AUTHOR AQA MODULAR STUDENT CHECKLIST (HIGHER)

Unit 1: Statistics and Number (26.7%) - Higher Calculator paper – 1 hour (54 marks) Grade D - Mean from a table. - Modal class from grouped data. - Construct an ordered stem and leaf diagram. - Interpret a time-series graph. - Draw and interpret a scatter graph. Be able to draw a line of best fit. - Design and use data collection sheets and questionnaires. - Probability from a two- way table. Know that mutually exclusive events add up to 1. - Construct a frequency polygon Grade C - Mean and median class for grouped data. - Identify the strength of correlation and interpret the line of best fit. - Identify bias in data collection and questionnaires. - Probability to estimate outcomes. Grade A - Construct and interpret histograms with unequal widths. - Use stratified sampling methods. - Calculate probability for dependent and independent outcomes. - Probability from tree diagrams of independent events. Grade B - Construct a time series graph and plot moving average. Use a trend line to estimate other values. - Construct and interpret a cumulative frequency diagram. - Use a cumulative frequency diagram to estimate the median and interquartile range. - Construct compare and interpret box and whisker plots. - Use relative frequency to find probabilities. - Complete a probability tree diagram. Grade A* - Probability from tree diagrams of dependent events. Topics also in Unit 2 - Rounding numbers to decimal places and significant figures. - Finding the upper and lower bound of a number. - Simplify fractions and find equivalent fractions. - Convert between fractions, decimals and percentages and calculate with them. - Interpret, order and calculate with numbers in standard form. - Interpret ratio as a fraction and be able to simplify. Use ratio to solve statistical and number problems.

Unit 2: Number and Algebra (33.3%) - Higher Non- calculator paper – 1 hour 15 minutes (66 marks) Grade C - Find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two simple numbers. - Find the reciprocal of a number. - Recognise prime numbers and write a number as a product of prime factors. - Estimate answers to division by numbers less than 1. Also divide numbers by a decimal. - Find upper and lower bounds of numbers. - Expand and simplify harder expressions. - Division of simple fractions. - Adding, subtracting and multiplying mixed numbers. - Use index laws for positive and negative powers. - Convert between ordinary numbers and standard form and vice versa. - Calculate percentage increase and decrease. - Sharing amounts into ratios. - Solving proportion problems. - Find the nth term of a sequence. - Find the midpoint of a line segment. - Use and understand co-ordinates in 3D. - Solve equations such as 3x – 4 = 2(x – 5) or (7-x)/3 = 2 - Changing the subject of linear formulae. - Solve linear inequalities with a variable on one side. Grade D - Estimate answers involving division. - Multiply out simple brackets. - Factorise simple expressions. - Multiply two decimals such as 2.4 x Convert fractions to decimals and vice versa. - Add, subtract and multiply simple fractions. - Calculate and recall square numbers, cube numbers, square roots and cube roots. - Increase or decrease a quantity by a given percentage. - Express one quantity as a percentage of another. - Write the terms of a sequence given the nth term. - Draw straight line graphs e.g. y = 2x Solve equations such as 2(5x+1) = 28 - Substitution of numbers into formulae.

Unit 2: Number and Algebra (33.3%) - Higher Non- calculator paper – 1 hour 15 minutes (66 marks) Grade A - Factorise harder quadratic expressions. - Rationalise the denominator of a surd. - Solve indices involving fractional powers such as 16^1/4. - Solve direct and inverse proportion problems. - Change the subject of formulae where the variable appears twice. - Solve quadratic equations using the quadratic formula. - Solve a pair of simultaneous equations where one is linear and one is non-linear e.g. y = 3x – 2 and y = x^2 Grade A* - Simplify harder rational expressions. - Simplify surds such as (3 – sqrt5)^2 in the form a + bsqrt5 -Solve indices involving fractional powers such as 16^3/4 -Solve equations such as 4/(x+2) + 3/(2x-1) = 2 - Write quadratic expressions in the form (x + a)^2 + b - Complete the square to solve equations and find the maximum and minimum values. - Solve simultaneous equations such as x + 5y=13 and x^2 + y^2 = 13. Grade B - Find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of larger numbers. - Round to significant figures (s.f.). - Expand and simplify quadratic expressions. - Factorise quadratic expressions. - Convert recurring decimals to fractions and vice versa. - Calculate compound interest. - Calculate reverse percentages. - Calculate proportional changes. - Solve standard form problems. - Solve equations such as (2x-1)/6 + (x+3)/3 = 5/2. - Changing the subject of formulae that include brackets, fractions and square roots. - Solve quadratic equations such as x^2-8x+15=0 by factorisation. -Solve linear inequalities such as x + 13 > 5x -3 - Solve a set of linear inequalities and represent the solution as a region of a graph - Solve a pair of linear simultaneous equations.

Unit 3: Geometry and Algebra (40%) - Higher Non- calculator paper – 1 hour 30 minutes (80 marks) Grade D - Find the area of a triangle, parallelogram, kite, trapezium and circle. - Find the circumference of a circle. - Calculate the area and perimeter of compound shapes. -Draw straight line graphs e.g. y = 2x Solve equations such as 2(5x+1) = 28 - Reflect shapes in lines such as x=2 or y=-1 - Rotate shapes about the origin. - Describe fully reflections and rotations about the origin. - Enlarge a shape by a positive scale factor. - Use trial and improvement to solve equations. - Calculate average speeds from distance-time graphs. - Substitution of numbers into formulae. - Draw a kite or parallelogram with given measurements. - Construct and recognise the nets of 3D solids. - Plans and elevations of 3D solids. - Draw graphs of simple quadratic functions e.g. y = 3x^2 and y = x^2 + 4 Grade C - Find the area and perimeter of a semi-circle. - Volume of prisms and cylinders. - Surface area of prisms and cylinders, - Classify a quadrilateral by its properties. - Calculate the interior and exterior angles of a regular polygon. - Find the midpoint of a line segment. - Use and understand co-ordinates in 3D. - Solve equations such as 3x – 4 = 2(x – 5) or (7-x)/3 = 2 - Reflect shapes in y = x and y = -x - Rotate shapes about any point. - Fully describe transformations. - Translate a shape by a vector. - Enlarge a shape by a fractional scale factor. - Calculate complex average speeds from a distance-time graphs. -Construct a perpendicular bisector, angle bisector and 60 degree angle. - Finding the equation of straight line graphs. - Pythagoras’ Theorem to calculate missing sides in right angles triangles. - Solve loci problems. -Graphs of harder quadratic functions e.g. x^2 – 2x + 1 Grade B - Solve equations such as (2x-1)/6 + (x+3)/3 = 5/2. - Apply circle theorems to find missing angles. - Dimensional analysis for perimeter, area and volume. - Interpret graphs modelling real situations. - Finding upper and lower bounds for simple calculations. - Solve a pair of linear simultaneous equations. - Trigonometry to calculate missing sides and angles. - Complete tables and draw graphs of cubic and reciprocal functions. Use them to solve equations. - Find sides and angles of similar triangles. - Find the distance between two points given their co-ordinates. - Solve quadratic equations such as x^2- 8x+15=0 by factorisation. Grade C cont. - Approximate solutions of quadratic equations and find points of intersection of quadratic graphs with lines. - Interpret maps and scale drawings and use bearings.

Unit 3: Geometry and Algebra (40%) - Higher Non- calculator paper – 1 hour 30 minutes (80 marks) Grade A - Prove the angle properties of a circle. - Use and prove the alternate segment theorem. - Enlarge a shape by a negative scale factor. - Compare areas and volumes of enlarged shapes. - Calculate the upper and lower bounds of difficult calculations. -Solve quadratic equations using the quadratic formula. - Solve a pair of simultaneous equations where one is linear and one is non-linear e.g. y = 3x – 2 and y = x^2 - Sketch and draw trigonometric graphs. - Use the sine and cosine rule to find missing sides and angles in any triangle. - Use the formula for the area of a non-right angled triangle. - Add, subtract and multiply vectors. - Find the area of a 2D shape given the area of a similar shape and the ratio. - Find the volume of a 3D solid given the volume of a similar solid and the ratio. - Solve simultaneous equations graphically such as y = 2x – 1 and x^2 + y^2 = 25 - Use points of intersection of a quadratic and linear graphs to solve equations like x^2 -2x -4 = 2x+1. Grade A* - Calculate the upper and lower bounds of complex calculations. - Write quadratic expressions in the form (x + a)^2 + b - Complete the square to solve equations and find the maximum and minimum values. - Solve simultaneous equations such as x + 5y=13 and x^2 + y^2 = Use trigonometry to find sides and angles in three dimensions. - Understand the graphs of trigonometric functions for angles of any size. - Solve cubic equations by drawing appropriate lines on graphs. - Plot and sketch graphs of exponential functions. - Recognise the shapes of graphs of functions. - Solve difficult vector geometry problems. - Solve equations such as 4/(x+2) + 3/(2x-1) = 2 - Transform graphs of linear, quadratic, cubic, sine and cosine functions using the transformations y = f(x) + a, y = f(x+a), y = af(x) and y = f(ax).