstand and use equivalent fractions, simplifying a fraction by cancelling common factorsUnit 1 (Foundation)
1.2Bunderstand and use mixed numbers and vulgar fractionsUnit 1 (Foundation)
1.2Cidentify common denominatorsUnit 1 (Foundation)
1.2Dorder fractions and calculate a given fraction of a given quantityUnit 1 (Foundation)
1.2Eexpress a given number as a fraction of another numberUnit 1 (Foundation)
1.2Fuse common denominators to add and subtract fractions and mixed numbersUnit 1 (Foundation)
1.2Gconvert a fraction to a decimal or a percentageUnit 1 (Foundation)
1.2Hunderstand and use unit fractions as multiplicative inversesUnit 1 (Foundation)
1.2Imultiply and divide fractions and mixed numbersUnit 1 (Foundation)

3. Numbers and the number system (1.3)

1.3Aconvert recurring decimals into fractionsUnit 1 (Higher)
1.3Bunderstand place valueUnit 1 (Foundation)
1.3Corder decimalsUnit 1 (Foundation)
1.3Dconvert a decimal to a fraction or a percentageUnit 1 (Foundation)
1.3Erecognise that a terminating decimal is a fractionUnit 1 (Foundation)

4. Numbers and the number system (1.4)

1.4Aunderstand the meaning of surdsUnit 1 (Higher)
1.4Bmanipulate surds, including rationalising a denominatorUnit 1 (Higher)
1.4Cuse index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powersUnit 1 (Higher)

5. Numbers and the number system (1.5)

1.5Aunderstand sets defined in algebraic terms, and understand and use subsetsUnit 1 (Higher)
1.5Buse Venn diagrams to represent sets and the number of elements in setsUnit 1 (Higher)
1.5Cuse the notation n(A) for the number of elements in the set AUnit 1 (Higher)
1.5Duse sets in practical situationsUnit 1 (Higher)
1.5Euse Venn diagrams to represent setsUnit 1 (Foundation)

6. Numbers and the number system (1.6)

1.6Aunderstand that ‛percentage’ means ‛number of parts per 100’Unit 1 (Foundation)
1.6Bexpress a given number as a percentage of another numberUnit 1 (Foundation)
1.6Cexpress a percentage as a fraction and as a decimalUnit 1 (Foundation)

7. Numbers and the number system (1.8)

1.8Asolve problems using upper and lower bounds where values are given to a degree of accuracyUnit 1 (Higher)
1.8Bround to a given number of significant figures or decimal placesUnit 1 (Foundation)
1.8Cidentify upper and lower bounds where values are given to a degree of accuracyUnit 1 (Foundation)
1.8Duse estimation to evaluate approximations to numerical calculationsUnit 1 (Foundation)

8. Numbers and the number system (1.10)

1.10Ause and apply number in everyday personal, domestic or community lifeUnit 1 (Foundation)
1.10Bcarry out calculations using standard units of mass, length, area, volume and capacityUnit 1 (Foundation)
1.10Cunderstand and carry out calculations using time, and carry out calculations using money, including converting between currenciesUnit 1 (Foundation)

9. Numbers and the number system (1.11)

1.11Ause a scientific electronic calculator to determine numerical resultsUnit 1 (Foundation)

2. Equations, formulae and identities

1. Equations, formulae and identities

2.1Ause index notation involving fractional, negative and zero powersUnit 1 (Higher)
2.1Bunderstand that algebraic expressions follow the generalised rules of arithmeticUnit 1 (Foundation)
2.1Cuse index notation for positive and negative integer powers (including zero)Unit 1 (Foundation)
2.1Duse index laws in simple casesUnit 1 (Foundation)

2. Equations, formulae and identities (2.2)

2.2Aexpand the product of two or more linear expressionsUnit 1 (Higher)
2.2Bunderstand the concept of a quadratic expression and be able to factorise such expressionsUnit 1 (Higher)
2.2Cmanipulate algebraic fractions where the numerator and/or the denominator can be numeric, linear or quadraticUnit 1 (Higher)
2.2Dcomplete the square for a given quadratic expressionUnit 1 (Higher)
2.2Eexpand the product of two simple linear expressionsUnit 1 (Foundation)
2.2Funderstand the concept of a quadratic expression and be able to factorise such expressions (limited to x² + bx + c)Unit 1 (Foundation)

3. Equations, formulae and identities (2.4)

2.4Asolve linear equations, with integer or fractional coefficients, in one unknown in which the unknown appears on either side or both sides of the equationUnit 1 (Foundation)
2.4Bset up simple linear equations from given dataUnit 1 (Foundation)

4. Equations, formulae and identities (2.7)

2.7Asolve quadratic equations by factorisationUnit 1 (Higher)
2.7Bsolve quadratic equations by using the quadratic formula or completing the squareUnit 1 (Higher)
2.7Cform and solve quadratic equations from data given in a contextUnit 1 (Higher)

3. Sequences, functions and graphs

1. Sequences, functions and graphs

3.3A
recognise, plot and draw graphs with equation: y = Ax³ + Bx² + Cx + D in which:
- (i) the constants are integers and some could be zero
- (ii) the letters x and y can be replaced with any other two letters or: y = Ax³ + Bx² + Cx + D + E/x + F/x² in which:
- (i) the constants are numerical and at least three of them are zero
- (ii) the letters x and y can be replaced with any other two letters y = sin x, y = cos x, y = tan x for angles of any size (in degrees)
Unit 1 (Higher)
3.3Bunderstand and use conventions for rectangular Cartesian coordinatesUnit 1 (Foundation)
3.3Cplot points (x, y) in any of the four quadrants or locate points with given coordinatesUnit 1 (Foundation)
3.3Ddetermine the coordinates of points identified by geometrical informationUnit 1 (Foundation)
3.3Edetermine the coordinates of the midpoint of a line segment, given the coordinates of the two end pointsUnit 1 (Foundation)
3.3Fcalculate the gradient of a straight line given the coordinates of two pointsUnit 1 (Higher)
3.3Gfind the equation of a straight line parallel to a given line; find the equation of a straight line perpendicular to a given lineUnit 1 (Higher)
3.3Hrecognise that equations of the form y = mx + c are straight line graphs with gradient m and intercept on the y-axis at the point (0, c)Unit 1 (Foundation)
3.3Irecognise, generate points and plot graphs of linear and quadratic functionsUnit 1 (Foundation)

4. Geometry

1. Geometry

4.1Adistinguish between acute, obtuse, reflex and right anglesUnit 1 (Foundation)
4.1Buse angle properties of intersecting lines, parallel lines and angles on a straight lineUnit 1 (Foundation)
4.1Cunderstand the exterior angle of a triangle property and the angle sum of a triangle propertyUnit 1 (Foundation)
4.1Dunderstand the terms ‛isosceles’, ‛equilateral’ and ‛right-angled triangles’ and the angle properties of these trianglesUnit 1 (Foundation)

2. Geometry (4.2)

4.2Arecognise and give the names of polygonsUnit 1 (Foundation)
4.2Bunderstand and use the term ‛quadrilateral’ and the angle sum property of quadrilateralsUnit 1 (Foundation)
4.2Cunderstand and use the properties of the parallelogram, rectangle, square, rhombus, trapezium and kiteUnit 1 (Foundation)

3. Geometry (4.4)

4.4Funderstand and use the relationship between average speed, distance and timeUnit 1 (Foundation)
4.4Guse compound measure such as speed, density and pressureUnit 1 (Foundation)

4. Geometry (4.7)

4.7Aprovide reasons, using standard geometrical statements, to support numerical values for angles obtained in any geometrical context involving lines, polygons and circlesUnit 1 (Higher)

5. Geometry (4.8)

4.8Aunderstand and use sine, cosine and tangent of obtuse anglesUnit 1 (Higher)
4.8Bunderstand and use angles of elevation and depressionUnit 1 (Higher)
4.8Cunderstand and use the sine and cosine rules for any triangleUnit 1 (Higher)
4.8Duse Pythagoras’ theorem in three dimensionsUnit 1 (Higher)
4.8Eunderstand and use the formula 1⁄2 ab sin C for the area of a triangleUnit 1 (Higher)
4.8Fapply trigonometrical methods to solve problems in three dimensions, including finding the angle between a line and a planeUnit 1 (Higher)

6. Geometry (4.9)

4.9Afind perimeters and areas of sectors of circlesUnit 1 (Higher)
4.9Bfind the perimeter of shapes made from triangles and rectanglesUnit 1 (Foundation)
4.9Cfind the area of simple shapes using the formulae for the areas of triangles and rectanglesUnit 1 (Foundation)
4.9Dfind the area of parallelograms and trapeziaUnit 1 (Foundation)
4.9Efind circumferences and areas of circles using relevant formulae; find perimeters and areas of semicirclesUnit 1 (Foundation)

7. Geometry (4.10)

4.10Arecognise and give the names of solidsUnit 1 (Foundation)
4.10Bunderstand the terms ‛face’, ‛edge’ and ‛vertex’ in the context of 3D solidsUnit 1 (Foundation)

5. Statistics and probability

1. Statistics and probability

6.1Aconstruct and interpret histogramsUnit 1 (Higher)

2. Statistics and probability (6.3)

6.3Adraw and use tree diagramsUnit 1 (Higher)
6.3Bdetermine the probability that two or more independent events will occurUnit 1 (Higher)
6.3Cuse simple conditional probability when combining eventsUnit 1 (Higher)
6.3Dapply probability to simple problemsUnit 1 (Higher)
6.3Eunderstand the concepts of a sample space and an event, and how the probability of an event happening can be determined from the sample spaceUnit 1 (Foundation)
6.3Flist all the outcomes for single events and for two successive events in a systematic wayUnit 1 (Foundation)
6.3Gestimate probabilities from previously collected dataUnit 1 (Foundation)
6.3Hcalculate the probability of the complement of an event happeningUnit 1 (Foundation)
6.3Iuse the addition rule of probability for mutually exclusive eventsUnit 1 (Foundation)
6.3Junderstand and use the term ‛expected frequency’Unit 1 (Foundation)