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Solutions to exercises in Harwood Clarke's textbook for additional mathematics, "Additional Pure Mathematics".
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Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
1
Solutions to Exercise 3 (p. 8−9) from Harwood Clarke’s Additional Pure Mathematics
Additional Pure Mathematics is a book used to teach Additional Mathematics in the
1960s and 1970s. The questions are good, and for selected topics, I require my GCE O-
Level students to attempt questions this book.
1.
√ √
√ √
√
2.
√ √
√ √
√
3.
√
√
√ √
√
4.
√
√
√ √
√
5.
√
√
√
√
√
6.
√ √
√ √
√
Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
2
7.
√ √ √
√
8.
√
√
√
√
√
9.
√
√
√
√
√
10.
√
√
√
√
√
11.
√
√
√ √
√
√
12.
√
√
√
√
√ √
√
Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
3
√
13.
√
√
√
√
√
√ √
√
√
14.
√
√
√ √
√
√
√
15.
√
√
√
√
√
Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
4
√ √
√
√
√
16.
√
√
√
√
√
√ √
√
√
Questions 17−20 makes use of the “conjugate surd” to rationalise the denominator.
Remember also to make use of this result: ( )( ) .
17. The conjugate surd of √ is √ .
√
√
√ √
√
√
(√ )
√
√
√
Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
5
18. The conjugate surd of √ is √ .
√
√
√ √
√
√
(√ )
√
√
√
19. The conjugate surd of √ is √ .
√
√
√ √
√
√
(√ )
√
√
√
20. The conjugate surd of √ is √
√
√
√ √
√
√
(√ )
Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
6
√
√
√
21.
√ (√ ) √ √ √
√
22.
√ (√ ) √ √ √
√
23.
(√ )(√ ) (√ )
24.
( √ )( √ ) (√ )
25.
( √ )( √ ) √ √ √ √
√ ( )
√
26.
(√ )( √ ) √ √ √ √
√
√
27.
(√ )( √ ) √ √ √ √
Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
7
( ) √
√
28.
(√ )(√ ) √ √ √ √
√
√
29.
(√ √ )(√ √ ) (√ ) (√ )
30.
(√ )(√ ) (√ )
Questions 31−40 makes use of the “conjugate surd” to rationalise the denominator.
Remember also to make use of this result: ( )( ) .
31. The conjugate surd of √ is √ .
√
√
√ √
√
√
(√ )
√
(√ )
32. The conjugate surd of √ is √ .
√
√
Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
8
√ √
√
√
( √ )
√
( √ )
33. The conjugate surd of √ √ is √ √ .
√ √
√ √
√ √ √ √
√ √
√ √
(√ ) (√ )
√ √
√ √
(√ √ )
34. The conjugate surd of √ √ is √ √ .
√ √
√ √
√ √ √ √
√ √
√ √
(√ ) (√ )
√ √
√ √
Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
9
(√ √ )
35. The conjugate surd of √ √ is √ √ .
√ √
√ √
√ √ √ √
√ √
√ √
(√ ) (√ )
√ √
√ √
√ √
36. The conjugate surd of √ √ is √ √ .
√ √
√ √
√ √ √ √
√ √
√ √
( √ ) (√ )
√ √
( √ √ )
37. The conjugate surd of √ is √ .
√
√
√ √
√
√
(√ )
Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
10
√
(√ )
38. The conjugate surd of √ is √ .
√
√
√ √
√
√
(√ )
√
(√ )
39. The conjugate surd of √ √ is √ √ .
√ √
√ √
√ √ √ √
√ √
√ √
( √ ) (√ )
√ √
( √ √ )
40. The conjugate surd of √ √ is √ √ .
√ √
√ √
√ √ √ √
√ √
Dr CK Lee’s Additional Mathematics Classes ( 91473612 or check out http://ascklee.org/)
11
√ √
(√ ) (√ )
√ √
(√ √ )
The End
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