year 10 set 3 higher

●        Use the angle sums of irregular polygons;

●        Calculate and use the sums of the interior angles of polygons, use the sum of angles in a triangle to deduce and use the angle sum in any polygon and to derive the properties of regular polygons;

●        Use the sum of the exterior angles of any polygon is 360°;

●        Use the sum of the interior angles of an n-sided polygon;

●        Use the sum of the interior angle and the exterior angle is 180°;

●        Find the size of each interior angle, or the size of each exterior angle, or the number of sides of a regular polygon, and use the sum of angles of irregular polygons;

●        Calculate the angles of regular polygons and use these to solve problems;

●        Use the side/angle properties of compound shapes made up of triangles, lines and quadrilaterals, including solving angle and symmetry problems for shapes in the first quadrant, more complex problems and using algebra;

●        Use angle facts to demonstrate how shapes would ‘fit together’, and work out interior angles of shapes in a pattern.

·         Factorise quadratic expressions in the form ax2 + bx + c;

·         Solve quadratic equations by factorisation and completing the square;

·         Solve quadratic equations that need rearranging;

·         Set up and solve quadratic equations;

Solve quadratic equations by using the quadratic formula 

·         Know the appropriate uses of histograms;

·         Construct and interpret histograms from class intervals with unequal width;

·         Use and understand frequency density;

·         From histograms:

·         complete a grouped frequency table;

·         understand and define frequency density;

·         Estimate the mean from a histogram;

·         Estimate the median from a histogram with unequal class widths or any other information from a histogram, such as the number of people in a given interval.

 Calculate the length of a line segment given the coordinates of the end points;

●        Find the coordinates of points identified by geometrical information.

●        Find the equation of the line through two given points.

 . 

·         Recognise a linear, quadratic, cubic, reciprocal and circle graph from its shape;

·         Generate points and plot graphs of simple quadratic functions, then more general quadratic functions;

·         Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function;

·         Interpret graphs of quadratic functions from real-life problems;

·         Draw graphs of simple cubic functions using tables of values;

·         Interpret graphs of simple cubic functions, including finding solutions to cubic equations;

·         Plot and draw graphs of y = a, x = a, y = x and y = –x, drawing and recognising lines parallel to axes, plus y = x and y = –x;

·         Identify and interpret the gradient of a line segment;

·         Recognise that equations of the form y = mx + c correspond to straight-line graphs in the coordinate plane;

·         Identify and interpret the gradient and y-intercept of a linear graph given by equations of the form y = mx + c;

·         Find the equation of a straight line from a graph in the form y = mx + c;

·         Plot and draw graphs of straight lines of the form y = mx + c with and without a table of values;

·         Sketch a graph of a linear function, using the gradient and y-intercept (i.e. without a table of values);

·         Find the equation of the line through one point with a given gradient;

·         Identify and interpret gradient from an equation ax + by = c;

·         Find the equation of a straight line from a graph in the form ax + by = c;

·         Plot and draw graphs of straight lines in the form ax + by = c;

·         Interpret and analyse information presented in a range of linear graphs:

·         use gradients to interpret how one variable changes in relation to another;

·         find approximate solutions to a linear equation from a graph;

·         identify direct proportion from a graph;

·         find the equation of a line of best fit (scatter graphs) to model the relationship between quantities;

·         Explore the gradients of parallel lines and lines perpendicular to each other;

·         Interpret and analyse a straight-line graph and generate equations of lines parallel and perpendicular to the given line;

·         Select and use the fact that when y = mx + c is the equation of a straight line, then the gradient of a line parallel to it will have a gradient of m and a line perpendicular to this line will have a gradient of .

       Factorise quadratic expressions of the form ax2 + bx + c;

 Factorise quadratic expressions using the difference of two squares.

·         Write probabilities using fractions, percentages or decimals;

·         Understand and use experimental and theoretical measures of probability, including relative frequency to include outcomes using dice, spinners, coins, etc;

·         Estimate the number of times an event will occur, given the probability and the number of trials;

·         Find the probability of successive events, such as several throws of a single dice;

·         List all outcomes for single events, and combined events, systematically;

·         Draw sample space diagrams and use them for adding simple probabilities;

·         Know that the sum of the probabilities of all outcomes is 1;

·         Use 1 – p as the probability of an event not occurring where p is the probability of the event occurring;

·         Work out probabilities from Venn diagrams to represent real-life situations and also ‘abstract’ sets of numbers/values;

·         Use union and intersection notation;

·         Find a missing probability from a list or two-way table, including algebraic terms;

·         Understand conditional probabilities and decide if two events are independent;

·         Calculate the upper and lowers bounds of numbers given to varying degrees of accuracy;

·         Calculate the upper and lower bounds of an expression involving the four operations;

·         Find the upper and lower bounds in real-life situations using measurements given to appropriate degrees of accuracy;

·         Find the upper and lower bounds of calculations involving perimeters, areas and volumes of 2D and 3D shapes;

·         Calculate the upper and lower bounds of calculations, particularly when working with measurements;

Use inequality notation to specify an error bound 

·         Set up simple equations from word problems and derive simple formulae;

·         Understand the ≠ symbol (not equal), e.g. 6x + 4 ≠ 3(x + 2), and introduce identity ≡ sign;

·         Solve linear equations, with integer coefficients, in which the unknown appears on either side or on both sides of the equation;

·         Solve linear equations which contain brackets, including those that have negative signs occurring anywhere in the equation, and those with a negative solution;

·         Solve linear equations in one unknown, with integer or fractional coefficients;

·         Set up and solve linear equations to solve to solve a problem;

·         Derive a formula and set up simple equations from word problems, then solve these equations, interpreting the solution in the context of the problem;

·         By writing the denominator in terms of its prime factors, decide whether fractions can be converted to recurring or terminating decimals;

·         Convert a fraction to a recurring decimal;

·         Convert a recurring decimal to a fraction;

·         Find the reciprocal of an integer, decimal or fraction.

·         Understand, use and recall the trigonometric ratios sine, cosine and tan, and apply them to find angles and lengths in general triangles in 2D figures;

·         Use the trigonometric ratios to solve 2D problems;

·         Find angles of elevation and depression;

·         Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°.

       Continue a quadratic sequence and use the nth term to generate terms;

·         Find the nth term of quadratic sequences;

·         Distinguish between arithmetic and geometric sequences;

·         Use finite/infinite and ascending/descending to describe sequences;

·         Recognise and use simple geometric progressions (rn where n is an integer, and r is a rational number > 0 or a surd);

·         Continue geometric progression and find term to term rule, including negative, fraction and decimal terms;

·         Solve problems involving sequences from real life situations.

·         Understand, recall and use Pythagoras’ Theorem in 2D;

·         Given three sides of a triangle, justify if it is right-angled or not;

·         Calculate the length of the hypotenuse in a right-angled triangle (including decimal lengths and a range of units);

·         Find the length of a shorter side in a right-angled triangle;

·         Calculate the length of a line segment AB given pairs of points;

Give an answer to the use of Pythagoras’ Theorem in surd form 

·         Use index notation for integer powers of 10, including negative powers;

·         Recognise powers of 2, 3, 4, 5;

·         Use the square, cube and power keys on a calculator and estimate powers and roots of any given positive number, by considering the values it must lie between, e.g. the square root of 42 must be between 6 and 7;

·         Find the value of calculations using indices including positive, fractional and negative indices;

·         Recall that n0 = 1 and n–1 =  for positive integers n as well as,  = √n and  = 3√n for any positive number n;

·         Understand that the inverse operation of raising a positive number to a power n is raising the result of this operation to the power ;

·         Use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integer powers, fractional and negative powers, and powers of a power;

·         Solve problems using index laws;

·         Use brackets and the hierarchy of operations up to and including with powers and roots inside the brackets, or raising brackets to powers or taking roots of brackets;

·         Use an extended range of calculator functions, including +, –, ×, ÷, x², √x, memory, x y, , brackets;

·         Use calculators for all calculations: positive and negative numbers, brackets, powers and roots, four operations.

·         Recall and use the formulae for the area of a triangle, rectangle, trapezium and parallelogram using a variety of metric measures;

·         Calculate the area of compound shapes made from triangles, rectangles, trapezia and parallelograms using a variety of metric measures;

·         Find the perimeter of a rectangle, trapezium and parallelogram using a variety of metric measures;

·         Calculate the perimeter of compound shapes made from triangles and rectangles;

·         Estimate area and perimeter by rounding measurements to 1 significant figure to check reasonableness of answers.

·         Recall the definition of a circle and name and draw parts of a circle;

·         Recall and use formulae for the circumference of a circle and the area enclosed by a circle (using circumference = 2πr = πd and area of a circle = πr2) using a variety of metric measures;

·         Use π ≈ 3.142 or use the π button on a calculator;

·         Calculate perimeters and areas of composite shapes made from circles and parts of circles (including semicircles, quarter-circles, combinations of these and also incorporating other polygons);

·         Calculate arc lengths, angles and areas of sectors of circles;

·         Find radius or diameter, given area or circumference of circles in a variety of metric measures;

·         Give answers in terms of π;

·         Form equations involving more complex shapes and solve these equations.

·         Express a given number as a fraction of another;

·         Find equivalent fractions and compare the size of fractions;

·         Write a fraction in its simplest form, including using it to simplify a calculation,
e.g. 50 ÷ 20 =  =  = 2.5;

·         Find a fraction of a quantity or measurement, including within a context;

·         Convert a fraction to a decimal to make a calculation easier;

·         Convert between mixed numbers and improper fractions;

·         Add, subtract, multiply and divide fractions;

·         Multiply and divide fractions, including mixed numbers and whole numbers and vice versa;

·         Add and subtract fractions, including mixed numbers;

Understand and use unit fractions as multiplicative inverses 

·         Factorise quadratic expressions in the form ax2 + bx + c;

·         Solve quadratic equations by factorisation and completing the square;

·         Solve quadratic equations that need rearranging;

·         Set up and solve quadratic equations;

·         Solve quadratic equations by using the quadratic formula;

·         Find the exact solutions of two simultaneous equations in two unknowns;

·         Use elimination or substitution to solve simultaneous equations;

·         Solve exactly, by elimination of an unknown, two simultaneous equations in two unknowns:

·         linear / linear, including where both need multiplying;

·         Find the original amount given the final amount after a percentage increase or decrease (reverse percentages), including VAT;

·         Use calculators for reverse percentage calculations by doing an appropriate division;

·         Use percentages in real-life situations, including percentages greater than 100%;

·         Describe percentage increase/decrease with fractions, e.g. 150% increase means  times as big;

·         Understand that fractions are more accurate in calculations than rounded percentage or decimal equivalents, and choose fractions, decimals or percentages appropriately for calculations.

·         Show inequalities on number lines;

·         Write down whole number values that satisfy an inequality;

·         Solve simple linear inequalities in one variable, and represent the solution set on a number line;

·         Solve two linear inequalities in x, find the solution sets and compare them to see which value of x satisfies both solve linear inequalities in two variables algebraically;

·         Use the correct notation to show inclusive and exclusive inequalities.

·       Write a ratio as a linear function;

·       Identify direct proportion from a table of values, by comparing ratios of values;

·       Use a ratio to compare a scale model to real-life object;

·       Use a ratio to convert between measures and currencies, e.g. £1.00 = €1.36;

·       Scale up recipes;

·       Convert between currencies.

·         Know the appropriate uses of histograms;

·         Construct and interpret histograms from class intervals with unequal width;

·         Use and understand frequency density;

·         From histograms:

·         complete a grouped frequency table;

·         understand and define frequency density;

·         Estimate the mean from a histogram;

·         Estimate the median from a histogram with unequal class widths or any other information from a histogram, such as the number of people in a given interval.

·         Factorise quadratic expressions in the form ax2 + bx + c;

·         Solve quadratic equations by factorisation and completing the square;

·         Solve quadratic equations that need rearranging;

·         Set up and solve quadratic equations;

Solve quadratic equations by using the quadratic formula