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YEAR 11 PROGRESS TRACKER NAME: ____________________________________ TEACHER:______________________ CLASS: ________________ Target Levels GCSE minimum target GCSE challenge target Term Test %/Grade How I Can Improve Year 10 mock Year 11 Mock 1 Year 11 Mock 2 Method Maths MyMaths UNIT: Integers, decimals and surds PASS: Understand and order integers and decimals Identify factors, multiples and prime numbers Recall integer squares from 2 × 2 to 15 × 15 and the corresponding square roots Recall the cubes of 2, 3, 4, 5 and 10 and cube roots Use index notation for squares and cubes Understand and use positive numbers and negative integers, both as positions and translations on a number line Round whole numbers to the nearest, 10, 100, 1000 Understand how place value can be used to solve problems, Eg if 23 x 87 = 2001, what does 2.3 x 870 = ? HIGHER: Find the prime factor decomposition of positive integers Find the highest common factor (hcf) and the lowest common multiple (lcm) Use brackets and the hierarchy of operations (bidmas) Add, subtract, multiply and divide integers, negative numbers and decimals Round decimals to appropriate numbers of decimal places or significant figures Check their calculations by rounding, eg 29 31 30 30 Know that eg 13.5 0.5 = 135 5 Find the upper and lower bounds of calculations involving perimeter, areas and volumes of 2-d and 3-d shapes Find the upper and lower bounds in real-life situations using measurements given to appropriate degrees of accuracy Be able to write very large and very small numbers presented in a context in standard form Convert between ordinary and standard form representations Interpret a calculator display using standard form Find the value of calculations using indices Use index laws to simplify and calculate numerical expressions involving powers, Eg (23 25) 24, 40 STAR: Convert between recurring decimals and exact fractions and use proof Calculate the upper and lower bounds of calculations, particularly when working with measurements Calculate with standard form Use index laws to simplify and calculate numerical expressions involving powers, Eg 5-2 811/3 Write 8 in the form 2 2 Write (3 3) 2 in the form a b 3 MEGASTAR Give the final answer to an appropriate degree of accuracy following an analysis of the upper and lower bounds of a calculation Use index laws to simplify and calculate numerical expressions involving powers, Eg 81-2/3 Know that, eg x3 = 64 x = 82/3 Rationalise the denominator, eg 1 = 3 and, eg write (18 +10) 2 in the form p + q2 3 3 FEED FORWARD UNIT: Fractions, decimals and percentages PASS: Find equivalent fractions Compare the sizes of fractions Write a fraction in its simplest form Find fractions of an amount Express a given number as a fraction of another number Convert between mixed numbers and improper fractions Understand that a percentage is a fraction in hundredths Convert between fractions, decimals and percentages HIGHER: Add, subtract, multiply and divide fractions Multiply and divide fractions including mixed numbers Solve problems using fractions Write one number as a percentage of another number Calculate the percentage of a given amount Find a percentage increase/decrease of an amount STAR: Find a reverse percentage, eg find the original cost of an item given the cost after a 10% deduction Use a multiplier to increase by a given percent over a given time, eg 1.18 64 increases 64 by 10% over 8 years Calculate simple and compound interest MEGASTAR Algebraic fractions FEED FORWARD UNIT: Ratio and Proportion PASS: Use ratios Write ratios in their simplest form HIGHER Divide a quantity in a given ratio Solve a ratio problem in a context Solve word problems involving proportion; recipe questions, mixtures, time problems. Calculate an unknown quantity from quantities that vary in direct or inverse proportion STAR: Set up and use equations to solve word and other problems involving direct proportion or inverse proportion and relate algebraic solutions to graphical representation of the equations MEGASTAR Set up and use equations to solve word and other problems involving direct proportion or inverse proportion including problems involving squares and cubes. FEED FORWARD UNIT: Algebra Expressions and Sequences PASS: Use notation and symbols correctly Write an expression Select an expression/identity/equation/formula from a list Manipulate algebraic expressions by collecting like terms Simplify expressions using index laws Generate simple sequences of numbers, squared integers and sequences derived from diagrams Describe the term-to-term definition of a sequence in words Use formulae from mathematics and other subjects Substitute numbers into a formula HIGHER: Identify which terms cannot be in a sequence Generate specific terms in a sequence using the position-to-term and term-to-term rules Find and use the nth term of an arithmetic sequence Multiply a single term over a bracket Factorise algebraic expressions by taking out common factors Expand the product of two linear expressions Substitute positive and negative numbers into expressions such as 3x² + 4 and 2x³ STAR: Use index laws for integer, negative, and fractional powers and powers of a power Factorise quadratic expressions, including using the difference of two squares Simplify rational expressions by cancelling, adding, subtracting and multiplying MEGASTAR Investigate quadratic sequences whose nth term is an2 + bn + c FEED FORWARD UNIT: Solving equations, inequalities and re-arranging PASS: Set up linear equations from word problems Solve simple linear equations HIGHER: I CAN... Use systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving them Solve linear equations, with integer coefficients, in which the unknown appears on either side or on both sides of the equation Solve linear equations that include brackets, 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 Solve simple linear inequalities in one variable, and represent the solution set on a number line Use the correct notation to show inclusive and exclusive inequalities Derive equations from practical situations (such as finding unknown angles in polygons or perimeter problems) Use elimination or substitution to solve simultaneous equations STAR: I CAN... Solve simple quadratic equations by factorisation and completing the square Solve simple quadratic equations by using the quadratic formula Change the subject of a formula including cases where the subject is on both sides of the original formula, or where a power of the subject appears Apply changing the subject to y = mx + c MEGASTAR Select and apply algebraic and graphical techniques to solve simultaneous equations where one is linear and one quadratic Solve equations involving algebraic fractions which lead to quadratic equations FEED FORWARD UNIT: Graphs and Functions PASS: Use axes and coordinates to specify points in all four quadrants in 2-d and 3-d Identify points with given coordinates Identify coordinates of given points (nb: points may be in the first quadrant or all four quadrants) HIGHER: Find the coordinates of the midpoint of a line segment, ab, given the coordinates of a and b Recognise that equations of the form y = mx + c correspond to straight-line graphs in the coordinate plane Draw and interpret straight-line graphs for real-life situations such as: ready reckoner graphs conversion graphs fuel bills, eg gas and electric fixed charge (standing charge) and cost per unit Plot and draw graphs of straight lines with equations of the form y = mx + c Find the gradient of a straight line from a graph Find the gradient of a straight line from its equation Analyse problems and use gradients to interpret how one variable changes in relation to another STAR: Explore the gradients of parallel lines and lines perpendicular to each other Write down the equation of a line parallel or perpendicular to a given line 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 1 m Interpret and analyse a straight-line graph and generate equations of lines parallel and perpendicular to the given line Interpret a pair of simultaneous equations as a pair of straight lines and their solution as the point of intersection Students should find the equation of the line through two given points Show the solution set of several inequalities in two variables on a graph MEGASTAR Plot and recognise cubic, reciprocal, exponential and circular functions y = sin x and y = cos x, within the range -360º to +360º Construct the graphs of simple loci including the circle x² + y ²= r² for a circle of radius r centred at the origin of the coordinate plane FEED FORWARD UNIT: Constructions PASS: Construct triangles using a protractor Identify and draw parallel lines Draw circles and arcs to a given radius Use and interpret maps and scale drawings Read and construct scale drawings drawing lines and shapes to scale Estimate lengths using a scale diagram HIGHER: Construct triangles using a compass (equilateral and right angled) Understand, from the experience of constructing them, that triangles satisfying sss, sas, asa and rhs are unique, but ssa triangles are not Construct the perpendicular bisector of a given line Construct the perpendicular from a point to a line Construct the perpendicular from a point on a line Construct the bisector of a given angle Construct angles of 60º, 90º , 30º and 45º Construct diagrams of everyday 2-d situations involving rectangles, triangles, perpendicular and parallel lines Construct a region bounded by a circle and an intersecting line: a given distance from a point and a given distance from a line equal distances from 2 points or 2 line segments regions which may be defined by ‘nearer to’ or ‘greater than’ Find and describe regions satisfying a combination of loci STAR: Construct a regular hexagon inside a circle FEED FORWARD UNIT: Shape and Angles PASS: Recall and use properties of: o angles at a point o angles at a point on a straight line o perpendicular lines o vertically opposite angles o Angles in a triangle add to 180º o Angles in quadrilaterals add to 360º Recognise and classify triangles and quadrilaterals Give reasons for angle calculations Tessellate shapes Use triangles to find the angle sums of polygons HIGHER: I CAN... Use the properties of corresponding, alternate and allied angles Calculate and use the sums of the interior and exterior angles of polygons Understand, draw and measure bearings Solve bearing problems using corresponding, alternate and allied angle properties Explain why some shapes tessellate when other shapes do not STAR: I CAN... Use the angle properties of triangles to find missing angles in combinations of triangles derive and apply the properties and definitions of special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; Solve harder problems involving multi-step calculations Solve problems that combine angle properties with algebraic expressions and solving equations Use angle facts and algebra notation to prove shape statements FEED FORWARD UNIT: Similarity and congruence PASS: Enlarge shapes by a given scale factor Work out missing lengths of a shape that has been enlarged by an integer scale factor Recognise that all corresponding angles in similar figures are equal in size when the lengths of sides are not HIGHER: Understand, from the experience of constructing them, that triangles satisfying sss, sas, asa and rhs are unique, but ssa triangles are not Understand and use SSS, SAS, ASA and RHS conditions to prove the congruence of triangles using formal arguments, and to verify standard ruler and a pair of compasses constructions Work out missing lengths of a shape that has been enlarged by a whole number or a decimal Understand similarity of triangles and of other plane figures, and use this to make geometric inferences Understand the effect of enlargement for perimeter, area and volume of shapes and solids Understand that enlargement does not have the same effect on area and volume Use simple examples of the relationship between enlargement and areas and volumes of simple shapes and solids STAR: I CAN... Provide formal geometric proof of similarity of two given triangles Use the effect of enlargement on areas and volumes of shapes and solids Know the relationships between linear, area and volume scale factors of mathematically similar shapes and solids MEGASTAR Provide formal geometric proof of similarity of two given shapes Work though complex similar shape problems involving surface area and volume FEED FORWARD UNIT: Pythagoras and Trigonometry PASS: Know and understand squares and square roots Understand, recall and use Pythagoras’ theorem in 2-D Understand the language of planes, and recognise the diagonals of a cuboid HIGHER: Understand, recall and use Pythagoras’ theorem in 2-D and 3-D problems Calculate the length of a diagonal of a cuboid Calculate the length of a line segment in 2-D Give an answer in the use of Pythagoras’ theorem as √13 Recall and use the trigonometric ratios to solve 2-D and 3-D problems STAR: Find the angle between a line and a plane (Trigonometry in 3D) Find angles of elevation and angles of depression using trigonometry Find bearings using trigonometry Solve multistep problems involving Pythagoras and trigonometry Find the area of different polygons using Pythagoras and trigonometry (parallelograms, hexagons etc) MEGASTAR Find the volume of different 3D shapes using Pythagoras and trigonometry Calculate the area of a triangle using 1 absinC 2 Use the sine and cosine rules to solve 2-D and 3-D problems 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° recognise, sketch and interpret graphs of the trigonometric functions: y = sin x, y = cos x and y = tan x FEED FORWARD UNIT: Circle theorems PASS: Recall the words centre, radius, diameter and circumference Draw circles with compasses HIGHER: Recall the definition of a circle and identify (name) and draw all the parts of a circle Draw a circle given the radius or diameter Recognise isosceles triangles in circles using radii Understand and use the fact that the tangent at any point on a circle is perpendicular to the radius at that point Understand and use the fact that tangents from an external point are equal in length Find missing angles on diagrams using: o the fact that the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference o the fact that the angle in a semicircle is a right angle o the fact that angles in the same segment are equal o the fact that opposite angles of a cyclic quadrilateral sum to 180º STAR: Give reasons for angle calculations Solve harder problems involving multi-stage angle calculations Find missing angles on diagrams using: o the alternate segment theorem the perpendicular line from the centre of a circle to a chord bisects the chord MEGASTAR Prove circle theorems FEED FORWARD UNIT: Measures and compound measures PASS: Knowledge of metric units, eg 1 m = 100 cm etc Know that 1 hour = 60 mins, 1 min = 60 seconds Experience of multiplying by powers of 10, eg 100 100 = 10 000 HIGHER: Convert between units of measure in the same system. Note: conversion between imperial units will be given, metric equivalents should be known Convert between imperial and metric measures when conversion given Use the relationship between distance, speed and time to solve problems Construct and interpret distance time graphs STAR: Know rough metric equivalents of pounds, feet, miles, pints and gallons, ie Metric Imperial 1 kg = 2.2 pounds 1 litre = 1.75 pints 4.5 l = 1 gallon 8 km = 5 miles 30 cm = 1 foot Convert between metric units of speed, eg km/h to m/s Know that density is found by mass ÷ volume Use the relationship between density, mass and volume to solve problems, eg find the mass of an object with a given volume and density Convert imperial units to metric units, eg mph into km/h when conversions given MEGASTAR Convert between metric units of density, eg kg/m³ to g/cm³ (ie convert between metric units of volume) Convert imperial units to metric units, eg mph into km/h when conversions not given Use other units (not assessed for GCSE) like hectares FEED FORWARD UNIT: Transformations PASS: Recognition of basic shapes Understanding of the concepts of rotation, reflection, translation and enlargement Coordinates in four quadrants Recognise the x and y axis Draw the lines symmetry and reflection lines Identify the order of rotational symmetry of a 2-d shape HIGHER: Know linear equations parallel to the coordinate axes (e.g. x = 4) State the line of reflection as a simple algebraic equation Reflect shapes in a given mirror line; parallel to the coordinate axes and then y = x or y = – x Translate a given shape by a vector Enlarge shapes by a positive integer scale factor from a given point Find the centre of enlargement Recognise that enlargements preserve angle but not length, linking to similarity Describe and transform 2-d shapes using single rotations Understand that rotations are specified by a centre and an (anticlockwise) angle Find the centre of rotation Describe a transformation Understand that images produced by translation, rotation and reflection are congruent to the object STAR: Enlarge shapes by a given scale factor from a given point; using positive, negative and fractional scale factors Describe and transform 2-d shapes using combined rotations, reflections, translations or enlargements MEGASTAR Use congruence to show that translations, rotations and reflections preserve length and angle, so that any figure is congruent to its image under any of these transformations Apply to the graph of y = f(x) the transformations y = f(x) + a, y = f(ax), y = f(x + a), y = af(x) for linear, quadratic, sine and cosine functions, f(x) FEED FORWARD UNIT: Vectors PASS: Translate a given shape by a vector HIGHER: Draw lines to represent vectors Use vectors to represent simple paths around shapes STAR: Use and interpret vectors paths around shapes Know that vectors are displacements in the plane (with an associated direction) Understand that 2a is parallel to a and twice its length Understand that a is parallel to a and in the opposite direction Use standard vector notation to combine vectors by addition, eg AB + BC = AC and a + b = c Calculate, and represent graphically, the sum of two vectors, the difference of two vectors and the scalar multiple of a vector MEGASTAR Interpret and represent difficult combinations of vectors Use fractions and ratios to help find complex vector paths Use vectors to prove parallel lines and shape properties FEED FORWARD UNIT: Probability PASS: Understand that a probability is a number between 0 and 1 Know how to add and multiply fractions and decimals Recognise the language of probability, eg words such as likely, certain, impossible Write probabilities using fractions, percentages or decimals HIGHER: Understand and use estimates or measures of probability, including relative frequency Use theoretical models to include outcomes using dice, spinners, coins etc Find the probability of successive events, such as several throws of a single dice Estimate the number of times an event will occur, given the probability and the number of trials List all outcomes for single events, and for two successive events, systematically Use and draw sample space diagrams Add simple probabilities, eg from sample space diagrams Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1 Use 1 − p as the probability of an event not occurring where p is the probability of the event occurring Find a missing probability from a list or table STAR: Understand conditional probabilities Understand selection with or without replacement Draw a probability tree diagram based on given information Use a tree diagram to calculate conditional probability Compare experimental data and theoretical probabilities Compare relative frequencies from samples of different sizes MEGASTAR Combine probability with algebra: o Draw tree diagrams using algebra to represent probabilities o Calculate conditional probability involving algebra FEED FORWARD UNIT: Averages and data PASS: An understanding of the importance of a knowledge of statistics in our society, and of why data needs to be collected Create tally charts/frequency tables Understand how to collect data from a variety of suitable primary and secondary sources Understand sample and population Design or criticise a question for a questionnaire Design and use data-collection sheets for grouped, discrete and continuous data Understand inequality notation used in tables, charts and graphs Produce bar charts (including composite bar charts, comparative and dual bar charts) Calculate mean, mode, median and range for small data sets Produce ordered stem and leaf diagrams and use them to find the range and averages HIGHER: Discuss how data relates to a problem, identify possible sources of bias and plan to minimise it Understand how different sample sizes may affect the reliability of conclusions drawn Group discrete and continuous data into class intervals of equal width Design and use two-way tables for discrete and grouped data Use information provided to complete a two-way table Produce and interpret pie charts, frequency polygons and scatter graphs Look at data to find patterns and exceptions, explain an isolated point on a scatter graph Draw and use a line of best fit, or otherwise, to predict values of one variable given valuesof the other variable Distinguish between positive, negative and zero correlation using lines of best fit Compare distributions and make inferences, using the shapes of distributions and measures of average and spread, including median and quartiles Recognise the advantages and disadvantages between measures of average Calculate averages and range from frequency tables Find modal class and interval containing the median Find quartile and interquartile range from data Draw and interpret cumulative frequency tables and graphs Use cumulative frequency graphs to find median, quartiles and interquartile range Draw box plots from a cumulative frequency graph and from raw data Compare the measures of spread between a pair of box plots/cumulative frequency graphs Interpret box plots to find, for example, median, quartiles, range and interquartile range Compare distributions and make inferences, using the shapes of distributions and measures of average and spread, including median and quartiles Find the mode, median, range and interquartile range, as well as the greatest and least values from the stem and leaf diagrams STAR: Select and justify a sampling scheme and a method to investigate a population, including random and stratified sampling Use stratified sampling Produce and interpret histograms From histograms: complete a grouped frequency table and understand and define frequency density MEGASTAR Find the median from a histogram or any other information from a histogram, such as the number of people in a given interval FEED FORWARD Autumn Mock Exam Paper: Mark: Grade: 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