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 163 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