01[a math cd]

1 © Penerbitan Pelangi Sdn. Bhd.

Paper 1

1. (n – 3) – 2(3 – n)= (n – 3) – (6 – 2n)= n – 3 – 6 + 2n= 3n – 9

Answer: A

2. 3(m – n) – (m + n)= (3m – 3n) – (m + n)= 3m – 3n – m – n= 2m – 4n

Answer: C

3. 3(h – 1) + 4(1 – 2h)= (3h – 3) + (4 – 8h)= 3h – 3 + 4 – 8h= –5h + 1

Answer: C

4. 4(p – 3) – 3(1 – 2p)= (4p – 12) – (3 – 6p)= 4p – 12 – 3 + 6p= 10p – 15

Answer: A

5. 3k(2 – k) – 5(2k – 1)= (6k – 3k2) – (10k – 5)= 6k – 3k2 – 10k + 5= –3k2 – 4k + 5

Answer: D

6. (4e – f )(2e – 3f )

= (4e)(2e) + (4e)(–3f ) + (–f )(2e) + (–f )(–3f )= 8e2 – 12ef – 2ef + 3f 2= 8e2 – 14ef + 3f 2

Answer: D

7. 4(h + 2k)(3h – k)

= (4h + 8k)(3h – k)

= (4h)(3h) + (4h)(–k) + (8k)(3h) + (8k)(–k)= 12h2 – 4hk + 24hk – 8k2

= 12h2 + 20hk – 8k2

Answer: B

8. (5 – x)(2 – 3x) – 2(x – 4)

= (10 – 15x – 2x + 3x2) – (2x – 8)= 3x2 – 17x + 10 – 2x + 8= 3x2 – 19x + 18

Answer: C

9. t + 3–––––2 + t—

4

= 2(t + 3)–––––––2 × 2

+ t—4

= 2t + 6––––––4

+ t—4

= 2t + 6 + t––––––––4

= 3t + 6–––––4

Answer: A

10. k + 1–––––6 + k – 2–––––

3

= k + 1–––––6 + 2(k – 2)–––––––

2 × 3

= k + 1–––––6 + 2k – 4––––––

6

= k + 1 + 2k − 4–––––––––––––6

= 3k – 3––––––6

= k – 1–––––2

Answer: A

CHAPTERCHAPTER

1 Algebraic Expressions

2

Mathematics SPM Chapter 1

© Penerbitan Pelangi Sdn. Bhd.

11. h – 3–––––15 – 1 – h–––––

5

= h – 3–––––15 – 3(1 – h)–––––––

3 × 5

= h – 3–––––15 – 3 – 3h––––––

15

= h – 3 – 3 + 3h–––––––––––––15

= 4h – 6––––––15

Answer: D

12. t + 4–––––2 – 3(1 – 2t)–––––––

5

= 5(t + 4)–––––––5 × 2

– 2 × 3(1 – 2t)–––––––––––2 × 5

= 5t + 20–––––––10

– 6 – 12t–––––––10

= 5t + 20 – 6 + 12t–––––––––––––––10

= 17t + 14–––––––10

Answer: C

13. 3–––4p – p + 3–––––

p

= 3–––4p – 4(p + 3)–––––––

4 × p

= 3–––4p – 4p + 12–––––––

4p

= 3 – 4p – 12––––––––––4p

= – 4p – 9–––––––4p

Answer: C

14. k + 1–––––5k – 2 – k–––––

k

= k + 1–––––5k – 5(2 – k)–––––––

5 × k

= k + 1–––––5k – 10 – 5k–––––––

5k

= k + 1 – 10 + 5k–––––––––––––5k

= 6k – 9––––––5k

Answer: D

15. 4 – m–––––m – m + 6––––––

3m

= 3(4 – m)––––––––3 × m

– m + 6––––––3m

= 12 – 3m–––––––3m

– m + 6––––––3m

= 12 – 3m – m – 6––––––––––––––3m

= 6 – 4m––––––3m

Answer: B

Paper 1

1. 3x(x + y) – (–x – 2y)2

= 3x2 + 3xy – (x2 + 2xy + 2xy + 4y2)= 3x2 + 3xy – (x2 + 4xy + 4y2)= 3x2 + 3xy – x2 – 4xy – 4y2

= 2x2 – xy – 4y2

Answer: B

2. h(h + k) – (h + k)(h – k)= h2 + hk – (h2 – k2)= h2 + hk – h2 + k2

= hk + k2

Answer: A

3. (3p – 1)(q – 1) + (p + 1)(q – 2)= 3pq – 3p – q + 1 + pq – 2p + q – 2= 4pq – 5p – 1

Answer: B

4. p – 4–––––p – 3(1 – 2p)––––––––

p2

= p(p – 4) – 3(1 – 2p)––––––––––––––––––p2

= p2 – 4p – 3 + 6p––––––––––––––p2

= p2 + 2p – 3–––––––––––p2

Answer: A

3



5. 6q – 2pqq2 – 4

÷ 8pqq + 2

= 2q(3 – p)(q – 2)(q + 2)

× q + 28pq

= 3 – pq – 2

× 14p

= 3 – p4p(q – 2)

Answer: B

6. 4hkk2 × kh – kw

hw

= 4hkk2 × k(h – w)

hw

= 4h – 4ww

Answer: D

7. h + 13

– 2 – h2

4h

= 4h(h + 1)4h × 3

– 3(2 – h2)3 × 4h

= 4h2 + 4h – 6 + 3h2

12h

= 7h2 + 4h – 612h

Answer: B

8. (3h – 2k)(4k – h)= (3h)(4k) + (3h)(–h) – (2k)(4k) – (2k)(–h)= 12hk – 3h2 – 8k2 + 2kh= –3h2 + 14hk – 8k2

Answer: A

9. k–––4h – 2 – k–––––

h

= k–––4h – 4(2 – k)–––––––

4 × h

= k–––4h – 8 – 4k––––––

4h

= k – 8 + 4k–––––––––4h

= 5k – 8––––––4h

Answer: A

1

4

1 1 1

1 1

10. 4(y – 2) – (1 – 2y)2

= 4y – 8 – (1 – 2y – 2y + 4y2)= 4y – 8 – (1 – 4y + 4y2)= 4y – 8 – 1 + 4y – 4y2

= –4y2 + 8y – 9

Answer: D

11. 3 – k–––––k ÷ 4 + k–––––

k2

= 3 – k–––––1 k

× k 2 1

–––––4 + k

= k(3 – k)––––––– 4 + k

= 3k – k2–––––––

4 + k

Answer: D

12. 7hk – 3(1 – hk)= 7hk – 3 + 3hk= 10hk – 3

Answer: D

13. (4p2 + pq) × q2

–––––––––p2(q + 4p)

= p(4p + q) × q2

–––––––––p2(q + 4p)

= pq2––––

p2

= q2

–––p

Answer: B

Paper 1

1. (a – b)2 + ab= (a – b)(a – b) + ab= a2 – ab – ab + b2 + ab= a2 + b2 – ab

Answer: D

2. (x – y)2 – xy= (x – y)(x – y) – xy= x2 – xy – xy + y2 – xy= x2 + y2 – 3xy

Answer: C

4



3. a2 + b2 – (a + b)2

= a2 + b2 – (a + b)(a + b)= a2 + b2 – (a2 + ab + ab + b2)= a2 + b2 – (a2 + 2ab + b2)= a2 + b2 – a2 – 2ab – b2

= –2ab

Answer: D

4. x2 + y2 – (2x – y)2

= x2 + y2 – (2x – y)(2x – y)= x2 + y2 – (4x2 – 2xy – 2xy + y2)= x2 + y2 – (4x2 – 4xy + y2)= x2 + y2 – 4x2 + 4xy – y2

= –3x2 + 4xy

Answer: C

5. m2 – n2 – (m – 3n)2

= m2 – n2 – (m – 3n)(m – 3n)= m2 – n2 – (m2 – 3mn – 3mn + 9n2)= m2 – n2 – (m2 – 6mn + 9n2)= m2 – n2 – m2 + 6mn – 9n2

= –10n2 + 6mn

Answer: B

6. (2h – p)2 – 2hp= (2h – p)(2h – p) – 2hp= 4h2 – 2hp – 2hp + p2 – 2hp= 4h2 – 6hp + p2

Answer: A

7. 6ef – (2e – f)2

= 6ef – (2e – f)(2e – f)= 6ef – (4e2 – 2ef – 2ef + f 2)= 6ef – 4e2 + 4ef – f 2= 10ef – 4e2 – f 2

Answer: A

8. (x – 4)2 – 8(2 – x)= (x – 4)(x – 4) – (16 – 8x)= x2 – 4x – 4x + 16 – 16 + 8x= x2

Answer: D

9. n(n – 1) – (1 – n)2

= (n2 – n) – (1 – n)(1 – n)= n2 – n – (1 – n – n + n2)= n2 – n – 1 + 2n – n2

= n – 1

Answer: C

10. 2(x – 3)2 + 3 – 2x2

= 2(x – 3)(x – 3) + 3 – 2x2

= 2(x2 – 3x – 3x + 9) + 3 – 2x2

= 2x2 – 12x + 18 + 3 – 2x2

= –12x + 21

Answer: B

11. (1 – m)2 – 3m(m – 1)= (1 – m)(1 – m) – (3m2 – 3m)= 1 – m – m + m2 – 3m2 + 3m= –2m2 + m + 1

Answer: A

12. (3p + q)2 – (p – 3q)2

= (3p + q)(3p + q) – (p – 3q)(p – 3q)= 9p2 + 3pq + 3pq + q2 – (p2 – 3pq – 3pq + 9q2)= 9p2 + 6pq + q2 – p2 + 6pq – 9q2

= 8p2 + 12pq – 8q2

Answer: C

13. (m – 3n)2 – (m2 + 9n2)= (m – 3n)(m – 3n) – (m2 + 9n2)= m2 – 3mn – 3mn + 9n2 – m2 – 9n2

= –6mn

Answer: A

14. 3x(4y – 1) – y(1 – 4y)= 3x(4y – 1) + y(4y – 1)= (4y – 1)(3x + y)

Answer: B

15. (2p – 3q)2 – (2p2 – q2)= (2p – 3q)(2p – 3q) – (2p2 – q2)= 4p2 – 6pq – 6pq + 9q2 – 2p2 + q2

= 2p2 – 12pq + 10q2

Answer: B

16. 6p(p + 2q) – (3p – q)2

= 6p2 + 12pq – (3p – q)(3p – q)= 6p2 + 12pq – (9p2 – 3pq – 3pq + q2)= 6p2 + 12pq – 9p2 + 6pq – q2

= –3p2 + 18pq – q2

Answer: D

5



17. m––3 – m2 – 4––––––

6m

= m × 2m–––––––3 × 2m

– m2 – 4––––––6m

= 2m2––––6m

– m2 – 4––––––6m

= 2m2 – m2 + 4–––––––––––6m

= m2 + 4––––––6m

Answer: A

18. 3–––4h – 2h – 5––––––

8h2

= 3 × 2h–––––––4h × 2h

– 2h – 5––––––8h2

= 6h–––8h2 – 2h – 5––––––

8h2

= 6h – 2h + 5–––––––––––8h2

= 4h + 5––––––8h2

Answer: B

19. 2h–––3 – h2 – 3––––––

15h

= 2h × 5h–––––––3 × 5h

– h2 – 3––––––15h

= 10h2––––15h – h2 – 3––––––

15h

= 10h2 – h2 + 3–––––––––––15h

= 9h2 + 3–––––––15h

= 3h2 + 1–––––––5h

Answer: C

20. m––6 – m2 + 8––––––

18m

= m × 3m–––––––6 × 3m

– m2 + 8––––––18m

= 3m2–––––18m – m2 + 8––––––

18m

= 3m2 – m2 – 8–––––––––––18m

= 2m2 – 8–––––––18m

= m2 – 4––––––9m

Answer: C

21. 1–––3m – 2m – 3–––––––

6m2

= 1 × 2m––––––––3m × 2m

– 2m – 3–––––––6m2

= 2m–––––6m2 – 2m – 3–––––––

6m2

= 2m – 2m + 3–––––––––––6m2

= 1––––2m2

Answer: D

22. 1 – e–––––3e – 2e + 1–––––––

5e

= 5(1 – e)–––––––5 × 3e

– 3(2e + 1)––––––––3 × 5e

= 5 – 5e––––––15e

– 6e + 3––––––15e

= 5 – 5e – 6e – 3–––––––––––––15e

= 2 – 11e–––––––15e

Answer: A

23. e – 5–––––3e – 3 + 2e ––––––

9

= 3(e – 5)–––––––3 × 3e

– e(3 + 2e)––––––––e × 9

= 3e – 15–––––––9e

– (3e + 2e2)–––––––––9e

= 3e – 15 – 3e – 2e2––––––––––––––––

9e

= –15 – 2e2––––––––

9eAnswer: A

6



24. m – n––––––mn

– m – 4––––––4m

= 4(m – n)–––––––4 × mn

– n(m – 4)–––––––n × 4m

= 4m – 4n–––––––4mn

– mn – 4n–––––––4mn

= 4m – 4n – mn + 4n––––––––––––––––4mn

= 4m – mn––––––––4mn

= 4 – n–––––4n

Answer: B

25. 5n + 4––––––4n

– 10 – 4n–––––––8

= 2(5n + 4)–––––––––2 × 4n

– n(10 – 4n)–––––––––n × 8

= 10n + 8–––––––8n

– 10n – 4n2––––––––

8n

= 10n + 8 – 10n + 4n2–––––––––––––––––

8n

= 8 + 4n2–––––––

8n

= 2 + n2––––––

2n

Answer: A

26. n + 1–––––5mn

– 3 + m–––––15m

= 3(n + 1)–––––––3 × 5mn

– n(3 + m)––––––––n × 15m

= 3n + 3––––––15mn

– 3n + mn––––––––15mn

= 3n + 3 – 3n – mn–––––––––––––––15mn

= 3 – mn––––––15mn

Answer: C

27. 3(q + 1)–––––––pq –

6 – p–––––

2p

= 2 × 3(q + 1)

–––––––––––2 × pq

– q(6 – p)–––––––q × 2p

= 6q + 6––––––

2pq –

6q – pq–––––––

2pq

= 6q + 6 – 6q + pq

–––––––––––––––2pq

= 6 + pq––––––

2pq

Answer: A

28. 2(h + 1)–––––––2eh

– 4 + e–––––4e

= 2 × 2(h + 1)–––––––––––2 × 2eh

– h(4 + e)–––––––h × 4e

= 4h + 4–––––––4eh

– 4h + eh–––––––4eh

= 4h + 4 – 4h – eh–––––––––––––––4eh

= 4 – eh–––––––4eh

Answer: B

29. 14(x – 1)

– 14(x + 1)

– 12(x2 + 1)

= (x + 1) – (x – 1)4(x2 – 1)

– 12(x2 + 1)

= 12(x2 – 1)

– 12(x2 + 1)

= 12

3 (x2 + 1) – (x2 – 1)(x2 – 1)(x2 + 1) 4

= 12

1 2x4 – 1 2

= 1x4 – 1

Answer: C

01[a math cd]

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