Recap manipulating surds and complete Ex 1.7A if required and then students go on to rationalise the denominator of algebraic fractions. B2 - use and manipulate including rationalising the denominator 8 Chapter review lesson Recap key points of chapter. Students to complete the exam-style questions, extension questions, or online test Identify areas of strength and development within the content of the chapter See below Assessment questions 1 in Student Book Exam-style extension questions 1 in Student Book End-of-chapter test 1 on Collins Connect CHAPTER 2 – Algebra and functions 2: Equations and inequalities (8 Prior knowledge needed Chapter 1 Technology Use a calculator to check solutions to quadratic equations that have been solved by hand. Use a graphing software to plot lines when solving simultaneous equations so that students can see that where the lines intersect is the solution. Use graphing software to show the solutions to quadratic inequalities. One hour lessons Learning objectives Subject content references Topic links Student Book references 1 Quadratic functions Students draw and work out key aspects of quadratic functions, they also work out equations of quadratic graphs. Make students aware that the notation f(x) may be used. Consider the difference between drawing and sketching. Work with quadratic functions and their graphs B3 – work with quadratics functions and graphs Make connections back to factorising in 1.4 Factorisation 2.1 Ex 2.1A
5 Solving simultaneous equations Students go through solving two linear simultaneous equations by elimination and then by substitution. They need to think about which is the best method and why. Solve simultaneous equations in two variables by elimination or by substitution, including one linear and one quadratic equation B4 – solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation This is used when finding points of intersection with circles and straight lines in Chapter 5 Coordinate geometry 2: Circles 2.5 Ex 2.5A Ex 2.5B 6 Solving linear and quadratic simultaneous equations Student solve linear and quadratic simultaneous equations considering which method is the most appropriate to use. Solve simultaneous equations in two variables by elimination or by substitution, including one linear and one quadratic equation B4 – solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation 2.6 Ex 2.6A 7 Solving linear and quadratic inequalities Students inequalities, use set notation to list integer members of two or more combined inequalities and represent inequalities graphically. Strict inequalities are represented with a dotted line, inclusive inequalities are represented with a solid line. Link to solving equations, drawing graphs and looking at inequalities from the sketch of a graph. Solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically, including inequalities with brackets and fractions Express solutions through correct use of ‘and’ and ‘or’, or through set notation B5 - solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically, including inequalities with brackets and fractions B5 - express solutions through correct use of ‘and’ and ‘or’, or through set notation This is used in Chapter 5 Coordinate geometry 2: Circles when solving problems involving equations of circles 2.7 Ex 2.7A 2.8 Ex 2.8A 8 Chapter review lesson Recap key points of chapter. Students to complete the exam-style questions, extension questions, or online test Identify of strength and development within the content of the chapter See below Assessment Exam-style questions 2 in Student Book extension questions 2 in Student Book End-of-chapter test 2 on Collins Connect
CHAPTER 7 – Exponentials and logarithms (8 Prior knowledge needed Chapter 1 Chapter 2 Chapter 3 Chapter 4 Technology Graph plotting software to draw the graphs . Use the log, of e and ln button on a calculator. Use spreadsheet software to calculate values of logarithms. One hour lessons Learning objectives Subject content references Topic links Student Book references 1 The function Students learn the terms exponential growth and exponential decay. The draw graphs of the form and are made aware that there is a difference in the shape of the graph when a < 1 and a > 1, they should understand this. Use and manipulate expressions in the form the variable x is an index Draw and interpret graphs of the form Use the to find approximate solutions F1 – Know and use the function and its where a is positive Links back to GCSE 7.1 Ex 7.1A 2 Logarithms Students start with the laws of logarithms in base 10 and the laws of logarithms are linked to laws of indices with a proof for each law. They work out basic logarithms in base 10 without a calculator. They then move onto using the laws for logarithms of any base and using the button on a calculator. Understand and use logarithms and their connection with indices Understand the proof of the laws of logarithms F3 – know and use the definition of as the inverse of , where is positive and F4 – understand and use the laws of logarithms The skills learnt in 1.6 Laws of indices are used here 7.2 Ex 7.2A Ex 7.2B 3 The equation Students solve equations of the form by taking the logarithms of both sides. The Solve equations in the form Understand a proof of the formula to change the base of a logarithm F5 – equations in the form 7.3 Ex 7.3A
linked to being the gradient of the graph and the rate of change. 6 Stationary points and the second derivative Differentiation is used to find stationary points, i.e. the point where . Students are shown that the second derivative will show if a turning point is a maximum or minimum point so there is no need to draw the graph to ascertain this information. Determine geometrical properties of a G1 – second derivatives G1 – understand and use the second derivative as the rate of change of gradient G3 – differentiation to find gradients, tangents and normal, maxima and minima and stationary points G3 – identify where functions are increasing and decreasing 8.6 Ex 8.6A 7 Tangents and normal The normal at any point on a curve is perpendicular to the tangent at that point. As the product of their gradients is -1 differentiation can be used to find the equations of the tangent and the normal. Find equations of tangents and normal using differentiation G3 – apply differentiation to find gradients, tangents and normal, maxima and minima and stationary points G3 – identify functions are increasing and decreasing 8.7 Ex 8.7A 8 Chapter review lesson Recap key points of chapter. Students to complete the exam-style questions, extension questions, or online test Identify areas of strength and development within the content of the chapter See below Assessment questions 8 in Student Book Exam-style extension questions 8 in Student Book End-of-chapter test 8 on Collins Connect CHAPTER 9 – Integration (5 Hours) Prior knowledge needed Chapter 1 Chapter 3
Chapter 8 Technology Graphics calculators/software can be used to look at areas under a curve and model changes. One hour lessons Learning objectives Subject content references Topic links Student Book references 1 Indefinite integrals Students look at integration being the reverse process of differentiation. Because the derivative of the final constant is zero the result of integration is sometimes called the indefinite integral because the value of is not fixed. Students integrate the sum or difference of terms by integrating them separately. Make use of the connections between differentiation and integration H1 – Know and use the Fundamental Theorem of Calculus H2 – Integrate (excluding ), and related sums, differences and constant multiples The fundamental theorem of calculus is used in 15.4 Displacement-time and velocity-time graphs 9.1 Ex 9.1A 2 Indefinite integrals continued Students move the learning from the first lesson forward by finding the equations of the curve given the derivative and a point on the curve Find the equation of a when you know the gradient and point on a curve H1 – Know and use the Fundamental Theorem of Calculus H2 – Integrate (excluding ), and related sums, differences and constant multiples 9.1 Ex 9.1B 3 The area under a curve Students move on to calculate definitive integrals and are introduced to the notation. This enables them to calculate the area under curves. Students complete the first 6 questions of exercise 9.2A Use a technique called integration to find the area under a curve H2 – Integrate (excluding ), and related sums, differences and constant multiples H3 – Evaluate definite integrals; use a definite integral to find the area a curve 9.2 Ex 9.2A 4 The area under a curve continued Recap knowledge from this and the previous chapter (differentiation) ensuring students clearly understand the link between differentiation and integration. Students finish exercise 9.2A. Use a technique called integration to find the area under a curve H2 – Integrate (excluding ), and related sums, differences and constant multiples H3 – Evaluate definite integrals; use a definite integral to find the area under a curve 9.2 Ex 9.2A
5 Chapter review lesson key points of chapter. Students to complete the exam-style questions, extension questions, or online test Identify areas of strength and development within the content of the chapter See Assessment Exam-style questions 9 in Student Book Exam-style extension questions 9 in Student Book End-of-chapter test 9 on Collins Connect CHAPTER 10 – Vectors (5 Hours) Prior knowledge needed Chapter 6 Technology Use a graphics package to plot vectors and investigate how the angle changes depending on the orientation. Plotting diagrams using graphics software enables you to visualise the situation and see how the vectors will still satisfy the rules even if the orientation of the vectors is not identical. One hour lessons Learning objectives Subject content references Topic links Student Book references 1 Definition of a vector Students look at vector notation and use Pythagoras’ theorem to calculate the magnitude of vectors. They use trigonometry to find the direct of a vector or use bearings. They calculate the unit vector and use this to find a velocity vector. Write a vector in i j or as a column vector Calculate the magnitude and direction of a vector as a bearing in two dimensions Identify a unit vector and scale it up as appropriate Find a velocity vector J1 – use vectors in two dimensions J2 – calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form J1 – use vectors in two dimensions J2 – calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form Trigonometric bearings were introduced in 6.2 The sine rule and the cosine rule 10.1 Ex 10.1A
2 Adding vectors Students add and subtract vectors in both i j and column notation. They are introduced to the three types of vectors (equal, opposite and parallel) and learn that parallel vectors contain a common factor. Add vectors Multiply a vector by a scalar J3 – add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars J3 – add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars Adding vectors is used to find resultant forces in Chapter 16 Forces 10.2 Ex 10.2A 3 Vector geometry Students add vectors using the triangle law and are introduced to the parallelogram law which shows that that the order in which vectors are added is not important. Students go on to be introduced to the ratio theorem and the midpoint rule (a special case of the midpoint theorem) Apply the triangle law to add vectors the ratio and midpoint theorems J3 – add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars and understand their geometric interpretations J3 – add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars and understand their geometric interpretations 10.3 Ex 10.3A Ex 10.3B 4 Position vectors Students learn that the position vector of a point is its position relative to the origin. They use this to calculate the relative displacement between two position vectors by subtracting the position vectors. Students calculate the distance between the two points by finding the magnitude of the relative displacement using Pythagoras’ theorem. Find the position vector of a point Find the relative displacement between two position vectors J4 – understand and use position vectors; calculate the distance between two points represented by position vectors J4 – understand and use position vectors; calculate the distance between two points represented by position vectors 10.4 Ex 10.4A 5 Chapter review lesson Recap key points of chapter. Students to complete the exam-style questions, extension questions, or online test Identify areas of strength and development within the content of the chapter See below
One hour lessons Learning objectives Subject content references Topic links Student Book references 1 Measures of central tendency Students review of data, the median, the mode and the mean. Students consider which is the best measure of central tendency to use and why. They use Data set activity 12.1 to calculate the median and mean and comment critically on findings. Use discrete or continuous data Use measures of central tendency: mean, median, mode L3 – interpret measure of central tendency and variation Links back to GCSE 12.1 DS 12.1 2 Measures of central tendency and spread Students review measures of spread; the range and interquartile range They use frequency table to calculate measure of central tendency and spread and estimate the mean from frequency tables. Use discrete, continuous, grouped or ungrouped data Use measures of variation: range and interpercentile ranges L3 – interpret measure of central tendency and variation back to GCSE 12.1 Ex 12.1A 3 Variance and standard deviation Students are introduced to variance and standard deviation and the fact that these measures use all the data items. Students go onto calculating variance and standard deviation using frequency tables. Use measure of variation: variance and standard deviation Use the statistic Use standard deviation L3 – interpret measures of variation, extending to standard deviation L3 – be able to calculate standard deviation, including from summary statistics L4 – select or critique data presentation techniques in the context of a statistical problem This is covered further in Book 2, Chapter 13 Statistical distributions 12.2 Ex 12.2A 4 Data cleaning Recap calculating variance and standard deviation from frequency tables and then introduce data cleaning as involving the identification and removal of any invalid Use measure of variation: variance and standard deviation Use the statistic Use standard deviation L4 – select or critique data presentation techniques in the context of a statistical problem 12.2 DS 12.2
probabilities of mutually exclusive and independent events using Venn diagrams and tree diagrams. 2 Discrete and continuous distributions – part 1 The term discrete and continuous data is recapped. A discrete random variable is then defined. Probability distribution tables are used to show all the possible values a discrete random variable can take along with the probability of each value occurring. When all events are equally likely they form a uniform distribution. Students go on to probability distributions of a random variable. Identify a discrete uniform distribution M1 – link to discrete and continuous distributions You will use knowledge from Chapter 12 Data presentation and interpretation 13.2 Ex 13.2A 3 Discrete and continuous distributions – part 2 Continuous random variables are considered and when graphed a continuous line is used. The graph is called a probability density function (PDF), the area under a pdf shows the probability and sums to 1. Students then go on to find cumulative probabilities. Identify a discrete uniform distribution M1 – link to discrete and continuous distributions You will use knowledge from Chapter 12 Data presentation and interpretation 13.2 Ex 13.2B 4 The binomial distribution Binomial distribution is about ‘success’ and ‘failure’ as there are only two possible outcomes to each trail. Students identify situations which can be modelled using the binomial distribution. They then calculate probabilities using the binomial Use a calculator to find individual or cumulative binomial probabilities Calculate binomial probabilities using the notation N1 – understand and use simple, discrete probability distributions (calculation of mean and variance of discrete random variables excluded), including the binomial distribution, as a model; calculate probabilities using the binomial distribution You will need the skills and techniques learnt in Chapter 1 Algebra and functions 1: Manipulating algebraic expressions Knowing how to calculate binomial probabilities will help you in Chapter 14 13.3 Ex 13.3A
distribution. Several examples are worked through. Statistical sampling and hypothesis testing 5 Chapter review lesson Recap key points of chapter. Students to complete the exam-style questions, extension questions, or online test Identify areas of strength and development within the content of the chapter See below Assessment Exam-style questions 13 in Student Book Exam-style extension questions 13 in Student Book End-of-chapter test 13 on Collins Connect CHAPTER 14 – Statistical sampling and hypothesis testing (6 Hours) Prior knowledge needed Chapter 12 Chapter 13 Technology Use a calculator to calculate binomial cumulative probabilities. Use spreadsheet packages for the data set activities. One hour lessons Learning objectives Subject content references links Student Book references 1 Populations and samples Discuss the different terms and terminology within populations including; finite and infinite population, census, sample survey, sampling unit, sampling frame and target population. Move onto Use sampling techniques, including simple random, stratified sampling, systemic sampling, quota sampling and opportunity (or convenience) sampling Select or critique sampling techniques in the context of solving a statistical problem, including A1 – mathematical proof K1 – Use sampling techniques, including simple random, stratified sampling, systemic sampling, quota sampling and opportunity (or convenience) sampling You will need to know how to data for Chapter 12 Data presentation and interpretation 14.1 DS 14.1 Ex 14.1A
distribution and interpret that results in context 4 Significance levels – part 1 Students look at significance levels being the probability of mistakenly rejecting the null hypothesis. The terms test statistic and critical region are explained and students move onto finding the critical region and critical value. They work through the examples up to the end of example 3. Appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis O2 – understand that a sample is being used to make an inference about the population and appreciate that they significance level is the probability of incorrectly rejecting the null hypothesis 14.2 5 Significance levels – part 2 Recap previous lesson, with a focus on how to calculate values using calculators instead of statistical tables. After working through the rest of the chapter from example 4 onwards, students go on to complete exercise 14.2B. Appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis O2 – understand that a sample is being used to make an inference about the population and appreciate that they significance level is the probability of incorrectly rejecting the null hypothesis 14.2 Ex 14.2B 6 Chapter review lesson Recap key points of chapter. Students to complete the exam-style questions, extension questions, or online test Identify of strength and development within the content of the chapter See below Assessment Exam-style questions 14 in Student Book Exam-style extension questions 14 in Student Book End-of-chapter test 14 on Collins Connect
CHAPTER 15 – Kinematics (10 Hours) Prior knowledge needed Chapter 2 Chapter 3 Chapter 4 Chapter 8 Chapter 9 Chapter 10 Technology Graphics packages can be used to visualise problems. One hour lessons Learning objectives Subject content references Topic links Student Book references 1 The language of kinematics Students are introduced to motion in a straight line and the vocabulary displacement, velocity and acceleration (vectors quantities) as opposed to distance, time and speed (scalar quantities). They use the SI unit for distance (metres) and time (seconds) to derive other units. Time permitting introduce the five SUVAT equations. Find the SI units of displacement, velocity and acceleration P1 – understand and use fundamental quantities and in the S.I. system: length, time, mass P1 – understand and use derived quantities and units; velocity and acceleration Q1 – understand and use the language of kinematics; position; displacement; distance travelled; velocity; speed; acceleration 15.1 Ex 15.1A 2 Equations of constant acceleration – part 1 The definition of acceleration () is used to derive the five equations. Students have to work out which of the equations to use to solve problems. Derive and use the equations of constant acceleration Q3 – understand, use and derive the formulae for constant acceleration for motion in a straight line The SUVAT equations are used in Chapter 16 Forces 15.2 Ex 15.2A 3 Equations of constant acceleration – part 2 Recap the five SUVAT equations from the previous lesson. Questions become more Derive and use the equations of constant acceleration Q3 – understand, use and derive the formulae for constant acceleration for motion in a straight line 15.2 Ex 15.2B
complicated in ex 15.2B and students are encouraged to draw a diagram to assist them in understanding the situation 4 Vertical motion – part 1 Students continue to solve problems using the equations of constant acceleration but this time the acceleration is equal to gravity. They need to decide if gravity is influencing the situation in a positive or negative way. Derive and use the equations of constant acceleration, including for situation with gravity Q3 – understand, use and derive the formulae for constant acceleration for motion in a straight line 15.3 Ex 15.3A 5 Vertical motion – part 2 Recap the previous lesson and move on to look at when two objects are launched in different ways, students are advised to look for what the journeys have in common. Derive and use the equations of constant acceleration, including for situation with gravity Q3 – understand, use and derive the formulae for constant acceleration for motion in a straight line 15.3 Ex 15.3B 6 Displacement-time and velocity-time graphs – part 1 Where acceleration is constant, students construct graphs using straight lines and the concepts that the gradient of a displacement-time graphs is velocity and the gradient of a velocity-time graph is acceleration. The area under a graph is used to calculate displacement. Students focus on displacement-time graphs. Draw and interpret displacement-time graphs and velocity-time graphs Q2 – understand, use and interpret graphs in kinematics for motion in a straight line; displacement against time and interpretation of gradient; velocity against time and interpretation of gradient and area under the graph 15.4 Ex 15.4A 7 Displacement-time graphs and graphs – part 2 Recap the facts from last lesson and students go on to answer questions focusing on velocity-time graphs. Draw and interpret displacement-time graphs and velocity-time graphs Q2 – understand, use and interpret graphs in kinematics for motion in a straight line; displacement against time and interpretation of gradient; velocity against time and interpretation of gradient and area under the graph 15.4 Ex 15.4B