Chapter 8 Technology Graphics calculators/software can be used to look at areas under a curve and model changes. Student Book One hour lessons Learning objectives Subject content references Topic links references Make use of the connections 1 Indefinite integrals H1 Know and use the The fundamental theorem 9.1 – between differentiation and Fundamental Theorem of Calculus of calculus is used in 15.4 Ex 9.1A Students look at integration being the integration H2 Integrate (excluding ), and Displacement-time and – reverse process of differentiation. related sums, differences and velocity-time graphs Because the derivative of the final constant multiples 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. Find the equation of a when 2 Indefinite integrals continued H1 Know and use the 9.1 – you know the gradient and point on Fundamental Theorem of Calculus Ex 9.1B Students move the learning from the first a curve H2 Integrate (excluding ), and – lesson forward by finding the equations of related sums, differences and the curve given the derivative and a point constant multiples on the curve Use a technique called integration H2 Integrate (excluding ), and 9.2 3 The area under a curve – to find the area under a curve related sums, differences and Ex 9.2A Students move on to calculate definitive constant multiples integrals and are introduced to the H3 Evaluate definite integrals; – notation. This enables them to calculate use a definite integral to find the the area under curves. Students complete area a curve the first 6 questions of exercise 9.2A 4 The area under a curve continued Use a technique called integration H2 Integrate (excluding ), and 9.2 – to find the area under a curve related sums, differences and Ex 9.2A Recap knowledge from this and the constant multiples previous chapter (differentiation) ensuring H3 Evaluate definite integrals; – students clearly understand the link use a definite integral to find the between differentiation and integration. area under a curve Students finish exercise 9.2A.
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
Collins%20A-level%20Maths%20SoW%20Year%201_final.docx