AQA GCSE Maths - Higher Self-Assessment Checklist

Transcription

1 AQA GCSE Maths - Higher Self-Assessment Checklist Number 1 Use place value when calculating with decimals. 1 Order positive and negative integers and decimals using the symbols =,, <, >, and. 1 Round to a number of decimal places or significant figures. 1 Add and subtract positive and negative integers and decimals. 1 Multiply and divide positive and negative integers and decimals. 1 Use BIDMAS in multistage calculations. 5 Convert between terminating decimals and their corresponding fractions. 5 Compare decimals and fractions using the symbols > and <. 5 Find fractions and percentages of amounts. 5 Add and subtract simple fractions and mixed numbers. 5 Multiply and divide simple fractions and mixed numbers. 5 Convert between fractions, decimals (including recurring decimals) and percentages. 5 Order fractions, decimals and percentages. 9 Round numbers and measures to an appropriate degree of accuracy. 9 Use approximation to make estimates. 9 Check calculations using approximation and estimation. 9 Use (and convert between) standard units of length, mass, volume, capacity, time and area and other measures including compound measures. 9 Use inequality notation to state error intervals and interpret limits of accuracy. 9 Solve problems involving compound measure such as speed and density. 9 Find upper and lower bounds on the value of a quantity that has been rounded. 9 Find upper and lower bounds on expressions that involve quantities that have been rounded. 13 Use mathematical language to describe factors, multiples and primes. 13 Use Venn diagrams or factor trees to systematically list the prime factors of a number. 13 Use prime factor decomposition to calculate the HCF and LCM of two or more numbers. 13 Write the HCF and LCM using product notation. 13 Calculate positive integer powers and their roots. 13 Recognise powers of 2, 3, 4 and Estimate the square or cube root of an integer. 13 Find square and cube roots of numbers and apply the laws of indices. 13 Simplify expressions involving surds including rationalising fractions. 17 Calculate with roots and with indices, including negative and fractional indices. 17 Calculate exactly with fractions, π and surds. 17 Calculate with and interpret numbers written in standard form.

2 Algebra 2 Use algebraic notation. 2 Substitute numbers into formulae and expressions. 2 Use and understand the words expressions, equations, formulae, terms and factors. 2 Collect like terms and simplify expressions involving sums, products, powers and surds. 2 Use the laws of indices. 2 Multiply a single term over a bracket. 2 Take out common factors in an expression. 2 Simplify algebraic fractions and carry out arithmetic operations with algebraic fractions. 6 Substitute numerical values into formulae and expressions. 6 Rearrange formulae to change the subject. 6 Identify inequalities, equations, formulae and identities. 6 Write an equation to represent a function and find inputs and outputs. 6 Find the inverse of a function and construct and use composite functions. 6 Use the terms expression, equation, formula, identity, inequality, term and factor. 6 Construct proofs of simple statements using algebra. 6 Expand double brackets. 6 Factorise quadratic expressions of the form x 2 + bx + c and the difference of two squares. 10 Derive and solve simple linear equations, including when an unknown appears on both sides. 10 Solve quadratic equations algebraically by factorising, completing the square and by using the quadratic formula. 10 Derive and solve two linear simultaneous equations in two variables. 10 Solve a linear plus quadratic simultaneous equation. 10 Use iterative processes to find approximate solutions to equations. 10 Find approximate solutions to two linear simultaneous equations using a graph. 10 Solve linear inequalities in one or more variables and represent the solution on a number line or a graph. 14 Work with coordinates in all four quadrants. 14 Plot straight-line graphs including diagonal, vertical and horizontal lines. 14 Identify gradients and intercepts of straight lines graphically and algebraically and relate these to the equation of the line in the form y = mx + c. 14 Use the form y = mx + c to identify parallel lines and perpendicular lines. 14 Use one point and the gradient of the line to finds its equation. 14 Use two points to find the equation of a line. 14 Interpret the gradient of a straight line graph as a rate of change. 14 Plot and interpret graphs involving distance, speed and acceleration. 14 Draw line graphs and quadratic curves. 14 Identify roots, intercepts and turning points of quadratic curves using graphical and algebraic methods. 18 Draw graphs to identify and interpret roots, intercepts and turning points of quadratic functions. 18 Solve a quadratic equation by finding approximate solutions using a graph. 18 Recognise, sketch and interpret graphs of linear, quadratic, cubic and reciprocal functions. 18 Recognise and draw the graphs of exponential functions.

3 Algebra continued 18 Recognise and sketch the graphs of trigonometric functions. 18 Recognise and sketch translations and reflections of graphs. 18 Draw and interpret graphs of non-standard functions and use them in real-life problems. 18 Approximate the gradient of a curve at a given point and the area under a graph. Interpret these values in real-life problems including kinematic graphs. 18 Recognise and use simple equations of circles and find the tangent to a circle at a point. 18 Plot and interpret real-life graphs. 21 Generate terms of a sequence from both a term-to-term and a position-to-term rule. 21 Write a formula for the nth term of a linear sequence. 21 Recognise a quadratic sequence and find a formula for its nth term. 21 Recognise special sequences and use them to solve problems. Statistics 4 Construct and interpret frequency tables and two-way tables. 4 Construct and interpret pictograms, bar-line charts and bar charts. 4 Interpret and construct pie charts and know their appropriate use. 4 Compare distributions using median, mean, mode and range and identify outliers. (Use averages and measures of spread to compare data sets). 4 Calculate the range and interquartile range of a data set. 4 Use frequency tables to represent grouped data. 4 Construct histograms with equal or unequal class widths. 16 Interpret and construct tables, graphs and charts for discrete, continuous and grouped data. 16 Construct and interpret cumulative frequency curves and box plots. 16 Use the median, mean, modal class and range to interpret and compare distributions. 16 Use correlation to describe scatter graphs but know that it does not imply causation. 16 Draw estimated lines of best fit and make predictions but understand their limitations. 16 Interpret and construct line graphs for time series data.

4 Ratio and Proportion 12 Use fractions and percentages to describe a proportion. 12 Write a ratio in its simplest form and divide a quantity in a given ratio. 12 Use scale factors, scale diagrams and maps. 12 Solve problems involving percentage change. 12 Find fractions and percentages of amounts and express one number as a fraction or percentage of another. 22 Use compound measures. 22 Calculate with and convert between standard and compound units. 22 Compare lengths, areas and volumes of similar shapes. 22 Solve direct and inverse proportion problems. 22 Describe direct and inverse proportion relationships using an equation. 22 Recognise graphs showing direct and inverse proportion and interpret the gradient of a straight line graph. 22 Find the instantaneous and average rate of change from a graph. 22 Solve repeated proportional change problems. 22 Interpret the gradient of a straight line graph as a rate of change. 22 Interpret graphs that illustrate direct and inverse proportion. 22 Set up, solve and interpret growth and decay problems. Probability 8 Use experimental data to estimate probabilities and expected frequencies. 8 Use tables to represent the outcomes of probability experiments. 8 Calculate theoretical probabilities and expected frequencies using the idea of equally likely events. 8 Compare theoretical probabilities with experimental probabilities. 8 Recognise mutually exclusive events and exhaustive events and know that the probabilities of mutually exclusive exhaustive events sum to Use Venn diagrams to record outcomes and calculate probabilities of events. 20 Construct possibility spaces and use these to calculate probabilities. 20 Use tree diagrams to show the frequencies or probabilities of two or more events. 20 Use tree diagrams to calculate the probability of independent and dependent events. 20 Calculate conditional probabilities.

5 Geometry 3 Describe and apply the properties of angles at a point, on a line and at intersecting and parallel lines. 3 Derive and use the sum of angles in a triangle. 3 Derive and apply the properties and definitions of special types of quadrilaterals. 3 Solve geometrical problems on coordinate axes. 3 Identify and use congruence and similarity. 3 Use congruence to prove geometric results. 3 Deduce and use the angle sum in any polygon and derive properties of regular polygons (including interior and exterior angles). 7 Accurately measure and draw line segments and angles. 7 Use standard units for lengths and areas. 7 Use bearings. 7 Interpret maps and scale drawings. 7 Know and apply formulae to calculate the area of triangles, parallelograms and trapezia (and composite shapes). 7 Identify, describe and construct reflections, rotations, translations (described as 2D vectors) and enlargements (including fractional and negative scale factors). 7 Identify what changes and what is invariant under a combination of transformations. 11 Identify and apply circle definitions, properties and formulae. 11 Calculate arc lengths, angles and areas of sectors. 11 Prove and apply circle theorems. 11 Construct triangles. 11 Use the standard ruler and compass constructions. 11 Solve loci problems. 15 Identify the numbers of faces, edges and vertices of 3D shapes. 15 Construct and interpret plans and elevations of 3D shapes. 15 Calculate the volume and surface area of cuboids, cylinders and other prisms. 15 Calculate the volume and surface area of spheres, pyramids, cones and composite solids. 15 Know and apply the relationship between lengths, areas and volumes of similar shapes. 19 Use the formulae for Pythagoras theorem: a 2 + b 2 = c 2 to find a missing side in a right-angled triangle or the length of a line segment on a coordinate grid. 19 Use the trigonometric ratios and apply them to find angles and lengths in right-angled triangles: sin θ =, cos θ =, tan θ =. 19 Know the exact values of sin θ and cos θ for θ = 0, 30, 45, 60 and 90 and tan θ for θ = 0, 30, 45 and Use the sine and cosine rules to find missing lengths and angles. 19 Use the sine formula for the area of a triangle. 19 Write column vectors and draw vector diagrams. 19 Add, subtract and find multiples of vectors. 19 Calculate with vectors and use them in geometric proofs.