Week 4 Point C (2,4) lies on a circle x2 + y2 - 8x - 6y + 20 = 0.

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Presentation transcript:

Week 4 Point C (2,4) lies on a circle x2 + y2 - 8x - 6y + 20 = 0. Find the equation of the tangent to the circle at C Find the first 3 terms in the expansion of (2 – 3x)8 Given that (x+3) is a factor of f(x) = x3 + 6x2 + 5x -12 factorise f(x) and sketch the graph of y = f(x) 𝑂𝐴 =−2𝑖+3𝑗 𝑂𝐵 =4𝑖+6𝑗 Calculate | 𝐴𝐵 | 20 g of a substance is dropped into a solution. The mass not dissolved after t seconds is modelled by M = Ae-kt After 5 seconds 10g remains. Find the value of A and k (3 s.f.)

1 Point C (2,4) lies on a circle x2 + y2 - 8x - 6y + 20 = 0. Find the equation of the tangent to the circle at C (x - 4)2 + (y – 3)2 = 5 Centre (4,3) Gradient of normal = - ½ Gradient of the tangent = 2 y – 4 = 2(x - 2) y = 2x CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

2 Find the first 3 terms in the expansion of (2 – 3x)8 28 + 8 × 27 × (-3x) + 28 × 26 × (-3x)2 256 – 3072x + 16128x2 CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

3 Given that (x+3) is a factor of f(x) = x3 + 6x2 + 5x -12 factorise f(x) and sketch the graph of y = f(x) f(x) = (x + 3)(x + 4)(x – 1) CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

4 𝐴𝐵 = 6i + 3j 𝐴𝐵 = 6 2 + 3 2 = 3 5 𝑂𝐴 =−2𝑖+3𝑗 𝑂𝐵 =4𝑖+6𝑗 𝑂𝐴 =−2𝑖+3𝑗 𝑂𝐵 =4𝑖+6𝑗 Calculate | 𝐴𝐵 | 𝐴𝐵 = 6i + 3j 𝐴𝐵 = 6 2 + 3 2 = 3 5 CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

5 20 g of a substance is dropped into a solution. The mass not dissolved after t seconds is modelled by M = Ae-kt After 5 seconds 10g remains. Find the value of A and k. (Give k correct to 3 significant figures) 𝑡=0 20=𝐴 𝑒 0 A = 20 t = 5 M = 10 10 = 20e-5k e-5k = 0.5 -5k = ln (0.5) k = 0.139 CLICK FOR SOLUTION CLICK FOR SOLUTION www.mathsbox.org.uk

Week 4 Point C (2,4) lies on a circle x2 + y2 - 8x - 6y + 20 = 0. Find the equation of the tangent to the circle at C y = 2x Find the first 3 terms in the expansion of (2 – 3x)8 256 – 3072x + 16128x2 Given that (x+3) is a factor of f(x) = x3 + 6x2 + 5x -12 factorise f(x) and sketch the graph of y = f(x) (x + 3)(x + 4)(x – 1) 𝑂𝐴 =−2𝑖+3𝑗 𝑂𝐵 =4𝑖+6𝑗 Calculate | 𝐴𝐵 | 3 5 20 g of a substance is dropped into a solution. The mass not dissolved after t seconds is modelled by M = Ae-kt After 5 seconds 10g remains. Find the value of A and k (3 s.f.) A = 20 k = 0.139