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

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 ?


•Let y = 0or f(x) = 0and solve for x

2.1

Unit 2 revision Q 3

•How do you solve equations like

100 x2

=0?4 -


•(i) multiply by the denominator of the

fraction (here x2)•(ii) factorise and solve

2.1

Unit 2 revision Q 4

•What is the condition for equal roots ?


•b2 – 4ac = 0

2.1

Unit 2 revision Q 5

•What is the quadratic formula and explain when it is used ?


•x = -b±√(b2-4ac)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

x2+5x-6 ≥ 0 ?


• (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 likex2 - 5x + 6 < 0 ?


•(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 ?


•b2 – 4ac < 0

2.1

Unit 2 revision Q 9

•How do you find where a curve crosses the y-axis ?


•Substitute x=0 into equation to find y value

2.1

Unit 2 revision Q 10

•What is the condition for real roots ?


• b2 – 4ac ≥ 0

2.4


•How do you find where a line and a circle intersect ?


•Rearrange line to getx = … or y = …

•Substitute into circle equation and solve

2.1


•How do you factorise a cubic expression like

x3-2x2-x+2 ?


•Synthetic division using factors of last number

Remainder=0

factor 1 -2 -1 2

2.2


•How do you find

∫ x3 dx ?aa

bb


• x3+1

3+1

then 1/4[(b4) - (a4)]

[[ ]]bb

aa

2.2


•How do you integrate xn ?


• xn+1

n+1+ C+ C

2.2


•How do you calculate the area under a curve ?


• (i) integrate•(ii) substitute in two

limits and subtract to find area

2.3


•How do you find the exact values ofsin(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


•How do you solve equations like

•Cos2xo - 5cosxo = 2 ?

(0 ≤ x ≤ 360)


•(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

2.4


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

•x2+y2+2gx+2fy+c=0 ?


•Centre (-g,-f)•Radius √(g2+f2-c)

2.4


•What is the centre and radius of a circle with equation x2 + y2 = r2 ?


• (i) centre (0,0)•(ii) radius = r

2.4


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

•(x-a)2+(y-b)2 = r2 ?


•Centre (a,b)•Radius = r

x

y

(a,b)C

r

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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