Maths 4MA1 — specification explorer

1. Numbers and the number system

• 1.1Aunderstand and use integers (positive, negative and zero)4MA1/1F4MA1/2FFoundation
• 1.1Bunderstand place value4MA1/1F4MA1/2FFoundation
• 1.1Cuse directed numbers in practical situations4MA1/1F4MA1/2FFoundation
• 1.1Dorder integers4MA1/1F4MA1/2FFoundation
• 1.1Euse the four rules of addition, subtraction, multiplication and division4MA1/1F4MA1/2FFoundation
• 1.1Fuse brackets and the hierarchy of operations4MA1/1F4MA1/2FFoundation
• 1.1Guse the terms ‘odd’, ‘even’, ’prime numbers’, ‘factors’ and ‘multiples’4MA1/1F4MA1/2FFoundation
• 1.1Hidentify prime factors, common factors and common multiples4MA1/1F4MA1/2FFoundation

2. Numbers and the number system (1.2)

• 1.2Aunderstand and use equivalent fractions, simplifying a fraction by cancelling common factors4MA1/1F4MA1/2FFoundation
• 1.2Bunderstand and use mixed numbers and vulgar fractions4MA1/1F4MA1/2FFoundation
• 1.2Cidentify common denominators4MA1/1F4MA1/2FFoundation
• 1.2Dorder fractions and calculate a given fraction of a given quantity4MA1/1F4MA1/2FFoundation
• 1.2Eexpress a given number as a fraction of another number4MA1/1F4MA1/2FFoundation
• 1.2Fuse common denominators to add and subtract fractions and mixed numbers4MA1/1F4MA1/2FFoundation
• 1.2Gconvert a fraction to a decimal or a percentage4MA1/1F4MA1/2FFoundation
• 1.2Hunderstand and use unit fractions as multiplicative inverses4MA1/1F4MA1/2FFoundation
• 1.2Imultiply and divide fractions and mixed numbers4MA1/1F4MA1/2FFoundation

3. Numbers and the number system (1.3)

• 1.3Ause decimal notation4MA1/1F4MA1/2FFoundation
• 1.3Bunderstand place value4MA1/1F4MA1/2FFoundation
• 1.3Corder decimals4MA1/1F4MA1/2FFoundation
• 1.3Dconvert a decimal to a fraction or a percentage4MA1/1F4MA1/2FFoundation
• 1.3Erecognise that a terminating decimal is a fraction4MA1/1F4MA1/2FFoundation

4. Numbers and the number system (1.4)

• 1.4Aidentify square numbers and cube numbers4MA1/1F4MA1/2FFoundation
• 1.4Bcalculate squares, square roots, cubes and cube roots4MA1/1F4MA1/2FFoundation
• 1.4Cuse index notation and index laws for multiplication and division of positive and negative integer powers including zero4MA1/1F4MA1/2FFoundation
• 1.4Dexpress integers as a product of powers of prime factors4MA1/1F4MA1/2FFoundation
• 1.4Efind highest common factors (HCF) and lowest common multiples (LCM)4MA1/1F4MA1/2FFoundation

5. Numbers and the number system (1.5)

• 1.5Aunderstand the definition of a set4MA1/1F4MA1/2FFoundation
• 1.5Buse the set notation∪, ∩ and ∈ and ∉4MA1/1F4MA1/2FFoundation
• 1.5Cunderstand the concept of the universal set and the empty set and the symbols for these sets4MA1/1F4MA1/2FFoundation
• 1.5Dunderstand and use the complement of a set4MA1/1F4MA1/2FFoundation
• 1.5Euse Venn diagrams to represent sets4MA1/1F4MA1/2FFoundation

6. Numbers and the number system (1.6)

• 1.6Aunderstand that ‘percentage’ means ‘number of parts per 100’4MA1/1F4MA1/2FFoundation
• 1.6Bexpress a given number as a percentage of another number4MA1/1F4MA1/2FFoundation
• 1.6Cexpress a percentage as a fraction and as a decimal4MA1/1F4MA1/2FFoundation
• 1.6Dunderstand the multiplicative nature of percentages as operators4MA1/1F4MA1/2FFoundation
• 1.6Esolve simple percentage problems, including percentage increase and decrease4MA1/1F4MA1/2FFoundation
• 1.6Fuse reverse percentages4MA1/1F4MA1/2FFoundation
• 1.6Guse compound interest and depreciation4MA1/1F4MA1/2FFoundation

7. Numbers and the number system (1.7)

• 1.7Ause ratio notation, including reduction to its simplest form and its various links to fraction notation4MA1/1F4MA1/2FFoundation
• 1.7Bdivide a quantity in a given ratio or ratios4MA1/1F4MA1/2FFoundation
• 1.7Cuse the process of proportionality to evaluate unknown quantities4MA1/1F4MA1/2FFoundation
• 1.7Dcalculate an unknown quantity from quantities that vary in direct proportion4MA1/1F4MA1/2FFoundation
• 1.7Esolve word problems about ratio and proportion4MA1/1F4MA1/2FFoundation

8. Numbers and the number system (1.8)

• 1.8Around integers to a given power of 104MA1/1F4MA1/2FFoundation
• 1.8Bround to a given number of significant figures or decimal places4MA1/1F4MA1/2FFoundation
• 1.8Cidentify upper and lower bounds where values are given to a degree of accuracy4MA1/1F4MA1/2FFoundation
• 1.8Duse estimation to evaluate approximations to numerical calculations4MA1/1F4MA1/2FFoundation

9. Numbers and the number system (1.9)

• 1.9Acalculate with and interpret numbers in the forma × 10 wherenis an integer and1≤ a < 104MA1/1F4MA1/2FFoundation

10. Numbers and the number system (1.10)

• 1.10Ause and apply number in everyday personal, domestic or community life4MA1/1F4MA1/2FFoundation
• 1.10Bcarry out calculations using standard units of mass, length, area, volume and capacity4MA1/1F4MA1/2FFoundation
• 1.10Cunderstand and carry out calculations using time, and carry out calculations using money, including converting between currencies4MA1/1F4MA1/2FFoundation

11. Numbers and the number system (1.11)

• 1.11Ause a scientific electronic calculator to determine numerical results4MA1/1F4MA1/2FFoundation

1. Equations, formulae and identities

• 2.1Aunderstand that symbols may be used to represent numbers in equations or variables in expressions and formulae4MA1/1F4MA1/2FFoundation
• 2.1Bunderstand that algebraic expressions follow the generalised rules of arithmetic4MA1/1F4MA1/2FFoundation
• 2.1Cuse index notation for positive and negative integer powers (including zero)4MA1/1F4MA1/2FFoundation
• 2.1Duse index laws in simple cases4MA1/1F4MA1/2FFoundation

2. Equations, formulae and identities (2.2)

• 2.2Aevaluate expressions by substituting numerical values for letters4MA1/1F4MA1/2FFoundation
• 2.2Bcollect like terms4MA1/1F4MA1/2FFoundation
• 2.2Cmultiply a single term over a bracket4MA1/1F4MA1/2FFoundation
• 2.2Dtake out common factors4MA1/1F4MA1/2FFoundation
• 2.2Eexpand the product of two simple linear expressions4MA1/1F4MA1/2FFoundation
• 2.2Funderstand the concept of a quadratic expression and be able to factorise such expressions (limited tox + bx + c)4MA1/1F4MA1/2FFoundation

3. Equations, formulae and identities (2.3)

• 2.3Aunderstand that a letter may represent an unknown number or a variable4MA1/1F4MA1/2FFoundation
• 2.3Buse correct notational conventions for algebraic expressions and formulae4MA1/1F4MA1/2FFoundation
• 2.3Csubstitute positive and negative integers, decimals and fractions for words and letters in expressions and formulae4MA1/1F4MA1/2FFoundation
• 2.3Duse formulae from mathematics and other real-life contexts expressed initially in words or diagrammatic form and convert to letters and symbols4MA1/1F4MA1/2FFoundation
• 2.3Ederive a formula or expression4MA1/1F4MA1/2FFoundation
• 2.3Fchange the subject of a formula where the subject appears once4MA1/1F4MA1/2FFoundation

4. 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 equation4MA1/1F4MA1/2FFoundation
• 2.4Bset up simple linear equations from given data4MA1/1F4MA1/2FFoundation

5. Equations, formulae and identities (2.6)

• 2.6Acalculate the exact solution of two simultaneous equations in two unknowns4MA1/1F4MA1/2FFoundation

6. Equations, formulae and identities (2.7)

• 2.7Asolve quadratic equations by factorisation (limited tox + bx + c = 0)4MA1/1F4MA1/2FFoundation

7. Equations, formulae and identities (2.8)

• 2.8Aunderstand and use the symbols>,<,≥ and ≤4MA1/1F4MA1/2FFoundation
• 2.8Bunderstand and use the convention for open and closed intervals on a number line4MA1/1F4MA1/2FFoundation
• 2.8Csolve simple linear inequalities in one variable and represent the solution set on a number line4MA1/1F4MA1/2FFoundation
• 2.8Drepresent simple linear inequalities on rectangular Cartesian graphs4MA1/1F4MA1/2FFoundation
• 2.8Eidentify regions on rectangular Cartesian graphs defined by simple linear inequalities4MA1/1F4MA1/2FFoundation

1. Sequences, functions and graphs

• 3.1Agenerate terms of a sequence using term-to-term and position-to-term definitions of the sequence4MA1/1F4MA1/2FFoundation
• 3.1Bfind subsequent terms of an integer sequence and the rule for generating it4MA1/1F4MA1/2FFoundation
• 3.1Cuse linear expressions to describe the nth term of arithmetic sequences4MA1/1F4MA1/2FFoundation

2. Sequences, functions and graphs (3.3)

• 3.3Ainterpret information presented in a range of linear and non-linear graphs4MA1/1F4MA1/2FFoundation
• 3.3Bunderstand and use conventions for rectangular Cartesian coordinates4MA1/1F4MA1/2FFoundation
• 3.3Cplot points(x, y)in any of the four quadrants or locate points with given coordinates4MA1/1F4MA1/2FFoundation
• 3.3Ddetermine the coordinates of points identified by geometrical information4MA1/1F4MA1/2FFoundation
• 3.3Edetermine the coordinates of the midpoint of a line segment, given the coordinates of the two end points4MA1/1F4MA1/2FFoundation
• 3.3Fdraw and interpret straight line conversion graphs4MA1/1F4MA1/2FFoundation
• 3.3Gfind the gradient of a straight line4MA1/1F4MA1/2FFoundation
• 3.3Hrecognise that equations of the form y = mx + care straight line graphs with gradientmand intercept on the y-axis at the point(0,c)4MA1/1F4MA1/2FFoundation
• 3.3Irecognise, generate points and plot graphs of linear and quadratic functions4MA1/1F4MA1/2FFoundation

1. Geometry

• 4.1Adistinguish between acute, obtuse, reflex and right angles4MA1/1F4MA1/2FFoundation
• 4.1Buse angle properties of intersecting lines, parallel lines and angles on a straight line4MA1/1F4MA1/2FFoundation
• 4.1Cunderstand the exterior angle of a triangle property and the angle sum of a triangle property4MA1/1F4MA1/2FFoundation
• 4.1Dunderstand the terms ‘isosceles’, ‘equilateral’ and ‘right-angled triangles’ and the angle properties of these triangles4MA1/1F4MA1/2FFoundation

2. Geometry (4.2)

• 4.2Arecognise and give the names of polygons4MA1/1F4MA1/2FFoundation
• 4.2Bunderstand and use the term ‘quadrilateral’ and the angle sum property of quadrilaterals4MA1/1F4MA1/2FFoundation
• 4.2Cunderstand and use the properties of the parallelogram, rectangle, square, rhombus, trapezium and kite4MA1/1F4MA1/2FFoundation
• 4.2Dunderstand the term ‘regular polygon’ and calculate interior and exterior angles of regular polygons4MA1/1F4MA1/2FFoundation
• 4.2Eunderstand and use the angle sum of polygons4MA1/1F4MA1/2FFoundation
• 4.2Funderstand congruence as meaning the same shape and size4MA1/1F4MA1/2FFoundation
• 4.2Gunderstand that two or more polygons with the same shape and size are said to be congruent to each other4MA1/1F4MA1/2FFoundation

3. Geometry (4.3)

• 4.3Aidentify any lines of symmetry and the order of rotational symmetry of a given two-dimensional figure4MA1/1F4MA1/2FFoundation

4. Geometry (4.4)

• 4.4Ainterpret scales on a range of measuring instruments4MA1/1F4MA1/2FFoundation
• 4.4Bcalculate time intervals in terms of the 24-hour and the 12-hour clock4MA1/1F4MA1/2FFoundation
• 4.4Cmake sensible estimates of a range of measures4MA1/1F4MA1/2FFoundation
• 4.4Dunderstand angle measure including three-figure bearings4MA1/1F4MA1/2FFoundation
• 4.4Emeasure an angle to the nearest degree4MA1/1F4MA1/2FFoundation
• 4.4Funderstand and use the relationship between average speed, distance and time4MA1/1F4MA1/2FFoundation
• 4.4Guse compound measure such as speed, density and pressure4MA1/1F4MA1/2FFoundation

5. Geometry (4.5)

• 4.5Ameasure and draw lines to the nearest millimetre4MA1/1F4MA1/2FFoundation
• 4.5Bconstruct triangles and other two-dimensional shapes using a combination of a ruler, a protractor and compasses4MA1/1F4MA1/2FFoundation
• 4.5Csolve problems using scale drawings4MA1/1F4MA1/2FFoundation
• 4.5D

  use straight edge and compasses to:

  • (i) construct the perpendicular bisector of a line segment
  • (ii) construct the bisector of an angle
  4MA1/1F4MA1/2FFoundation

6. Geometry (4.6)

• 4.6Arecognise the terms ‘centre’, ‘radius’, ‘chord’, ‘diameter’, ‘circumference’, ‘tangent’, ‘arc’, ‘sector’ and ‘segment’ of a circle4MA1/1F4MA1/2FFoundation
• 4.6Bunderstand chord and tangent properties of circles4MA1/1F4MA1/2FFoundation

7. Geometry (4.7)

• 4.7Agive informal reasons, where required, when arriving at numerical solutions to geometrical problems4MA1/1F4MA1/2FFoundation

8. Geometry (4.8)

• 4.8Aknow, understand and use Pythagoras’ theorem in two dimensions4MA1/1F4MA1/2FFoundation
• 4.8Bknow, understand and use sine, cosine and tangent of acute angles to determine lengths and angles of a right-angled triangle4MA1/1F4MA1/2FFoundation
• 4.8Capply trigonometrical methods to solve problems in two dimensions4MA1/1F4MA1/2FFoundation

9. Geometry (4.9)

• 4.9Aconvert measurements within the metric system to include linear and area units4MA1/1F4MA1/2FFoundation
• 4.9Bfind the perimeter of shapes made from triangles and rectangles4MA1/1F4MA1/2FFoundation
• 4.9Cfind the area of simple shapes using the formulae for the areas of triangles and rectangles4MA1/1F4MA1/2FFoundation
• 4.9Dfind the area of parallelograms and trapezia4MA1/1F4MA1/2FFoundation
• 4.9Efind circumferences and areas of circles using relevant formulae; find perimeters and areas of semicircles4MA1/1F4MA1/2FFoundation

10. Geometry (4.10)

• 4.10Arecognise and give the names of solids4MA1/1F4MA1/2FFoundation
• 4.10Bunderstand the terms ‘face’, ‘edge’ and ‘vertex’ in the context of 3D solids4MA1/1F4MA1/2FFoundation
• 4.10Cfind the surface area of simple shapes using the area formulae for triangles and rectangles4MA1/1F4MA1/2FFoundation
• 4.10Dfind the surface area of a cylinder4MA1/1F4MA1/2FFoundation
• 4.10Efind the volume of prisms, including cuboids and cylinders, using an appropriate formula4MA1/1F4MA1/2FFoundation
• 4.10Fconvert between units of volume within the metric system4MA1/1F4MA1/2FFoundation

11. Geometry (4.11)

• 4.11Aunderstand and use the geometrical properties that similar figures have corresponding lengths in the same ratio but corresponding angles remain unchanged4MA1/1F4MA1/2FFoundation
• 4.11Buse and interpret maps and scale drawings4MA1/1F4MA1/2FFoundation

1. Vectors and transformation geometry

• 5.2Aunderstand that rotations are specified by a centre and an angle4MA1/1F4MA1/2FFoundation
• 5.2Brotate a shape about a point through a given angle4MA1/1F4MA1/2FFoundation
• 5.2Crecognise that an anti-clockwise rotation is apositiveangle of rotation and a clockwise rotation is anegativeangle of rotation4MA1/1F4MA1/2FFoundation
• 5.2Dunderstand that reflections are specified by a mirror line4MA1/1F4MA1/2FFoundation
• 5.2Econstruct a mirror line given an object and reflect a shape given a mirror line4MA1/1F4MA1/2FFoundation
• 5.2Funderstand that translations are specified by a distance and direction4MA1/1F4MA1/2FFoundation
• 5.2Gtranslate a shape4MA1/1F4MA1/2FFoundation
• 5.2Hunderstand and use column vectors in translations4MA1/1F4MA1/2FFoundation
• 5.2Iunderstand that rotations, reflections and translations preserve length and angle so that a transformed shape under any of these transformations remains congruent to the original shape4MA1/1F4MA1/2FFoundation
• 5.2Junderstand that enlargements are specified by a centre and a scale factor4MA1/1F4MA1/2FFoundation
• 5.2Kunderstand that enlargements preserve angles and not lengths4MA1/1F4MA1/2FFoundation
• 5.2Lenlarge a shape given the scale factor4MA1/1F4MA1/2FFoundation
• 5.2Midentify and give complete descriptions of transformations4MA1/1F4MA1/2FFoundation

1. Statistics and probability

• 6.1Ause different methods of presenting data Pictograms, bar charts4MA1/1F4MA1/2FFoundation
• 6.1Buse appropriate methods of tabulation to enable the construction of statistical diagrams4MA1/1F4MA1/2FFoundation
• 6.1Cinterpret statistical diagrams4MA1/1F4MA1/2FFoundation

2. Statistics and probability (6.2)

• 6.2Aunderstand the concept of average4MA1/1F4MA1/2FFoundation
• 6.2Bcalculate the mean, median, mode and range for a discrete data set4MA1/1F4MA1/2FFoundation
• 6.2Ccalculate an estimate for the mean for grouped data4MA1/1F4MA1/2FFoundation
• 6.2Didentify the modal class for grouped data4MA1/1F4MA1/2FFoundation

3. Statistics and probability (6.3)

• 6.3Aunderstand the language of probability4MA1/1F4MA1/2FFoundation
• 6.3Bunderstand and use the probability scale4MA1/1F4MA1/2FFoundation
• 6.3Cunderstand and use estimates or measures of probability from theoretical models4MA1/1F4MA1/2FFoundation
• 6.3Dfind probabilities from a Venn diagram4MA1/1F4MA1/2FFoundation
• 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 space4MA1/1F4MA1/2FFoundation
• 6.3Flist all the outcomes for single events and for two successive events in a systematic way4MA1/1F4MA1/2FFoundation
• 6.3Gestimate probabilities from previously collected data4MA1/1F4MA1/2FFoundation
• 6.3Hcalculate the probability of the complement of an event happening4MA1/1F4MA1/2FFoundation
• 6.3Iuse the addition rule of probability for mutually exclusive events4MA1/1F4MA1/2FFoundation
• 6.3Junderstand and use the term ‘expected frequency’4MA1/1F4MA1/2FFoundation