Mathematics Standard Level for the IB Diploma Self-assessment answers: 3 Algebraic structures
2
1. Let y = x
2
y – 5y + 4 = 0
 (y – 1)(y – 4) = 0
 y = 1, 4
2
So, x = 1, 4
 x = 1, 2
2. Using a GDC, x = 0.241 (3SF)
[5 marks]
[4 marks]
3.
[4 marks]
2x
x
4. e + 2e – 15 = 0
 (e + 5)(e – 3) = 0
x
x
 e = −5 or 3. Reject the negative solution.
x
 x = ln 3
Copyright Cambridge University Press 2013. All rights reserved.
[5 marks]
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Mathematics Standard Level for the IB Diploma 5.
(a)
[3 marks]
 9x2 
2
(b) log3(9x ) – log3(6x) = log3 

 6x 
 3x 
= log3  
 2 
= log3 3x – log3 2
= log3 x + log3 3 – log3 2
= log3 x – log3 2 + 1
[5 marks]
2
(c) log3(9x ) – log3(6x) = 2x log3 x − log3 2 + 1
 log3 x – log3 2 + 1 = 2x log3 x − log3 2 + 1
 (1 – 2x) log3 x = 0
 1 – 2x = 0 or log3 x = 0
 x=
1
,1
2
Copyright Cambridge University Press 2013. All rights reserved.
[4 marks]
Page 2 of 2