MATHEMATICS GRADE PROGRESSION SUMMARY 9 Apply and interpret limits Find the equation of a tangent Interpret the gradient of accuracy to a curve at a given point of a straight line To manipulate surds Recognise and use the graph as a rate of equation of a circle change Plot and interpret graphs Interpret the gradient including reciprocals and at a point, on a curve, exponentials as the instantaneous rate of change Understand, construct and interpret equations that describe direct and inverse proportion Know and apply the sine and cosine rules to find unknown sides and angles Use vectors to construct geometric arguments and proofs Construct and interpret a histogram including unequal class intervals Calculate the probability for successive dependent events using tree diagrams and other representations 9 All previous content is assumed and higher order thinking skills are required to solve problems interlinking topic areas 8 Simplify surds such as Derive harder algebraic proofs Compare lengths, 4(3 + 3) and using reasoning and logic areas and volume (2-3)(4 + 3) in the Understand trigonometric using ratio notation form a + b 3 graphs for angles of any size Interpret equations Apply and interpret limits Solve a pair of simultaneous that describe direct of accuracy graphs where one is linear and inverse Set up, solve and and one is non-linear such as proportion interpret the answers in X+ 4y = 15 and x 2 + y 2 =9 growth and decay problems, including compound interest Use trigonometry to find sides and angles in 3-D Add, subtract and multiply vectors to solve geometry problems Transform the graphs of y=f(x) using transformations Interpret, analyse and compare the distributions of data sets through appropriate measures of median, mean, mode and range Calculate the probability for independent events using tree diagrams and other representations
8 Ofqual states that to achieve grade 8, candidates will be able to: perform procedures accurately interpret and communicate complex information accurately make deductions and inferences and draw conclusions construct substantial chains of reasoning, including convincing arguments and formal proofs generate efficient strategies to solve complex mathematical and non-mathematical problems by translating them into a series of mathematical processes make and use connections, which may not be immediately obvious, between different parts of mathematics interpret results in the context of the given problem critically evaluate methods, arguments, results and the assumptions made 7 Use index notation and Derive simple algebraic proofs Understand the Prove the circle theorems Use of mutually index laws for simple using reasoning difference between Prove the construction exclusive events fractional powers such as Recognise the shapes of direct and inverse theorems and independent 16 ¼ functions proportion Find bearings using events when solving Rationalise the Construct the graphs of loci, trigonometry probability problems denominator of a surd including the circle x 2 + y 2 =r 2 Calculate arc lengths, angles Interpret a such as 2/ 5 Use completing the square and areas of sectors of circles cumulative and the quadratic formula to solve quadratic equations Describe translations as 2-D vectors frequency diagram 6 Convert recurring decimals to fractions and vice versa Simplify rational expressions involving quadratic expressions Use sine, cosine and tangent to calculate angles and sides in a right angled triangle Work out reverse percentages Find the upper and lower bounds of simple calculations (addition and subtractions) involving quantities given to a particular degree of accuracy Complete tables for, and draw graphs of reciprocal functions Use reciprocal graphs to solve equations Show step-by-step deductions in providing a full mathematical explanation Understand how to use successive percentages written as multipliers and to be able to interpret the result Solve inequalities with unknowns on both sides Use index notation for multiplication and division Bisect an angle and a straight line Combinations of transformations Use a cumulative frequency diagram to estimate the median and interquartile range
5 Find the reciprocal of a number Find minimum and maximum values Divide a number by a decimal such as 1 0.2 and 2.8 0.07 Solving problems involving standard form 5 Find a solution to a problem by forming an equation and solving it Draw graphs of harder quadratics such as y=x 2 + 3x -5 Find the points of intersection of quadratic graphs with lines Use graphs to find the approximate solutions of quadratic equations Understand the difference between a demonstration ( show me ) and a proof ( prove ) Show step-by-step deductions in providing a basic algebraic explanation Ofqual states that to achieve grade 5, candidates will be able to: Solve more difficult speed problems Calculate proportional changes using a multiplier Convert between measures of area and volume Construct angles and perpendicular lines Use Pythagoras theorem to find the height of an isosceles triangle Understand how to match one side and one angle of congruent triangles Use relative frequency to compare outcomes of experiments perform routine single- and multi-step procedures effectively by recalling, applying and interpreting notation, terminology, facts, definitions and formulae interpret and communicate information effectively make deductions, inferences and draw conclusions construct chains of reasoning, including arguments generate strategies to solve mathematical and non-mathematical problems by translating them into mathematical processes, realising connections between different parts of mathematics interpret results in the context of the given problem evaluate methods and results 4 Estimate answers to calculations involving Solve problems involving straight lines Solve more complex ratio and proportion Draw a quadrilateral such as a kite of a parallelogram with Calculate the mean for a frequency division Draw graphs of simple problems, such as given measurements distribution Recall the cubes of 2, 3, 4, 5, and 10 quadratic functions such as y=x 2 and y=x 2 + 2 sharing out money between two groups Understand that the lengths of two sides and a non-included Find and compare averages
Perform calculations involving BIDMIS Do calculations with mixed Solve linear equations involving fractions Solve inequalities in the ratio of their 3 Round a number to one Substitute negative Understand and significant figure into a simple formula interpret percentage Calculate cubes and Complete a table of values for changes cube roots (with and equations such as y=3x + 3 Use reverse without a calculator) and draw the graph percentage to solve Multiply whole and Read from a conversion graph problems decimal for negative values Divide involving remainders Work out a percentage of an amount (with and without a calculator) Understand percentage, fraction and decimal equivalences Introduction to standard form 2 Change a percentage to Plot points of a conversion a fraction or a decimal graph and read off positive Use ratio to solve and vice versa values simple problems Arrange fractions in order Use a simple formula such as involving recipes and of size P=2w + 2h best buys Add and subtract Solve simple equations such negative integers as x/2 =9 or 4x 2 = 22 angle do not define a unique triangle Find interior and exterior angles of an irregular polygon Perform reflections of shapes in diagonal lines Introduction to Pythagoras theorem Enlarge a shape by a positive scale factor Find the measurements of the dimensions of an enlarged shape Recognise congruent shapes Rotate and translate shapes Understand the idea of a locus Understand the terms perpendicular lines and parallel lines Give the order of rotational symmetry of a 2-D shape Give a scale factor of an enlarged shape Compare the mean and range of two distributions Understand mutually exclusive events Work with discrete and continuous data Compare two distributions using the range and one of the mode, median or mean Place probabilities on a number line
Multiply and divide decimals to two places Round to a given number of decimal places Recognise sequences involving square and cube Plot the graphs of straight lines such as x=3 and y=4 Find the area and perimeter of compound shapes 2 Ofqual states that to achieve grade 2, candidates will be able to: recall and use notation, terminology, facts and definitions; perform routine procedures, including some multi-step procedures interpret and communicate basic information; make deductions and use reasoning to obtain results solve problems by translating simple mathematical and non-mathematical problems into mathematical processes provide basic evaluation of methods or results interpret results in the context of the given problem 1 Find equivalent fractions Simplify expressions Use ratio notationincluding Recognise cube Use a formula written in writing it in Add, subtract and words, such as cost = 20 x its simplest form multiply simple decimals distance travelled Division of integers with no remainders Simplify fractions Multiply two digit Use the word congruent when triangles are identical Find the volume of a solid by counting cubes and stating units Recognise, name and sketch three- dimensional (3-D) solids Understand and use the vocabulary of probability Design and use tally tables for grouped data Find the median of an odd set of Interpreting real life tables