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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.

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Presentation on theme: "Unit 2 revision Q 1 How do you find the root of an equation between two given values to 1 dp ? 2.1."— Presentation transcript:

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

2 Answer to Unit 2 revision Q 1
iteration

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

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

5 How do you solve equations like 100 x2 4 - =0?
Unit 2 revision Q 3 How do you solve equations like 100 x2 4 - =0? 2.1

6 Answer to Unit 2 revision Q 3
(i) multiply by the denominator of the fraction (here x2) (ii) factorise and solve

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

8 Answer to Unit 2 revision Q 4
b2 – 4ac = 0

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

10 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.

11 How do you solve quadratic inequations like
Unit 2 revision Q 6 How do you solve quadratic inequations like x2+5x-6 ≥ 0 ? 2.1

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

13 How do you solve quadratic inequations like
Unit 2 revision Q 7 How do you solve quadratic inequations like x2 - 5x + 6 < 0 ? 2.1

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

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

16 Answer to Unit 2 revision Q 8
b2 – 4ac < 0

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

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

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

20 Answer to Unit 2 revision Q 10
b2 – 4ac ≥ 0

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

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

23 How do you factorise a cubic expression like x3-2x2-x+2 ?
Unit 2 revision Q 12 How do you factorise a cubic expression like x3-2x2-x+2 ? 2.1

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

25 Unit 2 revision Q 13 How do you find ∫ x3 dx ? b a 2.2

26 Answer to Unit 2 revision Q 13
x3+1 3+1 then 1/4[(b4) - (a4)] [ ] b a

27 Unit 2 revision Q 14 How do you integrate xn ? 2.2

28 Answer to Unit 2 revision Q 14
xn+1 n+1 + C

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

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

31 How do you find the exact values of sin(A+B), cos(A-B) etc. given that
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

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

33 How do you solve equations like Cos2xo - 5cosxo = 2 ? (0 ≤ x ≤ 360)
Unit 2 revision Q 17 How do you solve equations like Cos2xo - 5cosxo = 2 ? (0 ≤ x ≤ 360) 2.3

34 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

35 What is the centre and radius of a circle of the form
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

36 Answer to Unit 2 revision Q 18
Centre (-g,-f) Radius √(g2+f2-c)

37 What is the centre and radius of a circle with equation x2 + y2 = r2 ?
Unit 2 revision Q 19 What is the centre and radius of a circle with equation x2 + y2 = r2 ? 2.4

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

39 What is the centre and radius of a circle of the form
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

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


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