2.1 Unit 2 revision Q 1 How do you find the root of an equation between two given values to 1 dp ?

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Presentation transcript:

2.1 Unit 2 revision Q 1 How do you find the root of an equation between two given values to 1 dp ?

Answer to Unit 2 revision Q 1 iteration

2.1 Unit 2 revision Q 2 How do you find where a curve crosses the x-axis ?

Answer to Unit 2 revision Q 2 Let y = 0 or f(x) = 0 and solve for x

2.1 Unit 2 revision Q 3 How do you solve equations like 100 x 2 =0? 4 -

Answer to Unit 2 revision Q 3 (i)multiply by the denominator of the fraction (here x 2 ) (ii)factorise and solve

2.1 Unit 2 revision Q 4 What is the condition for equal roots ?

Answer to Unit 2 revision Q 4 b 2 – 4ac = 0

2.1 Unit 2 revision Q 5 What is the quadratic formula and explain when it is used ?

Answer to Unit 2 revision Q 5 x = -b± √( b 2 -4ac) 2a It is used to find roots of a quadratic equation when it is difficult to factorise.

2.1 Unit 2 revision Q 6 How do you solve quadratic inequations like x 2 +5x-6 ≥ 0 ?

Answer to Unit 2 revision Q 6 (i)factorise (ii)draw graph (iii) read x values where graph is on or above x-axis

2.1 Unit 2 revision Q 7 How do you solve quadratic inequations like x 2 - 5x + 6 < 0 ?

Answer to Unit 2 revision Q 7 (i) factorise (ii) draw graph (iii) read x values where graph is below x-axis

2.1 Unit 2 revision Q 8 What is the condition for no real roots ?

Answer to Unit 2 revision Q 8 b 2 – 4ac < 0

2.1 Unit 2 revision Q 9 How do you find where a curve crosses the y-axis ?

Answer to Unit 2 revision Q 9 Substitute x=0 into equation to find y value

2.1 Unit 2 revision Q 10 What is the condition for real roots ?

Answer to Unit 2 revision Q 10 b 2 – 4ac ≥ 0

2.4 Unit 2 revision Q 11 How do you find where a line and a circle intersect ?

Answer to Unit 2 revision Q 11 Rearrange line to get x = …or y = … Substitute into circle equation and solve

2.1 Unit 2 revision Q 12 How do you factorise a cubic expression like x 3 -2x 2 -x+2 ?

Answer to Unit 2 revision Q 12 Synthetic division using factors of last number Remainder=0 factor 1-2 2

2.2 Unit 2 revision Q 13 How do you find ∫ x 3 dx ? a b

Answer to Unit 2 revision Q 13 x then 1 / 4 [(b 4 ) - (a 4 )] [] b a

2.2 Unit 2 revision Q 14 How do you integrate x n ?

Answer to Unit 2 revision Q 14 x n+1 n+1 + C

2.2 Unit 2 revision Q 15 How do you calculate the area under a curve ?

Answer to Unit 2 revision Q 15 (i)integrate (ii)substitute in two limits and subtract to find area

2.3 Unit 2 revision Q 16 How do you find the exact values of sin(A+B), cos(A-B) etc. given that cosA = 3 / 5 and sinB = 12 / 13 ?

Answer to Unit 2 revision Q 16 (i)draw two Δs (ii)find missing sides (iii)expand formula (iv)substitute in values from Δs using SOH CAH TOA A 3 5 B 12 13

2.3 Unit 2 revision Q 17 How do you solve equations like Cos2x o - 5cosx o = 2 ? (0 ≤ x ≤ 360)

Answer to Unit 2 revision Q 17 (i) Substitute 2cos 2 x o -1 for cos2x o (ii) Make RHS=0 and then factorise (use c for cos x o if you like) (iii)solve for cos x o and hence for x

2.4 Unit 2 revision Q 18 What is the centre and radius of a circle of the form x 2 +y 2 +2gx+2fy+c=0 ?

Answer to Unit 2 revision Q 18 Centre (-g,-f) Radius √( g 2 +f 2 -c)

2.4 Unit 2 revision Q 19 What is the centre and radius of a circle with equation x 2 + y 2 = r 2 ?

Answer to Unit 2 revision Q 19 (i)centre (0,0) (ii)radius = r

2.4 Unit 2 revision Q 20 What is the centre and radius of a circle of the form (x-a) 2 +(y-b) 2 = r 2 ?

Answer to Unit 2 revision Q 20 Centre (a,b) Radius = r x y (a,b) C r