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DMO’L.St Thomas More C4: Starters Revise formulae and develop problem solving skills

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DMO’L.St Thomas More Starter 1 Express in partial fractions. Hence find

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DMO’L.St Thomas More Starter 1 Express in partial fractions. Hence

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DMO’L.St Thomas More Starter 1 Back

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DMO’L.St Thomas More Starter 2 Express in partial fractions. Hence find

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DMO’L.St Thomas More Starter 2 Express in partial fractions. Hence

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DMO’L.St Thomas More Starter 2 Back

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DMO’L.St Thomas More Starter 3 Find the cartesian equation of the curve given by the parametric equations

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DMO’L.St Thomas More Starter 3 Find a way to eliminate t Back

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DMO’L.St Thomas More Starter 4 Find the cartesian equation of the curve given by the parametric equations

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DMO’L.St Thomas More Starter 4 Find a way to eliminate t Back

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DMO’L.St Thomas More Starter 5 Find the cartesian equation the curve given by the parametric equations

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DMO’L.St Thomas More Starter 5 Find a way to eliminate t Back

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DMO’L.St Thomas More Starter 6 Find the coordinates of the points where the following curves meet the x,y axes Back

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DMO’L.St Thomas More Starter 7 Find the coordinates of the points where the following curves meet the x,y axes Back

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DMO’L.St Thomas More Starter 8 Find dy / dx leaving your answer in terms of t. Back

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DMO’L.St Thomas More Starter 9 Find dy / dx leaving your answer in terms of t. Back

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DMO’L.St Thomas More Starter 10 Find the equation of the tangent to the curve defined by the following parametric equations at the point P where t = / 2 At P t = / 2 so that giving Back

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DMO’L.St Thomas More Starter 11 Evaluate Back

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DMO’L.St Thomas More Starter 12 Complete the table: Back

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DMO’L.St Thomas More Starter 13 Complete the table: Back

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DMO’L.St Thomas More Starter 14 Complete the table: Back

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DMO’L.St Thomas More Starter 15 Evaluate Back

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DMO’L.St Thomas More Starter 16 Evaluate Back

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DMO’L.St Thomas More Starter 17 In each case find Back in terms of x and y

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DMO’L.St Thomas More Starter 18 Find Back

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DMO’L.St Thomas More Starter 19 Find Back

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DMO’L.St Thomas More Starter 20 Find Back

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DMO’L.St Thomas More Starter 21 Use the trapezium rule with 6 strips to estimate x 1st/lastothers

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DMO’L.St Thomas More Starter 21 Use the trapezium rule with 6 strips to estimate x 1st/lastothers

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DMO’L.St Thomas More Starter 21 Use the trapezium rule with 6 strips to estimate x 1st/lastothers

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DMO’L.St Thomas More Starter 21 Use the trapezium rule with 6 strips to estimate x 1st/lastothers

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DMO’L.St Thomas More Starter 21 Use the trapezium rule with 6 strips to estimate x 1st/lastothers To 3 sig. fig. Back

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DMO’L.St Thomas More Starter 22 Use the trapezium rule with 4 strips to estimate x 1st/lastothers 01 / /6/ /4/ /3/

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DMO’L.St Thomas More Starter 22 Use the trapezium rule with 4 strips to estimate x 1st/lastothers 01 / /6/ /4/ /3/

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DMO’L.St Thomas More Starter 22 Use the trapezium rule with 4 strips to estimate x 1st/lastothers 01 / /6/ /4/ /3/

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DMO’L.St Thomas More Starter 22 Use the trapezium rule with 4 strips to estimate x 1st/lastothers 01 / /6/ /4/ /3/ To 3 sig. fig. Back

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DMO’L.St Thomas More Region A is bounded by the curve with equation, the lines x = 1, x = 0 and the x -axis. The region A is rotated through 360 o about the x -axis Find the volume generated. Starter 23 Volume Back

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DMO’L.St Thomas More Points A and B have position vectors i + j + k and 2i - 3j + 2k respectively. Find the vector equation of the straight line through A and B. Starter 24 AB = ( 2i - 3j + 2k) – (i + j + k)

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DMO’L.St Thomas More Points A and B have position vectors i + j + k and 2i - 3j + 2k respectively. Find the vector equation of the straight line through A and B. Starter 24 AB = ( 2i - 3j + 2k) – (i + j + k) = i – 4j + k Hence, a vector equation is; r = i + j + k + (i – 4j + k) Back

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DMO’L.St Thomas More angle Find the acute angle between the two lines with vector equations r = 2i + j + k +t(3i – 5j – k) and r = 7i + 4j + k +s(2i + j – 9k) Starter 25 Consider the angle between their direction vectors; a = (3i – 5j – k) and b = (2i + j – 9k) Cosine of angle Back

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DMO’L.St Thomas More Starter 26 The direction vector of the line is a = i + j +k A line has vector equation r = 3i + 5j - k +t(i + j +k) Find the position vector of the point P, on the line, such that OP is perpendicular to the line. When t = OP a

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DMO’L.St Thomas More Starter 26 The direction vector of the line is a = i + j +k A line has vector equation r = 3i + 5j - k +t(i + j +k) Find the position vector of the point P, on the line, such that OP is perpendicular to the line. When t = OP a OP. a = 0

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DMO’L.St Thomas More Starter 26 When t = OP a OP. a = 0 So P has position vector OP = 3i + 5j - k - 7 / 3 (i + j +k) Back

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DMO’L.St Thomas More Starter 27 Find the of the tangent to the given curve at the point (1,0). Differentiate; At (1,0) Hence tangent is Back

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DMO’L.St Thomas More Starter 28 A curve has parametric equations x = 4cos and y = 8sin (a)Find the gradient of the curve at P, the point where = / 4 (b)Find the equation of the tangent to the curve at P. (c)Find the coordinates of the point R where the tangent meets the x -axis. (d)Find the area of the region bounded by the curve, the tangent and the x -axis.

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DMO’L.St Thomas More Starter 28 A curve has parametric equations x = 4cos and y = 8sin (a)Find the gradient of the curve at P, the point where = / 4 At P = / 4;

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DMO’L.St Thomas More Starter 28 A curve has parametric equations x = 4cos and y = 8sin (b) Find the equation of the tangent to the curve at P. At P = / 4; Equation of tangent;

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DMO’L.St Thomas More Starter 28 A curve has parametric equations x = 4cos and y = 8sin (c) Find the coordinates of the point R where the tangent meets the x -axis. At R y = 0

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DMO’L.St Thomas More Starter 28 A curve has parametric equations x = 4cos and y = 8sin (d) Find the area of the region bounded by the curve, the tangent and the x -axis. Back

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DMO’L.St Thomas More Starter 29 Find the general solution of each differential equation: Back

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DMO’L.St Thomas More The region R is bounded by the curve C, the x -axis and the lines x = -8 and x = 8. The parametric equations for C are x = t 3 and y = t 2 Find the area of R. Area under curve Starter 30

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DMO’L.St Thomas More The region R is bounded by the curve C, the x -axis and the lines x = -8 and x = 8. The parametric equations for C are x = t 3 and y = t 2 The region R is rotated about the x -axis, find the volume generated. Volume Starter 30 Back

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DMO’L.St Thomas More A curve has equation Find the coordinates of the points on the curve where Differentiate w.r.t. x Starter 31 What’s this? Sub. back Back

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