Unit 2 revision Q 1

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## Unit 2 revision Q 1

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**Unit 2 revision Q 1**• How do you find the root of an equation between two given values to 1 dp ? 2.1**Answer to Unit 2 revision Q 1**• iteration**Unit 2 revision Q 2**• How do you find where a curve crosses the x-axis ? 2.1**Answer to Unit 2 revision Q 2**• Let y = 0 or f(x) = 0 and solve for x**Unit 2 revision Q 3**• How do you solve equations like 100 x2 4 - =0? 2.1**Answer to Unit 2 revision Q 3**• (i) multiply by the denominator of the fraction (here x2) • (ii) factorise and solve**Unit 2 revision Q 4**• What is the condition for equal roots ? 2.1**Answer to Unit 2 revision Q 4**• b2 – 4ac = 0**Unit 2 revision Q 5**• What is the quadratic formula and explain when it is used ? 2.1**Answer to Unit 2 revision Q 5**• x = -b±√(b2-4ac) 2a • It is used to find roots of a quadratic equation when it is difficult to factorise.**Unit 2 revision Q 6**• How do you solve quadratic inequations like x2+5x-6 ≥ 0 ? 2.1**Answer to Unit 2 revision Q 6**• (i) factorise • (ii) draw graph • (iii) read x values where graph is on or above x-axis**Unit 2 revision Q 7**• How do you solve quadratic inequations like x2 - 5x + 6 < 0 ? 2.1**Answer to Unit 2 revision Q 7**• (i) factorise • (ii) draw graph • (iii) read x values where graph is below x-axis**Unit 2 revision Q 8**• What is the condition for no real roots ? 2.1**Answer to Unit 2 revision Q 8**• b2 – 4ac < 0**Unit 2 revision Q 9**• How do you find where a curve crosses the y-axis ? 2.1**Answer to Unit 2 revision Q 9**• Substitute x=0 into equation to find y value**Unit 2 revision Q 10**• What is the condition for real roots ? 2.1**Answer to Unit 2 revision Q 10**• b2 – 4ac ≥ 0**Unit 2 revision Q 11**• How do you find where a line and a circle intersect ? 2.4**Answer to Unit 2 revision Q 11**• Rearrange line to get x = … or y = … • Substitute into circle equation and solve**Unit 2 revision Q 12**• How do you factorise a cubic expression like x3-2x2-x+2 ? 2.1**factor**1 -2 -1 2 Remainder=0 Answer to Unit 2 revision Q 12 • Synthetic division using factors of last number**Unit 2 revision Q 13**• How do you find ∫ x3 dx ? b a 2.2**Answer to Unit 2 revision Q 13**[ ] • x3+1 3+1 then 1/4[(b4) - (a4)] b a**Unit 2 revision Q 14**• How do you integrate xn ? 2.2**Answer to Unit 2 revision Q 14**• xn+1 n+1 + C**Unit 2 revision Q 15**• How do you calculate the area under a curve ? 2.2**Answer to Unit 2 revision Q 15**• (i) integrate • (ii) substitute in two limits and subtract to find area**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 ? 2.3**A**5 3 13 12 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 B**Unit 2 revision Q 17**• How do you solve equations like • Cos2xo - 5cosxo = 2 ? (0 ≤ x ≤ 360) 2.3**Answer to Unit 2 revision Q 17**• (i) Substitute 2cos2xo-1 for cos2xo • (ii) Make RHS=0 and then factorise (use c for cos xo if you like) • (iii) solve for cos xo and hence for x**Unit 2 revision Q 18**• What is the centre and radius of a circle of the form • x2+y2+2gx+2fy+c=0 ? 2.4**Answer to Unit 2 revision Q 18**• Centre (-g,-f) • Radius √(g2+f2-c)**Unit 2 revision Q 19**• What is the centre and radius of a circle with equation x2 + y2 = r2 ? 2.4**Answer to Unit 2 revision Q 19**• (i) centre (0,0) • (ii) radius = r**Unit 2 revision Q 20**• What is the centre and radius of a circle of the form • (x-a)2+(y-b)2 = r2 ? 2.4**y**r C (a,b) x Answer to Unit 2 revision Q 20 • Centre (a,b) • Radius = r