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Studyadz 3as-physique-c3-37-51

Engineering
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1 1 8 2019 03 0 ‫ﺩ‬ 4 0 0 01 0 08 0 4 0 0 08 ( 13 06 i . 14 13 ݉଴ ݉ 1 1 ( 13 1 - ܰ ଻ ଵଷ ‫ܥ‬ ௓ ஺ 2 ( ݈݊‫ܣ‬ ‫ݐ‬ ‫ܣ‬଴ ‫ܣ‬ λ λ λ ‫ܣ‬଴ 2 2 ‫ܣ‬଴ ‫ܣ‬ λ ‫ݐ‬భ మ 13 1 ݉଴ ii . ܲ‫ݑ‬ ଽସ ଶଷଽ ൅ ݊ ଴ ଵ ՜ ‫݋ܯ‬ ସଶ ଵ଴ଶ ൅ ܶ݁ ହଶ ଵଷହ ൅ ͵ ݊ ଴ ଵ 1 e n c y - e d u c a t i o n . c o m / e x a m s 1 13 3 06 14 1 1 s m s s 3as.ency-education.com
2 2 8 2019 1 - 2 - 2 2 - ο݉ଵ ο ο݉ଶ ο ο݉ଷ - ‫ܧ‬௟ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ܲ‫ݑ‬ ଽସ ଶଷଽ ܶ݁ ହଶ ଵଷହ . - ‫ܸ݁ܯ‬ 3 - ܲ ൌ ͵ ൈ ͳͲ଺ ܹ ܲ ρ ൌ ͺͷΨ - ܲ‫ݑ‬ ଽସ ଶଷଽ 45 ρ ൌ ா೐ ா ρ ‫ܧ‬௘ ‫ܧ‬ ‫ܧ‬௟൫ ܶ݁ ହଶ ଵଷହ ൯ ൌ ͳͳʹ͸Ǥͻ͸‫ܸ݁ܯ‬ ‫ܧ‬ ͳ‫ܸ݁ܯ‬ ൌ ͳǤ͸ ൈ ͳͲିଵଷ ݆ ͳ‫ݑ‬ ൌ ͻ͵ͳǤͷ ‫ܸ݁ܯ‬ ‫ܥ‬ଶ Τ ܰ஺ ൌ ͸ǤͲʹ ൈ ͳͲଶଷ ݉‫݈݋‬ିଵ 07 3 3 - ‫ܧ‬ - ܴ ൌ ͳ݇ȳ . - ‫ܥ‬ଵ ‫ܥ‬ ‫ܥ‬ଶ - ‫ܮ‬ ‫ܮ‬ ‫ܭ‬ ‫ܭ‬ ‫ݐ‬ ൌ Ͳ ሺͳሻ ሺ ‫ݑ‬஼భ ሺ‫ݐ‬ሻ ‫ݑ‬஼మ ሺ‫ݐ‬ሻ ‫ݑ‬ 3 ଵ ஼೐ ൌ ଵ ஼భ ൅ ଵ ஼మ ‫ݍ‬ ൌ ‫ݍ‬ଵ ൌ ‫ݍ‬ଶ ‫ݍ‬ ‫ݍ‬ ‫ܥ‬௘ 1 ( ‫ݍ‬ 3 2 e n c y - e d u c a t i o n . c o m / e x a m s - ο݉ ݉ଶ ଶ ο - - ܲ ଽସ ଶଷଽ ଶ ܶ݁ ܶ݁ ହଶ ହଶ ଵଷହ ଵଷହ . . ܲ ܲ ͷΨ ܲ ଽସ ଶଷଽ ଶ ρ ρ ‫ܧ‬ ‫ܧ‬௘ ௘ ൌ ͳ ͳǤ Ǥ͸ ͸ ൈ ൈ ͳͲ ͳͲିଵଷ ݆ ൌ ൌ ͸ ͸ǤͲʹ Ͳʹ ൈ ൈ ͳͲ ͳͲଶଷ ݉ ‫ܥ‬ ‫ܥ‬௘ ௘ d 3as.ency-education.com
3 3 8 2019 ‫ݍ‬ ൌ ‫ܥܧ‬௘ ቀͳ െ ݁ି ೟ ഓቁ ‫ݑ‬஼భ ሺ‫ݐ‬ሻ ‫ݑ‬ ‫ݑ‬஼మ ሺ‫ݐ‬ሻ 2 ( 4 4 ߬ ‫ܧ‬ ‫ܥ‬௘ 3 ( ‫ܥ‬ଵ ‫ܥ‬ ‫ܥ‬ଶ ‫ܥ‬ 4 ( ‫ݑ‬஼భ ൌ ‫ݑ‬ோ ‫ݐ‬ ൌ ߬ ݈݊ ͵Ǥͷ 5 ( ሺʹሻ ሺ 1 ( ‫ݑ‬஼భ ‫ݑ‬ 2 ( ‫ݑ‬஼భ ൌ ‫ݑ‬ଵ …‘• ቀ ଶగ ்బ ‫ݐ‬ ൅ ߮ቁ ‫ݑ‬ ‫ݑ‬ଵ ‫ݑ‬ ‫ܥ‬ଵ ‫ܥ‬ ‫ݐ‬ ൒ ͳǤʹ‫ݏ‬ . ܶ଴ 3 ( 4 ܶ଴ ܶ ‫ܮ‬ 7 7 I . ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ݉଴ ൌ ͲǤ͵݃ ݉ ͷͲͲ݉‫ܮ‬ ሺܵሻ . ܸ ௔ ൌ ʹͲ݉‫ܮ‬ ܸ ሺܵሻ ͺͲ݉‫ܮ‬ 4 e n c y c o m / e x a m s 2 ( 3 3 ( ( 4 4 ( ( 5 ( ʹሻ భ ൌ ‫ݑ‬ ‫ݑ‬ଵ ଵ …‘• …‘• ቀ ቀ ଶ ଶగ గ ்బ ் / e ‫ݐ‬ ൅ ‫ݐ‬ ൒ . 4 3as.ency-education.com
4 4 8 2019 ሺܰܽା ൅ ‫ܱܪ‬ିሻ ‫ܥ‬௕ ൌ ͲǤͲͳ݉‫݈݋‬Ȁ‫ܮ‬ ʹͷԨ ʹ 1 ( 2 ( 3 ( ‫ܪ݌‬ ൌ ݂ሺܸ௕ሻ ‫݌‬ 4 ( ‫ܥ‬௔ ሺܵሻ 5 ( ሺܵሻ ݉଴ ݉ 6 ( ‫ܽܭ݌‬ ሺ‫ܪܥ‬ଷ‫ܪܱܱܥ‬Ȁ‫ܪܥ‬ଷ‫ܱܱܥ‬ିሻ II . ͳͶͺ݃ ͳ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ͳʹͲ‰ ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ( ( ‫ݔ‬௙ ( ( ( ( ( ( ( ͵͹݃ ͻ݃ ͻ ‫ܯ‬ሺ‫ܪ‬ሻ ൌ ͳ ݃ ݉‫݈݋‬ Τ ‫ܯ‬ ‫ܯ‬ሺܱሻ ൌ ͳ͸ ݃ ݉‫݈݋‬ Τ ‫ܯ‬ ‫ܯ‬ሺ‫ܥ‬ሻ ൌ ͳʹ ݃ ݉‫݈݋‬ Τ 30 27 24 21 20.5 19.5 19 18 15 12 9 6 3 0 ܸ௕ሺ݉‫ܮ‬ሻ 11.3 11.1 10.9 10.4 10.0 6.4 6.0 5.7 5.2 4.9 4.7 4.4 4.0 3.8 ‫ܪ݌‬ 5 e n c y c a t i o n . c o m / e x a m s 1 1 ( ( 2 ( ݂ሺܸ ܸ௕ ௕ ܸ ܸ ܸ ሻ ሻ ‫ܭ݌‬ ଷ‫ܱܱܥ‬ ܱܱି ିሻ ሻ ‫ܪ‬ 1.3 s s s c y - 5 3as.ency-education.com
5 5 8 2019 4 0 0 5 0 0 08 0 08 0 08 ( 13 06 1 - ‫ܧ‬ - ܴ . - ‫ܥ‬ - ‫ܮ‬ ‫ݎ‬ ‫ݎ‬ - ‫ܭ‬ ‫ܭ‬ ‫ݐ‬ ൌ Ͳ ሺͳሻ ሺ ‫ݑ‬஼ ݅ 2 3 3 1 ( 2 ( ‫ݑ‬஼ ‫ݑ‬ 3 ( ‫ݑ‬஼ ൌ ‫ܣ‬ ൅ ‫݁ܤ‬ఈ௧ ‫ݑ‬ ‫ܣ‬ ‫ܣ‬ ‫ܤ‬ ‫ܤ‬ ߙ ߙ 4 ( ‫ݑ‬ோሺ‫ݐ‬ሻ ௨಴ ௨ೃ ൌ ݁ ೟ ഓ െ ͳ 5 ( 2 2 3 3 ‫ܧ‬ ܴ ߬ ߬ ‫ܥ‬ ‫ܥ‬ 1 3 2 e n c y - a t i o n . c o m / e x a m s - - - ‫ܥ‬ ‫ܥ‬ ‫ܥ‬ ‫ܥ‬ ‫ܮ‬ ‫ܮ‬ ‫ݐ‬ ‫ݑ‬ ‫ݑ‬஼ 2 y 3as.ency-education.com
6 6 8 2019 ‫ݐ‬ ൌ Ͳ ሺʹሻ 4 1 ( 2 ( ‫ݍ‬ሺ‫ݐ‬ሻ ( ܶ ൎ ʹߨξ‫ܥܮ‬ ܶ ‫ܮ‬ ( ( ‫ݐ‬ ൌ ܶ ‫ݐ‬ ( ‫ܫ‬଴ 07 ሺܵሻ ݉ ൌ ʹͲͲ݃ ݉ ‫ܣ‬ ‫ܣ‬ Ƚ ‫ݒ‬஺ ‫ݒ‬ ሺܵሻ ሺ‫ܤܣ‬ሻ ݂ ൌ ͲǤͺܰ ‫ܤ‬ ‫ܦ‬ ‫ܦ‬ 5 5 ݃ ൌ ͻǤͺ݉Ȁ‫ݏ‬ଶ ‫ܤܣ‬ ൌ ͳǤʹ݉ ‫ܣ‬ 1 ( ሺ࡭࡮ሻ ሺ - ሺܵሻ - - ‫ݐ‬ ൌ Ͳ ‫ݐ‬ ሺܵሻ ‫ܣ‬ - ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ . 4 5 ‫ݍ‬ሺ‫ݐ‬ ‫ݐ‬ሻ ሻ Ƚ Ƚ ݂ ݂ ൌ ൌ Ͳ ͲǤ Ǥͺ ͺܰ ܰ ݂ ݂ ݃ ݃ ൌ ൌ ͻ ͻǤͺ݉ ʹ݉ x a m s e n c e n 5 3as.ency-education.com
7 7 8 2019 2 ( ࡮ ࡮ ‫ݐ‬ ൌ Ͳ ‫ܤ‬ ‫ܤ‬ ሺܵሻ ሺ‫ݔܤ‬ǡ ‫ݕܤ‬ሻ 6 7 7 - ሺ‫ݔܤ‬ሻ ሺ‫ݕܤ‬ሻ - - - ‫ݒ‬஻௫ ሺ‫ݔܤ‬ሻ ሺ ‫ݒ‬஻௬ ‫ݒ‬ ሺ‫ݕܤ‬ሻ Ƚ Ƚ ‫ݒ‬஻ ‫ܤ‬ - ‫ܦܣ‬ . - ሺܵሻ 3 ( ܽ ܽ ሺܵሻ ሺ‫ܤܣ‬ሻ ‫ݒ‬஺ . 7 7 I . ݉଴ ൌ ͲǤ͵݃ ‫݈ܣ‬ ‫ܣ‬ ܸ ൌ ʹͲͲ݉‫ܮ‬ ܸ ሺ‫ܪ‬ଷܱା ൅ ‫݈ܥ‬ିሻ ܿ ൌ ͲǤʹ ݉‫݈݋‬ ݈ Τ ܸுమ ൌ ݂ሺ‫ݐ‬ሻ ܸ 6 7 e n c y - e d u c a t i o n . c o ሺ ሺ‫ݔܤ‬ ‫ݔܤ‬ሻ ሻ ሺ‫ݕܤ‬ ‫ݕܤ‬ሻ ሻ ‫ݔ‬ሻ ሻ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݒ‬ . x a m s ܵሻ x 3as.ency-education.com
8 8 8 2019 ʹ‫݈ܣ‬ሺ௦ሻ ൅ ͸‫ܪ‬ଷܱା ሺ௔௤ሻ ൌ ʹ‫݈ܣ‬ଷା ሺ௔௤ሻ ൅ ͵‫ܪ‬ଶሺ௚ሻ ൅ ͸‫ܪ‬ଶܱሺ௟ሻ - ሺܱ‫ݔ‬ ܴ݁݀ Τ ሻ - ‫ݔ‬௠௔௫ ‫ܪ‬ଷܱା - - - ‫ݐ‬ଵ ଶ Τ - ‫ݐ‬ ‫ݐ‬ ‫ݒ‬ ൌ ଵ ଷ௏ಾ ൈ ௗ௏ಹమ ሺ௧ሻ ௗ௧ ‫ݐ‬ ൌ ͳͲ݉݅݊ II . ܸ ௔ ൌ ʹͲ݉‫ܮ‬ ሺܰܽା ൅ ‫ܱܪ‬ି ሻ ሺ ‫ܥ‬௕ ൌ ͲǤͲͳ ݉‫݈݋‬ ‫ܮ‬ Τ ‫ܪ݌‬ ‫݌‬ 9 9 1 ( 2 ( ሺ‫ܪ‬ଷܱା ൅ ‫݈ܥ‬ିሻ ሺ ሺܰܽା ൅ ‫ܱܪ‬ି ሻ 3 ( 4 ( ( ‫ܥ‬௔ 5 ( ‫ݔ‬௠௔௫ ‫ݔ‬ ʹͷι ‫ܯ‬ሺ‫݈ܣ‬ሻ ൌ ʹ͹݃Ǥ ݉‫݈݋‬ିଵ ‫ܯ‬ ܸெ ൌ ʹͶ‫ܮ‬Ǥ ݉‫݈݋‬ିଵ ܸ ‫ܭ‬௘ ൌ ͳͲିଵସ 8 9 ૢ૙ e n c y - e d u c a t i o n . c o m / e x a m s - - ‫ܪ‬ ‫ܪ‬ଷ ଷܱ ܱା ା ‫ݐ‬ ‫ݐ‬ଵ ଶ Τ ‫ݐ‬ ‫ݐ‬ ‫ݒ‬ ‫ݒ‬ ൌ ൌ ଵ m ͳͲ݉݅݊ ݉݅݊ ሺ ሺܰܽ ܰ ା 3as.ency-education.com
9 9 8 06 3 ( α β γ γ 13 1 ߚା ߚ ‫݌‬ ଵ ଵ ՜ ݊ ଴ ଵ ൅ ݁ ାଵ ଴ ܰ ଻ ଵଷ ՜ ܺ ௓ ஺ ൅ ݁ ଵ ଴ ͳ͵ ൌ ‫ܣ‬ ͹ ൌ ܼ ൅ ͳ ֜ ܼ ൌ ͸ ܰ ଻ ଵଷ ՜ ‫ܥ‬ ଺ ଵଷ ൅ ݁ ାଵ ଴ 4 ( . ‫ܣ‬ሺ‫ݐ‬ሻ ൌ ‫ܣ‬଴݁ିఒ௧ ֜ Ž ‫ܣ‬ ൌ െߣ‫ݐ‬ ൅ Ž ‫ܣ‬଴ Ž ‫ܣ‬ ൌ ܽ‫ݐ‬ ൅ ܾ ܽ ൌ ʹͳǤ͸ െ ͵ʹ ͳͷͲ െ Ͳ ൌ െͲǤͲ͸ͻ͵݉݅݊ିଵ ܾ ൌ ͵ʹ Ž ‫ܣ‬ ൌ െͲǤͲ͸ͻ͵‫ݐ‬ ൅ ͵ʹ ߣ ൌ െͲǤͲ͸ͻ͵݉݅݊ିଵ Ž ‫ܣ‬଴ ൌ ͵ʹ ֜ ‫ܣ‬଴ ൌ ݁ଷଶ ൌ ͹Ǥͺͻ ൈ ͳͲଵଷ ‫ݍܤ‬ ݉଴ ݉ ‫ܣ‬଴ ൌ ߣܰ଴ ൌ ߣ ݉଴ܰ஺ ‫ܯ‬ ֜ ݉଴ ൌ ‫ܣ‬଴‫ܯ‬ ܰ஺ ൈ ߣ ൌ ͹Ǥͺͻ ൈ ͳͲଵଷ ൈ ͳ͵ ͸ǤͲʹ ൈ ͳͲଶଷ ൈ ͲǤͲ͸ͻ͵ ͸Ͳ ൌ ͳǤͶ͹ ൈ ͳͲି଺ ݃ 4 - 5 - - ο݉ଵ ο݉ଶ ο݉ଷ ο݉ଵ ൌ ʹͶͳǤͻͶͺ͸ͺ െ ʹͶͲǤͲͲʹͳ͸ ൌ ͳǤͻͶ͸ͷʹ‫ݑ‬ ο݉ଶ ൌ ʹͶͳǤͻͶͺ͸ͺ െ ʹ͵ͻǤͺͲͲ͹ͺ ൌ ʹǤͳͶ͹ͻ‫ݑ‬ ο݉ଷ ൌ ʹͶͲǤͲͲʹͳ͸ െ ʹ͵ͻǤͺͲͲ͹ͺ ൌ ͲǤʹͲͳ͵ͺ‫ݑ‬ - ‫ܧ‬௟ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ‫ܧ‬ ‫ܧ‬௟ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ൌ ο݉ଵ‫ܥ‬ଶ ൌ ͳǤͻͶ͸ͷʹ ൈ ͻ͵ͳǤͷ ൌ ͳͺͳ͵Ǥͳͺ‫ܸ݁ܯ‬ e n c y - e d u c a t i o n . c o m / e x a m s . ͸ͻ͵ ͵݉݅݊ ݉݅݊ି ିଵ ͵ʹ ͲǤͲ͸ͻ͵ ͻ͵‫ݐ‬ ‫ݐ‬ ൅ ൅ ͵ʹ ͵ʹ ߣ ൌ െ െͲ ͲǤͲ͸ͻ͵ Ͳ͸ͻ͵݉݅݊ ݉ ି ͵ʹ ֜ ֜ ‫ܣ‬ ‫ܣ‬଴ ଴ ൌ ൌ ݁ ݁ଷଶ ൌ ܰ஺ ܰ ‫ܯ‬ u ֜ ֜ ݉ ݉଴ ଴ ൌ ൌ ‫ܣ‬ ‫ܣ‬଴ ‫ܯ‬ ܰ c 3as.ency-education.com
10 1 8 - ܲ‫ݑ‬ ଽସ ଶଷଽ ଶ ܶ݁ ହଶ ଵଷହ . ‫ܧ‬௟ ‫ܣ‬ ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ൌ ͹Ǥͷͺ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ‫ܧ‬௟ ‫ܣ‬ ሺ ܶ݁ ହଶ ଵଷହ ሻ ൌ ͺǤ͵Ͷ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ܶ݁ ହଶ ଵଷହ - ‫ܸ݁ܯ‬ ‫ܧ‬௟௜௕ ൌ ο݉ଷ‫ܥ‬ଶ ൌ ͲǤʹͲͳ͵ͺ ൈ ͻ͵ͳǤͷ ൌ ͳͺ͹Ǥͷͺ‫ܸ݁ܯ‬ ൌ ͵ ൈ ͳͲିଵଵ ݆ - 6 - ‫ܧ‬ ൌ ܰ ൈ ‫ܧ‬௟௜௕ ֜ ‫ܧ‬ ൌ ݉ ൈ ܰ஺ ‫ܯ‬ ൈ ‫ܧ‬௟௜௕ ֜ ݉ ൌ ‫ܧ‬ ൈ ‫ܯ‬ ܰ஺ ൈ ‫ܧ‬௟௜௕ ρ ൌ ‫ܧ‬௘ ‫ܧ‬ ֜ ‫ܧ‬ ൌ ‫ܧ‬௘ ρ ܲ ൌ ‫ܧ‬௘ ‫ݐ‬ ֜ ‫ܧ‬௘ ൌ ܲ ൈ ‫ݐ‬ ֜ ‫ܧ‬ ൌ ܲ ൈ ‫ݐ‬ ρ ֜ ݉ ൌ ܲ ൈ ‫ݐ‬ ൈ ‫ܯ‬ ρ ൈ ܰ஺ ൈ ‫ܧ‬௟௜௕ ൌ ͵ ൈ ͳͲ଺ ൈ Ͷͷ ൈ ʹͶ ൈ ͵͸ͲͲ ൈ ʹ͵ͻ ͲǤͺͷ ൈ ͸ǤͲʹ ൈ ͳͲଶଷ ൈ ͵ ൈ ͳͲିଵଵ ൌ ͳͺͳǤͷͻ݃ 07 6 ( ‫ݑ‬ோ ൅ ‫ݑ‬஼భ ൅‫ݑ‬஼మ ൌ ‫ܧ‬ ֜ ܴ݅ ൅ ‫ݍ‬ଵ ‫ܥ‬ଵ ൅ ‫ݍ‬ଶ ‫ܥ‬ଶ ൌ ‫ܧ‬ ֜ ܴ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ൬ ͳ ‫ܥ‬ଵ ൅ ͳ ‫ܥ‬ଶ ൰ ൌ ‫ܧ‬ ֜ ܴ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ͳ ‫ܥ‬௘ ൌ ‫ܧ‬ ֜ ܴ‫ܥ‬௘ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ൌ ‫ܥܧ‬௘ ‫ݍ‬ ൌ ‫ܥܧ‬௘ ൬ͳ െ ݁ି ௧ ఛ൰ ݀‫ݍ‬ ݀‫ݐ‬ ൌ ‫ܥܧ‬௘ ߬ ݁ି ௧ ఛ ֜ ܴ‫ܥ‬௘ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ൌ ‫ܥܧ‬௘ ֜ ܴ‫ܥ‬௘ ‫ܥܧ‬௘ ߬ ݁ି ௧ ఛ ൅ ‫ܥܧ‬௘ ൬ͳ െ ݁ି ௧ ఛ൰ ൌ ‫ܥܧ‬௘ ֜ ‫ܥܧ‬௘݁ି ௧ ఛ ൅ ‫ܥܧ‬௘ െ ‫ܥܧ‬௘݁ି ௧ ఛ ൌ ‫ܥܧ‬௘ ֜ Ͳ ൌ Ͳ ‫ݑ‬஼భ ൌ ‫ݍ‬ଵ ‫ܥ‬ଵ ൌ ‫ݍ‬ ‫ܥ‬ଵ ൌ ‫ܥܧ‬௘ ‫ܥ‬ଵ ൬ͳ െ ݁ି ௧ ఛ൰ ‫ݑ‬஼మ ൌ ‫ݍ‬ଶ ‫ܥ‬ଶ ൌ ‫ݍ‬ ‫ܥ‬ଶ ൌ ‫ܥܧ‬௘ ‫ܥ‬ଶ ൬ͳ െ ݁ି ௧ ఛ൰ 7 ( ߬ ൌ ͲǤʹ‫ݏ‬ e n c y - e d u c a t i o n . c o m / e x a m s - - 6 - ௟௜௕ ௜௕ ͷ ൈ ʹͶ ʹͶ ൈ ൈ ͵͸ͲͲ ͸Ͳ ൈ ʹ ǤͲʹ ൈ ͳͲ ͳ ଶଷ ଷ ൈ ൈ ͵ ͵ ൈ c o ‫ܥ‬ଶ ൌ ൌ ‫ܧ‬ ‫ܧ‬ ֜ ֜ ܴ ܴ ݀‫ݍ‬ ݀‫ݍ‬ ݀‫ݐ‬ ݀ o ൅ ֜ ֜ ܴ ܴ‫ܥ‬ ‫ܥ‬௘ ௘ ‫ܥ‬ ‫ܥ‬ ݀‫ݍ‬ ݀‫ݍ‬ ݀‫ݐ‬ a t ൅ ֜ ֜ ܴ ܴ‫ܥ‬ ‫ܥ‬௘ ‫ܥ‬ ݀‫ݍ‬ ݀ ݀ e 3as.ency-education.com
11 1 8 ‫ݑ‬஼భ ൅‫ݑ‬஼మ ൌ ‫ܧ‬ ֜ Ͷ ൅ ͸ ൌ ‫ܧ‬ ֜ ‫ܧ‬ ൌ ͳͲܸ ߬ ൌ ܴ‫ܥ‬௘ ֜ ‫ܥ‬௘ ൌ ߬ ܴ ൌ ͲǤʹ ͳͲͲͲ ൌ ʹ ൈ ͳͲିସ ‫ܨ‬ 8 ( ‫ݑ‬஼భ ൌ ‫ܥܧ‬௘ ‫ܥ‬ଵ ֜ ‫ܥ‬ଵ ൌ ‫ܥܧ‬௘ ‫ݑ‬஼భ ൌ ͳͲ ൈ ʹ ൈ ͳͲିସ Ͷ ൌ Ͷ ൈ ͳͲିସ ‫ܨ‬ ‫ݑ‬஼మ ൌ ‫ܥܧ‬௘ ‫ܥ‬ଶ ֜ ‫ܥ‬ଶ ൌ ‫ܥܧ‬௘ ‫ݑ‬஼మ ൌ ͳͲ ൈ ʹ ൈ ͳͲିସ ͸ ൌ ͵Ǥ͵͵ ൈ ͳͲିସ ‫ܨ‬ 9 ( ‫ݑ‬஼భ ൌ ‫ݑ‬ோ ֜ Ͷ ൬ͳ െ ݁ି ௧ ఛ൰ ൌ ‫݁ܧ‬ି ௧ ఛ ֜ Ͷ െ Ͷ݁ି ௧ ఛ ൌ ͳͲ݁ି ௧ ఛ ֜ Ͷ ൌ ͳͶ݁ି ௧ ఛ ֜ Ͷ ͳͶ ൌ ݁ି ௧ ఛ ֜ ݈݊ Ͷ ͳͶ ൌ െ ‫ݐ‬ ߬ ֜ ݈݊ ͳͶ Ͷ ൌ ‫ݐ‬ ߬ ֜ ‫ݐ‬ ൌ ݈߬݊͵Ǥͷ 10 ( ( ‫ܧ‬ଵ ൌ ͳ ʹ ‫ܥ‬ଵ‫ݑ‬஼భ ଶ ൌ ͲǤͷ ൈ Ͷ ൈ ͳͲିସ ൈ Ͷଶ ൌ ͵Ǥʹ ൈ ͳͲିଷ ‫ܬ‬ ‫ܧ‬ଶ ൌ ͳ ʹ ‫ܥ‬ଶ‫ݑ‬஼మ ଶ ൌ ͲǤͷ ൈ ͵Ǥ͵͵ ൈ ͳͲିସ ൈ ͸ଶ ൌ ͸ ൈ ͳͲିଷ ‫ܬ‬ ‫ܧ‬௘ ൌ ͳ ʹ ‫ܥ‬௘‫ܧ‬ଶ ൌ ͲǤͷ ൈ ʹ ൈ ͳͲିସ ൈ ͳͲଶ ൌ ͲǤͲͳ‫ܬ‬ ሺʹሻ 7 ( ‫ݑ‬஼భ ‫ݑ‬௕ ൅ ‫ݑ‬஼భ ൌ Ͳ ֜ ‫ܮ‬ ݀݅ ݀‫ݐ‬ ൅ ‫ݑ‬஼భ ൌ Ͳ ֜ ‫ܮ‬ ݀ଶ ‫ݍ‬ ݀‫ݐ‬ଶ ൅ ‫ݑ‬஼భ ൌ Ͳ ֜ ‫ܮ‬ ݀ଶ ൫‫ݑ‬஼భ ‫ܥ‬ଵ൯ ݀‫ݐ‬ଶ ൅ ‫ݑ‬஼భ ൌ Ͳ ֜ ‫ܥܮ‬ଵ ݀ଶ ‫ݑ‬஼భ ݀‫ݐ‬ଶ ൅ ‫ݑ‬஼భ ൌ Ͳ ֜ ࢊ૛ ࢛࡯૚ ࢊ࢚૛ ൅ ૚ ࡸ࡯૚ ࢛࡯૚ ൌ ૙ ( ‫ݑ‬஼భ ൌ ‫ݑ‬ଵ …‘• ൬ ʹߨ ܶ଴ ‫ݐ‬ ൅ ߮൰ ֜ ݀ଶ ‫ݑ‬஼భ ݀‫ݐ‬ଶ ൌ െ‫ݑ‬ଵ ൬ ʹߨ ܶ଴ ൰ ଶ …‘• ൬ ʹߨ ܶ଴ ‫ݐ‬ ൅ ߮൰ ֜ ݀ଶ ‫ݑ‬஼భ ݀‫ݐ‬ଶ ൌ െ ൬ ʹߨ ܶ଴ ൰ ଶ ‫ݑ‬஼భ ֜ ࢊ૛ ࢛࡯૚ ࢊ࢚૛ ൅ ൬ ૛࣊ ࢀ૙ ൰ ૛ ࢛࡯૚ ൌ ૙ ൬ ʹߨ ܶ଴ ൰ ଶ ൌ ͳ ‫ܥܮ‬ଵ ֜ ܶ଴ ൌ ʹߨξ‫ܥܮ‬ ( ܶ ൌ ͲǤʹ‫ݏ‬ e n c y - e d u c a t i o n . c o m / e x a m s 8 8 ( ( ͳͶ݁ ݁ି ௧ ఛ / e ֜ ֜ Ͷ Ͷ ͳͶ ͳͶ e ൌ ݁ ݈߬݊͵Ǥ Ǥͷ ͷ ସ ൈ Ͷ Ͷଶ ଶ ൌ ͵ ͵Ǥʹ ʹ ൈ ͳͲ ͵͵ ൈ ൈ ͳͲ ͳͲି ିସ ସ ൈ ൈ ͸ ͸ଶ ൌ Ͳ ͲǤ Ǥͷ ͷ ൈ ʹ ʹ ൈ ͳͲ ͳͲି ିସ ସ ൈ Ͳ ֜ ֜ ‫ܮ‬ ‫ܮ‬ ݀݅ ݀݅ ݀‫ݐ‬ ݀‫ݐ‬ d u ൅ ൅ ‫ݑ‬ ‫ݑ‬஼భ ൌ ֜ ֜ ‫ܥܮ‬ଵ ‫ܥ‬ ݀ଶ d ‫ݑ‬ ‫ݑ‬஼ ஼ 3as.ency-education.com
12 1 8 ܶ଴ ൌ ʹߨξ‫ܥܮ‬ ֜ ܶ଴ ଶ ൌ Ͷߨଶ ‫ܥܮ‬ ֜ ‫ܮ‬ ൌ ܶ଴ ଶ Ͷߨଶ‫ܥ‬ ൌ ͲǤʹଶ Ͷߨଶ ൈ Ͷ ൈ ͳͲିସ ൌ ʹǤͷ͵‫ܪ‬ 7 7 ( ‫ܪ݌‬ ‫݌‬ - - 8 ( ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܱܪ‬ି ൌ ‫ܪܥ‬ଷ‫ܱܱܥ‬ି ൅ ‫ܪ‬ଶܱ 9 ( ‫ܪ݌‬ ൌ ݂ሺܸ௕ሻ 10 ( ( ‫ܪ݌‬ா ൌ ͺǢܸா ൌ ʹͲ݉‫ܮ‬ 11 (1 ( ‫ܥ‬௔ ሺܵሻ ሺ ‫ܥ‬௔ܸ ௔ ൌ ‫ܥ‬௕ܸா ֜ ‫ܥ‬௔ ൌ ‫ܥ‬௕ܸா ܸ ௔ ൌ ͲǤͲͳ ൈ ʹͲ ʹͲ ൌ ͲǤͲͳ݉‫݈݋‬Ȁ‫ܮ‬ 12 ( ( ሺܵሻ ݉ ൌ ‫ܯܸܥ‬ ൌ ͲǤͲͳ ൈ ͲǤͷ ൈ ͸Ͳ ൌ ͲǤ͵݃ - ݉଴ ൌ ݉ ݉ . - ( ‫ܽܭ݌‬ ൌ ͶǤͺ ( ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ Ͳ Ͳ ݊ଵ ݊଴ ‫ݔ‬ ‫ݔ‬ ݊ଵ െ ‫ݔ‬ ݊଴ െ ‫ݔ‬ ‫ݔ‬௙ ‫ݔ‬௙ ݊ଵ െ ‫ݔ‬௙ ݊଴ െ ‫ݔ‬௙ ( ݉௙ ൌ ͶǤͺ ൈ ͳͲ ൌ Ͷͺ݃ ݊௙ ൌ ݊଴ െ ‫ݔ‬௙ ֜ ‫ݔ‬௙ ൌ ݊଴ െ ݊௙ ֜ ‫ݔ‬௙ ൌ  ‫ܯ‬ െ ݉௙ ‫ܯ‬ ൌ ͳʹͲ ͸Ͳ െ Ͷͺ ͸Ͳ ൌ ͳǤʹ݉‫݈݋‬ ( ݇ ൌ ʹǤʹͷ ݇ ൌ ‫ݔ‬௙ ଶ ൫݊଴ െ ‫ݔ‬௙൯൫݊ଵ െ ‫ݔ‬௙൯ ֜ ʹǤʹͷ ൌ ͳǤʹଶ ሺʹ െ ͳǤʹሻሺ݊ଵ െ ͳǤʹሻ e n c y - e d u c a t i o n . c o m / e x a m s - 8 ( ‫ܱܱܥ‬ ܱି ൅ ൅ ‫ܪ‬ ‫ܪ‬ଶܱ ܱ ‫ܪ݌‬ ൌ ൌ ݂ ݂ሺ ሺܸ ܸ௕ ௕ ܸ ܸ ܸ ሻ ሻ Ͳ݉‫ܮ‬ ݉‫ܮ‬ ‫ܥ‬ ‫ܥ‬௔ ௔ ‫ܥ‬ ‫ܥ‬ ሺܵሻ o ൌ Ͳ ͲǤ ǤͲͳ Ͳͳ݉‫݈݋‬ ݉‫݈݋‬Ȁ Ȁ‫ܮ‬ ሺ ሺܵ ܵሻ ሻ ͲǤͷ ൈ ͸Ͳ Ͳ ൌ ൌ Ͳ ͲǤ͵݃ ‫ܪ‬ ‫ܪ‬ଷ ଷ‫ܪܱܱܥ‬ ܱܱ‫ܪ‬ ൅ ൅ ‫ܥ‬ ‫ܥ‬௡ ‫ܥ‬ ‫ܪ‬ ‫ܪ‬ଶ௡ ‫ܪ‬ଷ‫ܪܱܱܥ‬ ‫ܪܱܱܥ‬ ൅ ൅ ‫ܥ‬ ‫ܥ‬௡ ‫ܥ‬ ‫ܪ‬ଶ e d ݊ ݊଴ ଴ e d e d e d e d ݊ ݊଴ ଴ െ െ ‫ݔ‬ ‫ݔ‬ e e e y e ݊ ݊଴ ଴ െ ‫ݔ‬௙ ‫ݔ‬ y y - c y c y c y 3as.ency-education.com
13 1 8 ֜ ʹǤʹͷ ൌ ͳǤͶͶ ͲǤͺሺ݊ଵ െ ͳǤʹሻ ֜ ݊ଵ ൌ ʹ݉‫݈݋‬ ݊ଵ ൌ ݉ ‫ܯ‬ ֜ ‫ܯ‬ ൌ ݉ ݊ଵ ൌ ͳͶͺ ʹ ൌ ͹Ͷ݃Ȁ݉‫݈݋‬ ‫ܯ‬ ൌ ͳͶ݊ ൅ ͳͺ ֜ ݊ ൌ ‫ܯ‬ െ ͳͺ ͳͶ ൌ Ͷ ‫ܥ‬ସ‫ܪ‬ଽܱ‫ܪ‬ ‫ܥ‬ ‫ܪܥ‬ଷ െ ‫ܪܥ‬ଶ െ ‫ܪܥ‬ െ ‫ܪܥ‬ଷ ȁ ܱ‫ܪ‬ ‫ܪܥ‬ଷ‫ܱܱܥ‬ െ ‫ܪܥ‬ െ ‫ܪܥ‬ଶ െ ‫ܪܥ‬ଷ ȁ ‫ܪܥ‬ଷ ( ‫ݎ‬ ൌ ͲǤͳʹ ʹ ൈ ͳͲͲ ൌ ͸ͲΨ - - - ( ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ ͳǤʹ ͳǤʹ ͲǤͺ ͲǤͺ ݊ ൌ ଽ ଵ଼ ൌ ͲǤͷ ݊ ൌ ଷ଻ ଻ସ ൌ ͲǤͷ ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ ͳǤʹ ൅ ͲǤͷ ͳǤʹ ͲǤͺ ൅ ͲǤͷ ͲǤͺ ܳ‫ݎ‬௜ ൌ ͳǤʹ ൈ ͳǤ͹ ͲǤͺ ൈ ͳǤ͵ ൌ ͳǤͻ͸ ൏ ݇ e n c y - e d u c a t i o n . c o m / e x a m s ൌ ͸ͲΨ ͸Ͳ ‫ܪ‬ଷ‫ܪܱܱܥ‬ ܱܱ‫ܪ‬ ൅ ൅ ‫ܥ‬ ‫ܥ‬௡ ௡ ‫ܥ‬ ‫ܥ‬ ‫ܥ‬ ‫ܪ‬ ‫ܪ‬ଶ d ͲǤ Ǥͺ ͺ e d e d e d e e d e e c c c 3as.ency-education.com
14 1 8 13 06 ‫ݐ‬ ൌ Ͳ ሺͳሻ ሺ 1 ( 2 ( ‫ݑ‬஼ ‫ݑ‬ோ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ܴ݅ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ܴ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ܴ ݀ሺ‫ݑ‬஼‫ܥ‬ሻ ݀‫ݐ‬ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ܴ‫ܥ‬ ݀‫ݑ‬஼ ݀‫ݐ‬ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ 3 ( ‫ܣ‬ ‫ܣ‬ ‫ܤ‬ ‫ܤ‬ ߙ ‫ݑ‬஼ ൌ ‫ܣ‬ ൅ ‫݁ܤ‬ఈ௧ ݀‫ݑ‬஼ ݀‫ݐ‬ ൌ ‫݁ߙܤ‬ఈ௧ ֜ ܴ‫ܥ‬ ݀‫ݑ‬஼ ݀‫ݐ‬ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ܴ‫݁ߙܤܥ‬ఈ௧ ൅ ‫ܣ‬ ൅ ‫݁ܤ‬ఈ௧ ൌ ‫ܧ‬ ֜ ‫݁ܤ‬ఈ௧ሺܴ‫ߙܥ‬ ൅ ͳሻ ൅ ‫ܣ‬ െ ‫ܧ‬ ൌ Ͳ ֜ ቄ‫݁ܤ‬ఈ௧ሺܴ‫ߙܥ‬ ൅ ͳሻ ൌ Ͳ ‫ܣ‬ െ ‫ܧ‬ ൌ Ͳ ֜ ቄ ܴ‫ߙܥ‬ ൅ ͳ ൌ Ͳ ‫ܣ‬ ൌ ‫ܧ‬ ֜ ൝ࢻ ൌ െ૚ ࡾ࡯ ࡭ ൌ ࡱ ‫ݐ‬ ൌ Ͳ ֜ ‫ݑ‬஼ ൌ Ͳ ֜ Ͳ ൌ ‫ܣ‬ ൅ ‫݁ܤ‬଴ ֜ Ͳ ൌ ‫ܣ‬ ൅ ‫ܤ‬ ֜ ࡮ ൌ െ࡭ ൌ ࡱ 4 ( ‫ݑ‬ோሺ‫ݐ‬ሻ ‫ݑ‬ோ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ‫ݑ‬ோ ൌ ‫ܧ‬ െ ‫ݑ‬஼ ൌ ‫ܧ‬ െ ‫ܧ‬ሺͳ െ ݁ఈ௧ሻ ֜ ‫ݑ‬ோ ൌ ‫ܧ‬ െ ‫ܧ‬ ൅ ‫݁ܧ‬ఈ௧ ֜ ‫ݑ‬ோ ൌ ‫݁ܧ‬ఈ௧ ௨಴ ௨ೃ ൌ ݁ ೟ ഓ െ ͳ ‫ݑ‬஼ ‫ݑ‬ோ ൌ ‫ܧ‬ ൬ͳ െ ݁ି ௧ ఛ൰ ‫݁ܧ‬ି ௧ ఛ ൌ ͳ െ ݁ି ௧ ఛ ݁ି ௧ ఛ ൌ ݁ ௧ ఛ െ ͳ 5 ( 5 6 6 ‫ܧ‬ ܴ ߬ ߬ ‫ܥ‬ ‫ܥ‬ ‫ܧ‬ ൌ ͳʹܸ ‫ܫ‬଴ ൌ ‫ܧ‬ ܴ ֜ ܴ ൌ ‫ܧ‬ ‫ܫ‬଴ ൌ ͳʹ ͲǤͲͳʹ ൌ ͳͲͲͲȳ ‫ݐ‬ ൌ ߬ ֜ ‫ݑ‬஼ ‫ݑ‬ோ ൌ ݁ି ௧ ఛ െ ͳ ൌ݁ଵ െ ͳ ൌ ͳǤ͹ ߬ ൌ ͲǤͲͶ‫ݏ‬ e n c y - e d u c a t i o n . c o m / e x a m s 1 1 ( ( 2 ( ( ‫ݑ‬஼ ൌ ൌ ‫ܧ‬ ‫ܧ‬ ֜ ֜ ܴ ܴ ݀‫ݍ‬ ݀ ݀‫ݐ‬ x ൅ ܴ ݀ሺ‫ݑ‬ ‫ݑ‬஼ ஼‫ܥ‬ ‫ܥ‬ሻ ሻ ݀‫ݐ‬ ݀‫ݐ‬ m / ൅ ൅ ‫ݑ‬ ‫ݑ‬஼ ൌ ൅ ‫݁ܤ‬ఈ௧ ஼ ݀‫ݐ‬ o ൌ ‫ߙܤ‬ ‫݁ߙܤ‬ఈ௧ ఈ௧ ൅ ൅ ‫ܣ‬ ‫ܣ‬ ൅ ൅ ‫ܤ‬ ‫ܤ‬݁ ݁ఈ௧ ఈ௧ ൌ ‫ܧ‬ ߙ ൅ ͳ ͳሻ ሻ ൌ ൌ Ͳ Ͳ ൌ Ͳ Ͳ ֜ ֜ ቄ ܴ ‫ݑ‬஼ ൌ ൌ Ͳ Ͳ ֜ ֜ Ͳ Ͳ ൌ ‫ܣ‬ ‫ݑ‬ ‫ݑ‬ோ ோ ൅ ൅ ‫ݑ‬ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ 3as.ency-education.com
15 1 8 ߬ ൌ ܴ‫ܥ‬ ֜ ‫ܥ‬ ൌ ߬ ܴ ൌ ͲǤͲͶ ͳͲͲͲ ൌ Ͷ ൈ ͳͲିହ ‫ܨ‬ ሺʹሻ 1 ( 2 ( ‫ݍ‬ሺ‫ݐ‬ሻ ‫ݑ‬௕ ൅ ‫ݑ‬஼ ൌ Ͳ ֜ ‫ܮ‬ ݀݅ ݀‫ݐ‬ ൅ ‫݅ݎ‬ ൅ ‫ݍ‬ ‫ܥ‬ ൌ Ͳ ֜ ‫ܮ‬ ݀ଶ ‫ݍ‬ ݀‫ݐ‬ଶ ൅ ‫ݎ‬ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ‫ܥ‬ ൌ Ͳ ֜ ݀ଶ ‫ݍ‬ ݀‫ݐ‬ଶ ൅ ‫ݎ‬ ‫ܮ‬ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ‫ܮܥ‬ ൌ Ͳ ( ܶ ൌ ͲǤͲͶ‫ݏ‬ ܶ ൎ ʹߨξ‫ܥܮ‬ ֜ ܶଶ ൌ Ͷߨଶ ‫ܥܮ‬ ֜ ‫ܮ‬ ൌ ܶଶ Ͷߨଶ‫ܥ‬ ൌ ͲǤͲͶଶ Ͷߨଶ ൈ Ͷ ൈ ͳͲିହ ൌ ͳ‫ܪ‬ ( ‫ܿܧ‬௠௔௫ ൌ ͳ ʹ ‫ܧܥ‬ଶ ൌ ͲǤͷ ൈ Ͷ ൈ ͳͲିହ ൈ ͳʹଶ ൌ ʹǤͺͺ ൈ ͳͲିଷ ݆ ( ‫ݐ‬ ൌ ܶ ‫ݐ‬ ο‫ܧ‬ ൌ ‫ܿܧ‬௠௔௫ െ ‫ܿܧ‬ሺ‫ݐ‬ሻ ൌ ‫ܿܧ‬௠௔௫ െ ͳ ʹ ൈ ‫ݍ‬ଶ ‫ܥ‬ ൌ ʹǤͺͺ ൈ ͳͲିଷ െ ͲǤͷ ൈ ሺ͵ǤͺͶ ൈ ͳͲିସሻଶ Ͷ ൈ ͳͲିହ ൌ ͳǤͲ͵ ൈ ͳͲିଷ ݆ ( ‫ܫ‬଴ ‫ܿܧ‬௠௔௫ ൌ ‫ܧ‬௅೘ೌೣ ֜ ‫ܿܧ‬௠௔௫ ൌ ͳ ʹ ‫ܫܮ‬଴ ଶ ֜ ‫ܫ‬଴ ൌ ඨ ʹ‫ܿܧ‬௠௔௫ ‫ܮ‬ ൌ ඨ ʹ ൈ ʹǤͺͺ ൈ ͳͲିଷ ͳ ൌ ͲǤͲ͹ͷ‫ܣ‬ 04 4 ( ሺ࡭࡮ሻ ሺ - ሺܵሻ σ ‫ܨ‬ Ԧ ൌ ݉ܽ Ԧ ֜ ܲ ሬԦ ൅ ܴ ሬԦ ൅ ݂ Ԧ ൌ ݉ܽ Ԧ ֜ െ݉݃‫ߙ݊݅ݏ‬ െ ݂ ൌ ݉ܽ ֜ ܽ ൌ െ݃‫ߙ݊݅ݏ‬ െ ݂ ݉ ‫ݒ‬ ൌ ܽ‫ݐ‬ ൅ ‫ݒ‬஺ ‫ݔ‬ ൌ ܽ ʹ ‫ݐ‬ଶ ൅ ‫ݒ‬஺‫ݐ‬ ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ ‫ݒ‬ ൌ ܽ‫ݐ‬ ൅ ‫ݒ‬஺ ֜ ‫ݐ‬ ൌ ‫ݒ‬ െ ‫ݒ‬஺ ܽ ‫ݔ‬ ൌ ܽ ʹ ‫ݐ‬ଶ ൅ ‫ݒ‬஺‫ݐ‬ ֜ ‫ݔ‬ ൌ ܽ ʹ ቀ ‫ݒ‬ െ ‫ݒ‬஺ ܽ ቁ ଶ ൅ ‫ݒ‬஺ ቀ ‫ݒ‬ െ ‫ݒ‬஺ ܽ ቁ ֜ ‫ݔ‬ ൌ ܽ ʹ ‫ݒ‬ଶ ൅ ‫ݒ‬஺ ଶ െ ʹ‫ݒݒ‬஺ ܽଶ ൅ ‫ݒݒ‬஺ െ ‫ݒ‬஺ ଶ ܽ ֜ ‫ݔ‬ ൌ ‫ݒ‬ଶ ൅ ‫ݒ‬஺ ଶ െ ʹ‫ݒݒ‬஺ ʹܽ ൅ ʹ‫ݒݒ‬஺ െ ʹ‫ݒ‬஺ ଶ ʹܽ 2 e n c y - e d u c a t i o n . c o m / e x a m s ( ( ( ‫ܪ‬ ͳͲ Ͳି ିଷ ݆ ݆ ͲǤͷ ͷ ൈ ൈ ሺ ሺ͵ ͵Ǥ ǤͺͶ Ͷ ൈ ൈ ͳͲି Ͷ Ͷ ൈ ͳ o m ൌ ඨ ඨ ʹ‫ܿܧ‬ ‫ܿܧ‬௠௔௫ ௠ ‫ܮ‬ n c ൌ ൌ ඨ ඨ ʹ ൈ c c y - e d u c 3as.ency-education.com
16 1 8 ֜ ‫ݔ‬ ൌ ‫ݒ‬ଶ െ ‫ݒ‬஺ ଶ ʹܽ ֜ ʹܽ‫ݔ‬ ൌ ‫ݒ‬ଶ െ ‫ݒ‬஺ ଶ ֜ ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ 5 ( ࡮ ࡮ - ሺ‫ݔܤ‬ሻ ሺ‫ݕܤ‬ሻ ሺ‫ݔܤ‬ሻ ሺ ሺ‫ݕܤ‬ሻ ሺ Ͳ ൑ ‫ݐ‬ ൑ ͺͷ݉‫ݏ‬ ͺͷ݉‫ݏ‬ ൑ ‫ݐ‬ ൑ ͵ͶͲ݉‫ݏ‬ σ ‫ܨ‬ Ԧ ൌ ݉ܽ Ԧ ֜ ܲ ሬԦ ൌ ݉ܽ Ԧ ֜ ݃ Ԧ ൌ ܽ Ԧ ֜ ൜ ܽ௫ ൌ Ͳ ܽ௬ ൌ െ݃ ֜ ൜ ‫ݒ‬௫ ൌ ‫ݒ‬஻ …‘• ߙ ‫ݒ‬௬ ൌ െ݃‫ݐ‬ ൅ ‫ݒ‬஻ •‹ ߙ ֜ ൝ ‫ݔ‬ ൌ ‫ݒ‬஻ …‘• ߙ ‫ݐ‬ ‫ݕ‬ ൌ െ ͳ ʹ ݃‫ݐ‬ଶ ൅ ‫ݒ‬஻ •‹ ߙ ‫ݐ‬ ‫ݐ‬ ൌ ௫ ௩ಳ ୡ୭ୱ ఈ ‫ݔ‬ ൌ ‫ݒ‬஻ …‘• ߙ ‫ݐ‬ ֜ ‫ݕ‬ ൌ െ ͳ ʹ ݃ ൬ ‫ݔ‬ ‫ݒ‬஻ …‘• ߙ ൰ ଶ ൅ ‫ݒ‬଴ •‹ ߙ ൬ ‫ݔ‬ ‫ݒ‬஻ …‘• ߙ ൰ ֜ ‫ݕ‬ ൌ െ ݃‫ݔ‬ଶ ʹ‫ݒ‬஻ ଶܿ‫ݏ݋‬ଶߙ ൅ ‫݊ܽݐ‬ ߙ ‫ݔ‬ - ‫ݒ‬஻௫ ൌ ο௫ ο௧ ൌ ଴Ǥସି଴ ଴Ǥଵ଻ି଴ ൌ ʹǤ͵ͷ݉Ȁ‫ݏ‬ ‫ݒ‬஻௬ ൌ ͲǤͺͷͷ݉Ȁ‫ݏ‬ –ƒ ߙ ൌ ‫ݒ‬஻௬ ‫ݒ‬஻௫ ൌ ͲǤͺͷͷ ʹǤ͵ͷ ൌ ͲǤ͵͸͵ ֜ ߙ ൌ ͳͻǤͻ͸ ൎ ʹͲι ‫ݒ‬஻ ൌ ඥ‫ݒ‬஻௫ ଶ ൅ ‫ݒ‬஻௬ ଶ ൌ ξʹǤ͵ͷଶ ൅ ͲǤͺͷͷଶ ൌ ʹǤͷ݉Ȁ‫ݏ‬ - ‫ܦܣ‬ ‫ܣ‬ ‫ܦܣ‬ ൌ ‫ߙ݊݅ݏܤܣ‬ ൅ ‫ݔ‬ ൌ ͳǤʹ ൈ ‫Ͳʹ݊݅ݏ‬ ൅ ͲǤͺ ൌ ͳǤʹͳ݉ ‫ݕ‬ ൌ ͲǤͲͺͷ ൈ ͲǤͺͷͷ ʹ ൅ ͳǤʹ‫Ͳʹ݊݅ݏ‬ ൌ ͲǤͶͶ݉ 6 ( ܽ ܽ ሺܵሻ ሺ‫ܤܣ‬ሻ ‫ݒ‬஺ . ܽ ൌ െ݃‫ߙ݊݅ݏ‬ െ ݂ ݉ ൌ െͻǤͺ ൈ ‫Ͳʹ݊݅ݏ‬ െ ͲǤͺ ͲǤʹ ൌ െ͹Ǥ͵ͷ݉Ȁ‫ݏ‬ଶ ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ ֜ ‫ݒ‬஻ ଶ െ ʹܽ ൈ ‫ܤܣ‬ ൌ ‫ݒ‬஺ ଶ e n c y - e d u c a t i o n . c o m / e x a m s ൅ ‫ݒ‬஻ •‹ ߙ ߙ ‫ݐ‬ ‫ݐ‬ ‫ݐ‬ ‫ݐ‬ ൌ ൌ ௫ ௩ …‘• ‘• ߙ ‫ݐ‬ ‫ݐ‬ ֜ ֜ ൬ ‫ݔ‬ ‫ݒ‬஻ ஻ …‘• …‘• ߙ ߙ a t i ൰ ൰ ଶ ଶ ൅ ൅ ‫ݒ‬଴ • ֜ ‫ݕ‬ ‫ݕ‬ ൌ െ െ ݃‫ݔ‬ଶ ʹ‫ݒ‬஻ ଶ c a –ƒ –ƒ ߙ ߙ ൌ ‫ݒ‬஻ ‫ݒ‬஻ ൌ 3as.ency-education.com
17 1 8 ֜ ‫ݒ‬஺ ଶ ൌ ʹǤͷଶ ൅ ʹ ൈ ͹Ǥ͵ͷ ൈ ͳǤʹ ֜ ‫ݒ‬஺ ൌ ͶǤͺͺ݉Ȁ‫ݏ‬ 7 II . - ሺܱ‫ݔ‬ ܴ݁݀ Τ ሻ ‫݈ܣ‬ଷା ‫݈ܣ‬ Τ ‫ܣ‬ ‫ܪ‬ଷܱା ‫ܪ‬ଶ Τ ‫ܪ‬ - ʹ‫݈ܣ‬ሺ௦ሻ ൅ ͸‫ܪ‬ଷܱା ሺ௔௤ሻ ൌ ʹ‫݈ܣ‬ଷା ሺ௔௤ሻ ൅ ͵‫ܪ‬ଶሺ௚ሻ ൅ ͸‫ܪ‬ଶܱሺ௟ሻ Ͳ Ͳ ݊ଶ ݊ଵ ͵‫ݔ‬ ʹ‫ݔ‬ ݊ଶ െ ͸‫ݔ‬ ݊ଵ െ ʹ‫ݔ‬ ͵‫ݔ‬௙ ʹ‫ݔ‬௙ ݊ଶ െ ͸‫ݔ‬௙ ݊ଵ െ ʹ‫ݔ‬௙ ‫ݔ‬௠௔௫ ܸுమ ܸெ ൌ ͵‫ݔ‬௙ ֜ ‫ݔ‬௙ ൌ ܸுమ ͵ܸெ ൌ ͲǤ͵͸ ͵ ൈ ʹͶ ൌ ͷ ൈ ͳͲିଷ ݉‫݈݋‬ ‫ܪ‬ଷܱା ݊ଶ െ ͸‫ݔ‬௙ ൌ ܸܿ െ ͸‫ݔ‬௙ ൌ ͲǤʹ ൈ ͲǤʹ െ ͸ ൈ ͷ ൈ ͳͲିଷ ൌ ͲǤͲͳ ് Ͳ ‫ܪ‬ଷܱା - ݊ଵ െ ʹ‫ݔ‬௙ ൌ Ͳ ֜ ݊ଵ ൌ ʹ‫ݔ‬௙ ൌ ʹ ൈ ͷ ൈ ͳͲିଷ ൌ ͲǤͲͳ݉‫݈݋‬ ݊ଵ ൌ ݉ ‫ܯ‬ ֜ ݉ ൌ ݊‫ܯ‬ ൌ ͲǤͲͳ ൈ ʹ͹ ൌ ͲǤʹ͹݃ - ܲ ൌ ݉ ݉଴ ൈ ͳͲͲ ൌ ͲǤʹ͹ ͲǤ͵ ൈ ͳͲͲ ൌ ͻͲΨ - ‫ݐ‬ଵ ଶ Τ ൌ ͵Ǥͷ݉݅݊ - ‫ݒ‬ ൌ ݀‫ݔ‬ ݀‫ݐ‬ ൌ ݀ ൬ ܸுమ ͵ܸெ ൰ ݀‫ݐ‬ ൌ ͳ ͵ܸெ ൈ ܸ݀ுమ ሺ‫ݐ‬ሻ ݀‫ݐ‬ ‫ݐ‬ ൌ ͳͲ݉݅݊ ‫ݐ‬ ‫ݒ‬ ൌ ͳ ͵ܸெ ൈ ܸ݀ுమ ሺ‫ݐ‬ሻ ݀‫ݐ‬ ൌ ͸Ǥʹͷ ൈ ͳͲିହ ݉‫݈݋‬Ȁ݉݅݊ III . 6 ( 7 ( ሺ‫ܪ‬ଷܱା ൅ ‫݈ܥ‬ିሻ ሺ ሺܰܽା ൅ ‫ܱܪ‬ି ሻ ‫ܪ‬ଷܱା ൅ ‫ܱܪ‬ି ൌ ‫ܪ‬ଶܱ e n c y - e d u c a t i o n . c o m / e x a m s - - e e e ‫ݔ‬௠௔௫ ௠௔ ͳͲିଷ ଷ ݉‫݈݋‬ ݉‫݈݋‬ ͸ ൈ ͷ ͷ ൈ ൈ ͳͲି ିଷ ଷ ൌ Ͳ ʹ‫ݔ‬௙ ௙ ‫ݔ‬ ൌ ൌ ʹ ʹ ൈ ൈ ͷ ͷ ൈ ͳͲ ݉ ‫ܯ‬ a ֜ ֜ ݉ ݉ ൌ ൌ ݊‫ܯ‬ ݊‫ܯ‬ ൌ ܲ ܲ ൌ ൌ ݉ ݉ ݉ ݉଴ u c ൈ ͳ 3as.ency-education.com
18 1 8 ‫ܭ‬ ൌ ͳ ሾ‫ܪ‬ଷܱାሿሾ‫ܱܪ‬ିሿ ൌ ͳ ‫݁ܭ‬ ൌ ͳͲଵସ 8 ( ‫ܪ݌‬ ൌ ͹Ǣܸா ൌ ʹͲ݉‫ܮ‬ 9 ( ‫ܥ‬௔ ‫ܥ‬௔ܸ ௔ ൌ ‫ܥ‬௕ܸா ֜ ‫ܥ‬௔ ൌ ͲǤͲͳ ൈ ʹͲ ʹͲ ൌ ͲǤͲͳ݉‫݈݋‬Ȁ‫ܮ‬ 10 ( ‫ݔ‬௠௔௫ ‫ݔ‬ ݊௙ ൌ ݊ଶ െ ͸‫ݔ‬௠௔௫ ֜ ‫ݔ‬௠௔௫ ൌ ݊ଶ െ ݊௙ ͸ ൌ ܸܿ െ ͷ‫ܥ‬௔ܸ ͸ ൌ ͲǤʹ ൈ ͲǤʹ െ ͷ ൈ ͲǤͲͳ ൈ ͲǤʹ ͸ ֜ ‫ݔ‬௠௔௫ ൌ ͷ ൈ ͳͲିଷ ݉‫݈݋‬ ‫ݔ‬௠௔௫ ‫ݔ‬ e n c y - e d u c a t i o n . c o m / e x a m s 8 ( 9 9 ( ( ௔ ( ͷ ൈ ͲǤͲͳ Ͳͳ ൈ ൈ Ͳ ͲǤ Ǥʹ ʹ ͸ e x 3as.ency-education.com

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  • 2. 2 2 8 2019 1 - 2 - 2 2 - ο݉ଵ ο ο݉ଶ ο ο݉ଷ - ‫ܧ‬௟ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ܲ‫ݑ‬ ଽସ ଶଷଽ ܶ݁ ହଶ ଵଷହ . - ‫ܸ݁ܯ‬ 3 - ܲ ൌ ͵ ൈ ͳͲ଺ ܹ ܲ ρ ൌ ͺͷΨ - ܲ‫ݑ‬ ଽସ ଶଷଽ 45 ρ ൌ ா೐ ா ρ ‫ܧ‬௘ ‫ܧ‬ ‫ܧ‬௟൫ ܶ݁ ହଶ ଵଷହ ൯ ൌ ͳͳʹ͸Ǥͻ͸‫ܸ݁ܯ‬ ‫ܧ‬ ͳ‫ܸ݁ܯ‬ ൌ ͳǤ͸ ൈ ͳͲିଵଷ ݆ ͳ‫ݑ‬ ൌ ͻ͵ͳǤͷ ‫ܸ݁ܯ‬ ‫ܥ‬ଶ Τ ܰ஺ ൌ ͸ǤͲʹ ൈ ͳͲଶଷ ݉‫݈݋‬ିଵ 07 3 3 - ‫ܧ‬ - ܴ ൌ ͳ݇ȳ . - ‫ܥ‬ଵ ‫ܥ‬ ‫ܥ‬ଶ - ‫ܮ‬ ‫ܮ‬ ‫ܭ‬ ‫ܭ‬ ‫ݐ‬ ൌ Ͳ ሺͳሻ ሺ ‫ݑ‬஼భ ሺ‫ݐ‬ሻ ‫ݑ‬஼మ ሺ‫ݐ‬ሻ ‫ݑ‬ 3 ଵ ஼೐ ൌ ଵ ஼భ ൅ ଵ ஼మ ‫ݍ‬ ൌ ‫ݍ‬ଵ ൌ ‫ݍ‬ଶ ‫ݍ‬ ‫ݍ‬ ‫ܥ‬௘ 1 ( ‫ݍ‬ 3 2 e n c y - e d u c a t i o n . c o m / e x a m s - ο݉ ݉ଶ ଶ ο - - ܲ ଽସ ଶଷଽ ଶ ܶ݁ ܶ݁ ହଶ ହଶ ଵଷହ ଵଷହ . . ܲ ܲ ͷΨ ܲ ଽସ ଶଷଽ ଶ ρ ρ ‫ܧ‬ ‫ܧ‬௘ ௘ ൌ ͳ ͳǤ Ǥ͸ ͸ ൈ ൈ ͳͲ ͳͲିଵଷ ݆ ൌ ൌ ͸ ͸ǤͲʹ Ͳʹ ൈ ൈ ͳͲ ͳͲଶଷ ݉ ‫ܥ‬ ‫ܥ‬௘ ௘ d 3as.ency-education.com
  • 3. 3 3 8 2019 ‫ݍ‬ ൌ ‫ܥܧ‬௘ ቀͳ െ ݁ି ೟ ഓቁ ‫ݑ‬஼భ ሺ‫ݐ‬ሻ ‫ݑ‬ ‫ݑ‬஼మ ሺ‫ݐ‬ሻ 2 ( 4 4 ߬ ‫ܧ‬ ‫ܥ‬௘ 3 ( ‫ܥ‬ଵ ‫ܥ‬ ‫ܥ‬ଶ ‫ܥ‬ 4 ( ‫ݑ‬஼భ ൌ ‫ݑ‬ோ ‫ݐ‬ ൌ ߬ ݈݊ ͵Ǥͷ 5 ( ሺʹሻ ሺ 1 ( ‫ݑ‬஼భ ‫ݑ‬ 2 ( ‫ݑ‬஼భ ൌ ‫ݑ‬ଵ …‘• ቀ ଶగ ்బ ‫ݐ‬ ൅ ߮ቁ ‫ݑ‬ ‫ݑ‬ଵ ‫ݑ‬ ‫ܥ‬ଵ ‫ܥ‬ ‫ݐ‬ ൒ ͳǤʹ‫ݏ‬ . ܶ଴ 3 ( 4 ܶ଴ ܶ ‫ܮ‬ 7 7 I . ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ݉଴ ൌ ͲǤ͵݃ ݉ ͷͲͲ݉‫ܮ‬ ሺܵሻ . ܸ ௔ ൌ ʹͲ݉‫ܮ‬ ܸ ሺܵሻ ͺͲ݉‫ܮ‬ 4 e n c y c o m / e x a m s 2 ( 3 3 ( ( 4 4 ( ( 5 ( ʹሻ భ ൌ ‫ݑ‬ ‫ݑ‬ଵ ଵ …‘• …‘• ቀ ቀ ଶ ଶగ గ ்బ ் / e ‫ݐ‬ ൅ ‫ݐ‬ ൒ . 4 3as.ency-education.com
  • 4. 4 4 8 2019 ሺܰܽା ൅ ‫ܱܪ‬ିሻ ‫ܥ‬௕ ൌ ͲǤͲͳ݉‫݈݋‬Ȁ‫ܮ‬ ʹͷԨ ʹ 1 ( 2 ( 3 ( ‫ܪ݌‬ ൌ ݂ሺܸ௕ሻ ‫݌‬ 4 ( ‫ܥ‬௔ ሺܵሻ 5 ( ሺܵሻ ݉଴ ݉ 6 ( ‫ܽܭ݌‬ ሺ‫ܪܥ‬ଷ‫ܪܱܱܥ‬Ȁ‫ܪܥ‬ଷ‫ܱܱܥ‬ିሻ II . ͳͶͺ݃ ͳ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ͳʹͲ‰ ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ( ( ‫ݔ‬௙ ( ( ( ( ( ( ( ͵͹݃ ͻ݃ ͻ ‫ܯ‬ሺ‫ܪ‬ሻ ൌ ͳ ݃ ݉‫݈݋‬ Τ ‫ܯ‬ ‫ܯ‬ሺܱሻ ൌ ͳ͸ ݃ ݉‫݈݋‬ Τ ‫ܯ‬ ‫ܯ‬ሺ‫ܥ‬ሻ ൌ ͳʹ ݃ ݉‫݈݋‬ Τ 30 27 24 21 20.5 19.5 19 18 15 12 9 6 3 0 ܸ௕ሺ݉‫ܮ‬ሻ 11.3 11.1 10.9 10.4 10.0 6.4 6.0 5.7 5.2 4.9 4.7 4.4 4.0 3.8 ‫ܪ݌‬ 5 e n c y c a t i o n . c o m / e x a m s 1 1 ( ( 2 ( ݂ሺܸ ܸ௕ ௕ ܸ ܸ ܸ ሻ ሻ ‫ܭ݌‬ ଷ‫ܱܱܥ‬ ܱܱି ିሻ ሻ ‫ܪ‬ 1.3 s s s c y - 5 3as.ency-education.com
  • 5. 5 5 8 2019 4 0 0 5 0 0 08 0 08 0 08 ( 13 06 1 - ‫ܧ‬ - ܴ . - ‫ܥ‬ - ‫ܮ‬ ‫ݎ‬ ‫ݎ‬ - ‫ܭ‬ ‫ܭ‬ ‫ݐ‬ ൌ Ͳ ሺͳሻ ሺ ‫ݑ‬஼ ݅ 2 3 3 1 ( 2 ( ‫ݑ‬஼ ‫ݑ‬ 3 ( ‫ݑ‬஼ ൌ ‫ܣ‬ ൅ ‫݁ܤ‬ఈ௧ ‫ݑ‬ ‫ܣ‬ ‫ܣ‬ ‫ܤ‬ ‫ܤ‬ ߙ ߙ 4 ( ‫ݑ‬ோሺ‫ݐ‬ሻ ௨಴ ௨ೃ ൌ ݁ ೟ ഓ െ ͳ 5 ( 2 2 3 3 ‫ܧ‬ ܴ ߬ ߬ ‫ܥ‬ ‫ܥ‬ 1 3 2 e n c y - a t i o n . c o m / e x a m s - - - ‫ܥ‬ ‫ܥ‬ ‫ܥ‬ ‫ܥ‬ ‫ܮ‬ ‫ܮ‬ ‫ݐ‬ ‫ݑ‬ ‫ݑ‬஼ 2 y 3as.ency-education.com
  • 6. 6 6 8 2019 ‫ݐ‬ ൌ Ͳ ሺʹሻ 4 1 ( 2 ( ‫ݍ‬ሺ‫ݐ‬ሻ ( ܶ ൎ ʹߨξ‫ܥܮ‬ ܶ ‫ܮ‬ ( ( ‫ݐ‬ ൌ ܶ ‫ݐ‬ ( ‫ܫ‬଴ 07 ሺܵሻ ݉ ൌ ʹͲͲ݃ ݉ ‫ܣ‬ ‫ܣ‬ Ƚ ‫ݒ‬஺ ‫ݒ‬ ሺܵሻ ሺ‫ܤܣ‬ሻ ݂ ൌ ͲǤͺܰ ‫ܤ‬ ‫ܦ‬ ‫ܦ‬ 5 5 ݃ ൌ ͻǤͺ݉Ȁ‫ݏ‬ଶ ‫ܤܣ‬ ൌ ͳǤʹ݉ ‫ܣ‬ 1 ( ሺ࡭࡮ሻ ሺ - ሺܵሻ - - ‫ݐ‬ ൌ Ͳ ‫ݐ‬ ሺܵሻ ‫ܣ‬ - ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ . 4 5 ‫ݍ‬ሺ‫ݐ‬ ‫ݐ‬ሻ ሻ Ƚ Ƚ ݂ ݂ ൌ ൌ Ͳ ͲǤ Ǥͺ ͺܰ ܰ ݂ ݂ ݃ ݃ ൌ ൌ ͻ ͻǤͺ݉ ʹ݉ x a m s e n c e n 5 3as.ency-education.com
  • 7. 7 7 8 2019 2 ( ࡮ ࡮ ‫ݐ‬ ൌ Ͳ ‫ܤ‬ ‫ܤ‬ ሺܵሻ ሺ‫ݔܤ‬ǡ ‫ݕܤ‬ሻ 6 7 7 - ሺ‫ݔܤ‬ሻ ሺ‫ݕܤ‬ሻ - - - ‫ݒ‬஻௫ ሺ‫ݔܤ‬ሻ ሺ ‫ݒ‬஻௬ ‫ݒ‬ ሺ‫ݕܤ‬ሻ Ƚ Ƚ ‫ݒ‬஻ ‫ܤ‬ - ‫ܦܣ‬ . - ሺܵሻ 3 ( ܽ ܽ ሺܵሻ ሺ‫ܤܣ‬ሻ ‫ݒ‬஺ . 7 7 I . ݉଴ ൌ ͲǤ͵݃ ‫݈ܣ‬ ‫ܣ‬ ܸ ൌ ʹͲͲ݉‫ܮ‬ ܸ ሺ‫ܪ‬ଷܱା ൅ ‫݈ܥ‬ିሻ ܿ ൌ ͲǤʹ ݉‫݈݋‬ ݈ Τ ܸுమ ൌ ݂ሺ‫ݐ‬ሻ ܸ 6 7 e n c y - e d u c a t i o n . c o ሺ ሺ‫ݔܤ‬ ‫ݔܤ‬ሻ ሻ ሺ‫ݕܤ‬ ‫ݕܤ‬ሻ ሻ ‫ݔ‬ሻ ሻ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݒ‬ . x a m s ܵሻ x 3as.ency-education.com
  • 8. 8 8 8 2019 ʹ‫݈ܣ‬ሺ௦ሻ ൅ ͸‫ܪ‬ଷܱା ሺ௔௤ሻ ൌ ʹ‫݈ܣ‬ଷା ሺ௔௤ሻ ൅ ͵‫ܪ‬ଶሺ௚ሻ ൅ ͸‫ܪ‬ଶܱሺ௟ሻ - ሺܱ‫ݔ‬ ܴ݁݀ Τ ሻ - ‫ݔ‬௠௔௫ ‫ܪ‬ଷܱା - - - ‫ݐ‬ଵ ଶ Τ - ‫ݐ‬ ‫ݐ‬ ‫ݒ‬ ൌ ଵ ଷ௏ಾ ൈ ௗ௏ಹమ ሺ௧ሻ ௗ௧ ‫ݐ‬ ൌ ͳͲ݉݅݊ II . ܸ ௔ ൌ ʹͲ݉‫ܮ‬ ሺܰܽା ൅ ‫ܱܪ‬ି ሻ ሺ ‫ܥ‬௕ ൌ ͲǤͲͳ ݉‫݈݋‬ ‫ܮ‬ Τ ‫ܪ݌‬ ‫݌‬ 9 9 1 ( 2 ( ሺ‫ܪ‬ଷܱା ൅ ‫݈ܥ‬ିሻ ሺ ሺܰܽା ൅ ‫ܱܪ‬ି ሻ 3 ( 4 ( ( ‫ܥ‬௔ 5 ( ‫ݔ‬௠௔௫ ‫ݔ‬ ʹͷι ‫ܯ‬ሺ‫݈ܣ‬ሻ ൌ ʹ͹݃Ǥ ݉‫݈݋‬ିଵ ‫ܯ‬ ܸெ ൌ ʹͶ‫ܮ‬Ǥ ݉‫݈݋‬ିଵ ܸ ‫ܭ‬௘ ൌ ͳͲିଵସ 8 9 ૢ૙ e n c y - e d u c a t i o n . c o m / e x a m s - - ‫ܪ‬ ‫ܪ‬ଷ ଷܱ ܱା ା ‫ݐ‬ ‫ݐ‬ଵ ଶ Τ ‫ݐ‬ ‫ݐ‬ ‫ݒ‬ ‫ݒ‬ ൌ ൌ ଵ m ͳͲ݉݅݊ ݉݅݊ ሺ ሺܰܽ ܰ ା 3as.ency-education.com
  • 9. 9 9 8 06 3 ( α β γ γ 13 1 ߚା ߚ ‫݌‬ ଵ ଵ ՜ ݊ ଴ ଵ ൅ ݁ ାଵ ଴ ܰ ଻ ଵଷ ՜ ܺ ௓ ஺ ൅ ݁ ଵ ଴ ͳ͵ ൌ ‫ܣ‬ ͹ ൌ ܼ ൅ ͳ ֜ ܼ ൌ ͸ ܰ ଻ ଵଷ ՜ ‫ܥ‬ ଺ ଵଷ ൅ ݁ ାଵ ଴ 4 ( . ‫ܣ‬ሺ‫ݐ‬ሻ ൌ ‫ܣ‬଴݁ିఒ௧ ֜ Ž ‫ܣ‬ ൌ െߣ‫ݐ‬ ൅ Ž ‫ܣ‬଴ Ž ‫ܣ‬ ൌ ܽ‫ݐ‬ ൅ ܾ ܽ ൌ ʹͳǤ͸ െ ͵ʹ ͳͷͲ െ Ͳ ൌ െͲǤͲ͸ͻ͵݉݅݊ିଵ ܾ ൌ ͵ʹ Ž ‫ܣ‬ ൌ െͲǤͲ͸ͻ͵‫ݐ‬ ൅ ͵ʹ ߣ ൌ െͲǤͲ͸ͻ͵݉݅݊ିଵ Ž ‫ܣ‬଴ ൌ ͵ʹ ֜ ‫ܣ‬଴ ൌ ݁ଷଶ ൌ ͹Ǥͺͻ ൈ ͳͲଵଷ ‫ݍܤ‬ ݉଴ ݉ ‫ܣ‬଴ ൌ ߣܰ଴ ൌ ߣ ݉଴ܰ஺ ‫ܯ‬ ֜ ݉଴ ൌ ‫ܣ‬଴‫ܯ‬ ܰ஺ ൈ ߣ ൌ ͹Ǥͺͻ ൈ ͳͲଵଷ ൈ ͳ͵ ͸ǤͲʹ ൈ ͳͲଶଷ ൈ ͲǤͲ͸ͻ͵ ͸Ͳ ൌ ͳǤͶ͹ ൈ ͳͲି଺ ݃ 4 - 5 - - ο݉ଵ ο݉ଶ ο݉ଷ ο݉ଵ ൌ ʹͶͳǤͻͶͺ͸ͺ െ ʹͶͲǤͲͲʹͳ͸ ൌ ͳǤͻͶ͸ͷʹ‫ݑ‬ ο݉ଶ ൌ ʹͶͳǤͻͶͺ͸ͺ െ ʹ͵ͻǤͺͲͲ͹ͺ ൌ ʹǤͳͶ͹ͻ‫ݑ‬ ο݉ଷ ൌ ʹͶͲǤͲͲʹͳ͸ െ ʹ͵ͻǤͺͲͲ͹ͺ ൌ ͲǤʹͲͳ͵ͺ‫ݑ‬ - ‫ܧ‬௟ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ‫ܧ‬ ‫ܧ‬௟ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ൌ ο݉ଵ‫ܥ‬ଶ ൌ ͳǤͻͶ͸ͷʹ ൈ ͻ͵ͳǤͷ ൌ ͳͺͳ͵Ǥͳͺ‫ܸ݁ܯ‬ e n c y - e d u c a t i o n . c o m / e x a m s . ͸ͻ͵ ͵݉݅݊ ݉݅݊ି ିଵ ͵ʹ ͲǤͲ͸ͻ͵ ͻ͵‫ݐ‬ ‫ݐ‬ ൅ ൅ ͵ʹ ͵ʹ ߣ ൌ െ െͲ ͲǤͲ͸ͻ͵ Ͳ͸ͻ͵݉݅݊ ݉ ି ͵ʹ ֜ ֜ ‫ܣ‬ ‫ܣ‬଴ ଴ ൌ ൌ ݁ ݁ଷଶ ൌ ܰ஺ ܰ ‫ܯ‬ u ֜ ֜ ݉ ݉଴ ଴ ൌ ൌ ‫ܣ‬ ‫ܣ‬଴ ‫ܯ‬ ܰ c 3as.ency-education.com
  • 10. 10 1 8 - ܲ‫ݑ‬ ଽସ ଶଷଽ ଶ ܶ݁ ହଶ ଵଷହ . ‫ܧ‬௟ ‫ܣ‬ ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ൌ ͹Ǥͷͺ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ‫ܧ‬௟ ‫ܣ‬ ሺ ܶ݁ ହଶ ଵଷହ ሻ ൌ ͺǤ͵Ͷ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ܶ݁ ହଶ ଵଷହ - ‫ܸ݁ܯ‬ ‫ܧ‬௟௜௕ ൌ ο݉ଷ‫ܥ‬ଶ ൌ ͲǤʹͲͳ͵ͺ ൈ ͻ͵ͳǤͷ ൌ ͳͺ͹Ǥͷͺ‫ܸ݁ܯ‬ ൌ ͵ ൈ ͳͲିଵଵ ݆ - 6 - ‫ܧ‬ ൌ ܰ ൈ ‫ܧ‬௟௜௕ ֜ ‫ܧ‬ ൌ ݉ ൈ ܰ஺ ‫ܯ‬ ൈ ‫ܧ‬௟௜௕ ֜ ݉ ൌ ‫ܧ‬ ൈ ‫ܯ‬ ܰ஺ ൈ ‫ܧ‬௟௜௕ ρ ൌ ‫ܧ‬௘ ‫ܧ‬ ֜ ‫ܧ‬ ൌ ‫ܧ‬௘ ρ ܲ ൌ ‫ܧ‬௘ ‫ݐ‬ ֜ ‫ܧ‬௘ ൌ ܲ ൈ ‫ݐ‬ ֜ ‫ܧ‬ ൌ ܲ ൈ ‫ݐ‬ ρ ֜ ݉ ൌ ܲ ൈ ‫ݐ‬ ൈ ‫ܯ‬ ρ ൈ ܰ஺ ൈ ‫ܧ‬௟௜௕ ൌ ͵ ൈ ͳͲ଺ ൈ Ͷͷ ൈ ʹͶ ൈ ͵͸ͲͲ ൈ ʹ͵ͻ ͲǤͺͷ ൈ ͸ǤͲʹ ൈ ͳͲଶଷ ൈ ͵ ൈ ͳͲିଵଵ ൌ ͳͺͳǤͷͻ݃ 07 6 ( ‫ݑ‬ோ ൅ ‫ݑ‬஼భ ൅‫ݑ‬஼మ ൌ ‫ܧ‬ ֜ ܴ݅ ൅ ‫ݍ‬ଵ ‫ܥ‬ଵ ൅ ‫ݍ‬ଶ ‫ܥ‬ଶ ൌ ‫ܧ‬ ֜ ܴ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ൬ ͳ ‫ܥ‬ଵ ൅ ͳ ‫ܥ‬ଶ ൰ ൌ ‫ܧ‬ ֜ ܴ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ͳ ‫ܥ‬௘ ൌ ‫ܧ‬ ֜ ܴ‫ܥ‬௘ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ൌ ‫ܥܧ‬௘ ‫ݍ‬ ൌ ‫ܥܧ‬௘ ൬ͳ െ ݁ି ௧ ఛ൰ ݀‫ݍ‬ ݀‫ݐ‬ ൌ ‫ܥܧ‬௘ ߬ ݁ି ௧ ఛ ֜ ܴ‫ܥ‬௘ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ൌ ‫ܥܧ‬௘ ֜ ܴ‫ܥ‬௘ ‫ܥܧ‬௘ ߬ ݁ି ௧ ఛ ൅ ‫ܥܧ‬௘ ൬ͳ െ ݁ି ௧ ఛ൰ ൌ ‫ܥܧ‬௘ ֜ ‫ܥܧ‬௘݁ି ௧ ఛ ൅ ‫ܥܧ‬௘ െ ‫ܥܧ‬௘݁ି ௧ ఛ ൌ ‫ܥܧ‬௘ ֜ Ͳ ൌ Ͳ ‫ݑ‬஼భ ൌ ‫ݍ‬ଵ ‫ܥ‬ଵ ൌ ‫ݍ‬ ‫ܥ‬ଵ ൌ ‫ܥܧ‬௘ ‫ܥ‬ଵ ൬ͳ െ ݁ି ௧ ఛ൰ ‫ݑ‬஼మ ൌ ‫ݍ‬ଶ ‫ܥ‬ଶ ൌ ‫ݍ‬ ‫ܥ‬ଶ ൌ ‫ܥܧ‬௘ ‫ܥ‬ଶ ൬ͳ െ ݁ି ௧ ఛ൰ 7 ( ߬ ൌ ͲǤʹ‫ݏ‬ e n c y - e d u c a t i o n . c o m / e x a m s - - 6 - ௟௜௕ ௜௕ ͷ ൈ ʹͶ ʹͶ ൈ ൈ ͵͸ͲͲ ͸Ͳ ൈ ʹ ǤͲʹ ൈ ͳͲ ͳ ଶଷ ଷ ൈ ൈ ͵ ͵ ൈ c o ‫ܥ‬ଶ ൌ ൌ ‫ܧ‬ ‫ܧ‬ ֜ ֜ ܴ ܴ ݀‫ݍ‬ ݀‫ݍ‬ ݀‫ݐ‬ ݀ o ൅ ֜ ֜ ܴ ܴ‫ܥ‬ ‫ܥ‬௘ ௘ ‫ܥ‬ ‫ܥ‬ ݀‫ݍ‬ ݀‫ݍ‬ ݀‫ݐ‬ a t ൅ ֜ ֜ ܴ ܴ‫ܥ‬ ‫ܥ‬௘ ‫ܥ‬ ݀‫ݍ‬ ݀ ݀ e 3as.ency-education.com
  • 11. 11 1 8 ‫ݑ‬஼భ ൅‫ݑ‬஼మ ൌ ‫ܧ‬ ֜ Ͷ ൅ ͸ ൌ ‫ܧ‬ ֜ ‫ܧ‬ ൌ ͳͲܸ ߬ ൌ ܴ‫ܥ‬௘ ֜ ‫ܥ‬௘ ൌ ߬ ܴ ൌ ͲǤʹ ͳͲͲͲ ൌ ʹ ൈ ͳͲିସ ‫ܨ‬ 8 ( ‫ݑ‬஼భ ൌ ‫ܥܧ‬௘ ‫ܥ‬ଵ ֜ ‫ܥ‬ଵ ൌ ‫ܥܧ‬௘ ‫ݑ‬஼భ ൌ ͳͲ ൈ ʹ ൈ ͳͲିସ Ͷ ൌ Ͷ ൈ ͳͲିସ ‫ܨ‬ ‫ݑ‬஼మ ൌ ‫ܥܧ‬௘ ‫ܥ‬ଶ ֜ ‫ܥ‬ଶ ൌ ‫ܥܧ‬௘ ‫ݑ‬஼మ ൌ ͳͲ ൈ ʹ ൈ ͳͲିସ ͸ ൌ ͵Ǥ͵͵ ൈ ͳͲିସ ‫ܨ‬ 9 ( ‫ݑ‬஼భ ൌ ‫ݑ‬ோ ֜ Ͷ ൬ͳ െ ݁ି ௧ ఛ൰ ൌ ‫݁ܧ‬ି ௧ ఛ ֜ Ͷ െ Ͷ݁ି ௧ ఛ ൌ ͳͲ݁ି ௧ ఛ ֜ Ͷ ൌ ͳͶ݁ି ௧ ఛ ֜ Ͷ ͳͶ ൌ ݁ି ௧ ఛ ֜ ݈݊ Ͷ ͳͶ ൌ െ ‫ݐ‬ ߬ ֜ ݈݊ ͳͶ Ͷ ൌ ‫ݐ‬ ߬ ֜ ‫ݐ‬ ൌ ݈߬݊͵Ǥͷ 10 ( ( ‫ܧ‬ଵ ൌ ͳ ʹ ‫ܥ‬ଵ‫ݑ‬஼భ ଶ ൌ ͲǤͷ ൈ Ͷ ൈ ͳͲିସ ൈ Ͷଶ ൌ ͵Ǥʹ ൈ ͳͲିଷ ‫ܬ‬ ‫ܧ‬ଶ ൌ ͳ ʹ ‫ܥ‬ଶ‫ݑ‬஼మ ଶ ൌ ͲǤͷ ൈ ͵Ǥ͵͵ ൈ ͳͲିସ ൈ ͸ଶ ൌ ͸ ൈ ͳͲିଷ ‫ܬ‬ ‫ܧ‬௘ ൌ ͳ ʹ ‫ܥ‬௘‫ܧ‬ଶ ൌ ͲǤͷ ൈ ʹ ൈ ͳͲିସ ൈ ͳͲଶ ൌ ͲǤͲͳ‫ܬ‬ ሺʹሻ 7 ( ‫ݑ‬஼భ ‫ݑ‬௕ ൅ ‫ݑ‬஼భ ൌ Ͳ ֜ ‫ܮ‬ ݀݅ ݀‫ݐ‬ ൅ ‫ݑ‬஼భ ൌ Ͳ ֜ ‫ܮ‬ ݀ଶ ‫ݍ‬ ݀‫ݐ‬ଶ ൅ ‫ݑ‬஼భ ൌ Ͳ ֜ ‫ܮ‬ ݀ଶ ൫‫ݑ‬஼భ ‫ܥ‬ଵ൯ ݀‫ݐ‬ଶ ൅ ‫ݑ‬஼భ ൌ Ͳ ֜ ‫ܥܮ‬ଵ ݀ଶ ‫ݑ‬஼భ ݀‫ݐ‬ଶ ൅ ‫ݑ‬஼భ ൌ Ͳ ֜ ࢊ૛ ࢛࡯૚ ࢊ࢚૛ ൅ ૚ ࡸ࡯૚ ࢛࡯૚ ൌ ૙ ( ‫ݑ‬஼భ ൌ ‫ݑ‬ଵ …‘• ൬ ʹߨ ܶ଴ ‫ݐ‬ ൅ ߮൰ ֜ ݀ଶ ‫ݑ‬஼భ ݀‫ݐ‬ଶ ൌ െ‫ݑ‬ଵ ൬ ʹߨ ܶ଴ ൰ ଶ …‘• ൬ ʹߨ ܶ଴ ‫ݐ‬ ൅ ߮൰ ֜ ݀ଶ ‫ݑ‬஼భ ݀‫ݐ‬ଶ ൌ െ ൬ ʹߨ ܶ଴ ൰ ଶ ‫ݑ‬஼భ ֜ ࢊ૛ ࢛࡯૚ ࢊ࢚૛ ൅ ൬ ૛࣊ ࢀ૙ ൰ ૛ ࢛࡯૚ ൌ ૙ ൬ ʹߨ ܶ଴ ൰ ଶ ൌ ͳ ‫ܥܮ‬ଵ ֜ ܶ଴ ൌ ʹߨξ‫ܥܮ‬ ( ܶ ൌ ͲǤʹ‫ݏ‬ e n c y - e d u c a t i o n . c o m / e x a m s 8 8 ( ( ͳͶ݁ ݁ି ௧ ఛ / e ֜ ֜ Ͷ Ͷ ͳͶ ͳͶ e ൌ ݁ ݈߬݊͵Ǥ Ǥͷ ͷ ସ ൈ Ͷ Ͷଶ ଶ ൌ ͵ ͵Ǥʹ ʹ ൈ ͳͲ ͵͵ ൈ ൈ ͳͲ ͳͲି ିସ ସ ൈ ൈ ͸ ͸ଶ ൌ Ͳ ͲǤ Ǥͷ ͷ ൈ ʹ ʹ ൈ ͳͲ ͳͲି ିସ ସ ൈ Ͳ ֜ ֜ ‫ܮ‬ ‫ܮ‬ ݀݅ ݀݅ ݀‫ݐ‬ ݀‫ݐ‬ d u ൅ ൅ ‫ݑ‬ ‫ݑ‬஼భ ൌ ֜ ֜ ‫ܥܮ‬ଵ ‫ܥ‬ ݀ଶ d ‫ݑ‬ ‫ݑ‬஼ ஼ 3as.ency-education.com
  • 12. 12 1 8 ܶ଴ ൌ ʹߨξ‫ܥܮ‬ ֜ ܶ଴ ଶ ൌ Ͷߨଶ ‫ܥܮ‬ ֜ ‫ܮ‬ ൌ ܶ଴ ଶ Ͷߨଶ‫ܥ‬ ൌ ͲǤʹଶ Ͷߨଶ ൈ Ͷ ൈ ͳͲିସ ൌ ʹǤͷ͵‫ܪ‬ 7 7 ( ‫ܪ݌‬ ‫݌‬ - - 8 ( ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܱܪ‬ି ൌ ‫ܪܥ‬ଷ‫ܱܱܥ‬ି ൅ ‫ܪ‬ଶܱ 9 ( ‫ܪ݌‬ ൌ ݂ሺܸ௕ሻ 10 ( ( ‫ܪ݌‬ா ൌ ͺǢܸா ൌ ʹͲ݉‫ܮ‬ 11 (1 ( ‫ܥ‬௔ ሺܵሻ ሺ ‫ܥ‬௔ܸ ௔ ൌ ‫ܥ‬௕ܸா ֜ ‫ܥ‬௔ ൌ ‫ܥ‬௕ܸா ܸ ௔ ൌ ͲǤͲͳ ൈ ʹͲ ʹͲ ൌ ͲǤͲͳ݉‫݈݋‬Ȁ‫ܮ‬ 12 ( ( ሺܵሻ ݉ ൌ ‫ܯܸܥ‬ ൌ ͲǤͲͳ ൈ ͲǤͷ ൈ ͸Ͳ ൌ ͲǤ͵݃ - ݉଴ ൌ ݉ ݉ . - ( ‫ܽܭ݌‬ ൌ ͶǤͺ ( ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ Ͳ Ͳ ݊ଵ ݊଴ ‫ݔ‬ ‫ݔ‬ ݊ଵ െ ‫ݔ‬ ݊଴ െ ‫ݔ‬ ‫ݔ‬௙ ‫ݔ‬௙ ݊ଵ െ ‫ݔ‬௙ ݊଴ െ ‫ݔ‬௙ ( ݉௙ ൌ ͶǤͺ ൈ ͳͲ ൌ Ͷͺ݃ ݊௙ ൌ ݊଴ െ ‫ݔ‬௙ ֜ ‫ݔ‬௙ ൌ ݊଴ െ ݊௙ ֜ ‫ݔ‬௙ ൌ  ‫ܯ‬ െ ݉௙ ‫ܯ‬ ൌ ͳʹͲ ͸Ͳ െ Ͷͺ ͸Ͳ ൌ ͳǤʹ݉‫݈݋‬ ( ݇ ൌ ʹǤʹͷ ݇ ൌ ‫ݔ‬௙ ଶ ൫݊଴ െ ‫ݔ‬௙൯൫݊ଵ െ ‫ݔ‬௙൯ ֜ ʹǤʹͷ ൌ ͳǤʹଶ ሺʹ െ ͳǤʹሻሺ݊ଵ െ ͳǤʹሻ e n c y - e d u c a t i o n . c o m / e x a m s - 8 ( ‫ܱܱܥ‬ ܱି ൅ ൅ ‫ܪ‬ ‫ܪ‬ଶܱ ܱ ‫ܪ݌‬ ൌ ൌ ݂ ݂ሺ ሺܸ ܸ௕ ௕ ܸ ܸ ܸ ሻ ሻ Ͳ݉‫ܮ‬ ݉‫ܮ‬ ‫ܥ‬ ‫ܥ‬௔ ௔ ‫ܥ‬ ‫ܥ‬ ሺܵሻ o ൌ Ͳ ͲǤ ǤͲͳ Ͳͳ݉‫݈݋‬ ݉‫݈݋‬Ȁ Ȁ‫ܮ‬ ሺ ሺܵ ܵሻ ሻ ͲǤͷ ൈ ͸Ͳ Ͳ ൌ ൌ Ͳ ͲǤ͵݃ ‫ܪ‬ ‫ܪ‬ଷ ଷ‫ܪܱܱܥ‬ ܱܱ‫ܪ‬ ൅ ൅ ‫ܥ‬ ‫ܥ‬௡ ‫ܥ‬ ‫ܪ‬ ‫ܪ‬ଶ௡ ‫ܪ‬ଷ‫ܪܱܱܥ‬ ‫ܪܱܱܥ‬ ൅ ൅ ‫ܥ‬ ‫ܥ‬௡ ‫ܥ‬ ‫ܪ‬ଶ e d ݊ ݊଴ ଴ e d e d e d e d ݊ ݊଴ ଴ െ െ ‫ݔ‬ ‫ݔ‬ e e e y e ݊ ݊଴ ଴ െ ‫ݔ‬௙ ‫ݔ‬ y y - c y c y c y 3as.ency-education.com
  • 13. 13 1 8 ֜ ʹǤʹͷ ൌ ͳǤͶͶ ͲǤͺሺ݊ଵ െ ͳǤʹሻ ֜ ݊ଵ ൌ ʹ݉‫݈݋‬ ݊ଵ ൌ ݉ ‫ܯ‬ ֜ ‫ܯ‬ ൌ ݉ ݊ଵ ൌ ͳͶͺ ʹ ൌ ͹Ͷ݃Ȁ݉‫݈݋‬ ‫ܯ‬ ൌ ͳͶ݊ ൅ ͳͺ ֜ ݊ ൌ ‫ܯ‬ െ ͳͺ ͳͶ ൌ Ͷ ‫ܥ‬ସ‫ܪ‬ଽܱ‫ܪ‬ ‫ܥ‬ ‫ܪܥ‬ଷ െ ‫ܪܥ‬ଶ െ ‫ܪܥ‬ െ ‫ܪܥ‬ଷ ȁ ܱ‫ܪ‬ ‫ܪܥ‬ଷ‫ܱܱܥ‬ െ ‫ܪܥ‬ െ ‫ܪܥ‬ଶ െ ‫ܪܥ‬ଷ ȁ ‫ܪܥ‬ଷ ( ‫ݎ‬ ൌ ͲǤͳʹ ʹ ൈ ͳͲͲ ൌ ͸ͲΨ - - - ( ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ ͳǤʹ ͳǤʹ ͲǤͺ ͲǤͺ ݊ ൌ ଽ ଵ଼ ൌ ͲǤͷ ݊ ൌ ଷ଻ ଻ସ ൌ ͲǤͷ ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ ͳǤʹ ൅ ͲǤͷ ͳǤʹ ͲǤͺ ൅ ͲǤͷ ͲǤͺ ܳ‫ݎ‬௜ ൌ ͳǤʹ ൈ ͳǤ͹ ͲǤͺ ൈ ͳǤ͵ ൌ ͳǤͻ͸ ൏ ݇ e n c y - e d u c a t i o n . c o m / e x a m s ൌ ͸ͲΨ ͸Ͳ ‫ܪ‬ଷ‫ܪܱܱܥ‬ ܱܱ‫ܪ‬ ൅ ൅ ‫ܥ‬ ‫ܥ‬௡ ௡ ‫ܥ‬ ‫ܥ‬ ‫ܥ‬ ‫ܪ‬ ‫ܪ‬ଶ d ͲǤ Ǥͺ ͺ e d e d e d e e d e e c c c 3as.ency-education.com
  • 14. 14 1 8 13 06 ‫ݐ‬ ൌ Ͳ ሺͳሻ ሺ 1 ( 2 ( ‫ݑ‬஼ ‫ݑ‬ோ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ܴ݅ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ܴ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ܴ ݀ሺ‫ݑ‬஼‫ܥ‬ሻ ݀‫ݐ‬ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ܴ‫ܥ‬ ݀‫ݑ‬஼ ݀‫ݐ‬ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ 3 ( ‫ܣ‬ ‫ܣ‬ ‫ܤ‬ ‫ܤ‬ ߙ ‫ݑ‬஼ ൌ ‫ܣ‬ ൅ ‫݁ܤ‬ఈ௧ ݀‫ݑ‬஼ ݀‫ݐ‬ ൌ ‫݁ߙܤ‬ఈ௧ ֜ ܴ‫ܥ‬ ݀‫ݑ‬஼ ݀‫ݐ‬ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ܴ‫݁ߙܤܥ‬ఈ௧ ൅ ‫ܣ‬ ൅ ‫݁ܤ‬ఈ௧ ൌ ‫ܧ‬ ֜ ‫݁ܤ‬ఈ௧ሺܴ‫ߙܥ‬ ൅ ͳሻ ൅ ‫ܣ‬ െ ‫ܧ‬ ൌ Ͳ ֜ ቄ‫݁ܤ‬ఈ௧ሺܴ‫ߙܥ‬ ൅ ͳሻ ൌ Ͳ ‫ܣ‬ െ ‫ܧ‬ ൌ Ͳ ֜ ቄ ܴ‫ߙܥ‬ ൅ ͳ ൌ Ͳ ‫ܣ‬ ൌ ‫ܧ‬ ֜ ൝ࢻ ൌ െ૚ ࡾ࡯ ࡭ ൌ ࡱ ‫ݐ‬ ൌ Ͳ ֜ ‫ݑ‬஼ ൌ Ͳ ֜ Ͳ ൌ ‫ܣ‬ ൅ ‫݁ܤ‬଴ ֜ Ͳ ൌ ‫ܣ‬ ൅ ‫ܤ‬ ֜ ࡮ ൌ െ࡭ ൌ ࡱ 4 ( ‫ݑ‬ோሺ‫ݐ‬ሻ ‫ݑ‬ோ ൅ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ ‫ݑ‬ோ ൌ ‫ܧ‬ െ ‫ݑ‬஼ ൌ ‫ܧ‬ െ ‫ܧ‬ሺͳ െ ݁ఈ௧ሻ ֜ ‫ݑ‬ோ ൌ ‫ܧ‬ െ ‫ܧ‬ ൅ ‫݁ܧ‬ఈ௧ ֜ ‫ݑ‬ோ ൌ ‫݁ܧ‬ఈ௧ ௨಴ ௨ೃ ൌ ݁ ೟ ഓ െ ͳ ‫ݑ‬஼ ‫ݑ‬ோ ൌ ‫ܧ‬ ൬ͳ െ ݁ି ௧ ఛ൰ ‫݁ܧ‬ି ௧ ఛ ൌ ͳ െ ݁ି ௧ ఛ ݁ି ௧ ఛ ൌ ݁ ௧ ఛ െ ͳ 5 ( 5 6 6 ‫ܧ‬ ܴ ߬ ߬ ‫ܥ‬ ‫ܥ‬ ‫ܧ‬ ൌ ͳʹܸ ‫ܫ‬଴ ൌ ‫ܧ‬ ܴ ֜ ܴ ൌ ‫ܧ‬ ‫ܫ‬଴ ൌ ͳʹ ͲǤͲͳʹ ൌ ͳͲͲͲȳ ‫ݐ‬ ൌ ߬ ֜ ‫ݑ‬஼ ‫ݑ‬ோ ൌ ݁ି ௧ ఛ െ ͳ ൌ݁ଵ െ ͳ ൌ ͳǤ͹ ߬ ൌ ͲǤͲͶ‫ݏ‬ e n c y - e d u c a t i o n . c o m / e x a m s 1 1 ( ( 2 ( ( ‫ݑ‬஼ ൌ ൌ ‫ܧ‬ ‫ܧ‬ ֜ ֜ ܴ ܴ ݀‫ݍ‬ ݀ ݀‫ݐ‬ x ൅ ܴ ݀ሺ‫ݑ‬ ‫ݑ‬஼ ஼‫ܥ‬ ‫ܥ‬ሻ ሻ ݀‫ݐ‬ ݀‫ݐ‬ m / ൅ ൅ ‫ݑ‬ ‫ݑ‬஼ ൌ ൅ ‫݁ܤ‬ఈ௧ ஼ ݀‫ݐ‬ o ൌ ‫ߙܤ‬ ‫݁ߙܤ‬ఈ௧ ఈ௧ ൅ ൅ ‫ܣ‬ ‫ܣ‬ ൅ ൅ ‫ܤ‬ ‫ܤ‬݁ ݁ఈ௧ ఈ௧ ൌ ‫ܧ‬ ߙ ൅ ͳ ͳሻ ሻ ൌ ൌ Ͳ Ͳ ൌ Ͳ Ͳ ֜ ֜ ቄ ܴ ‫ݑ‬஼ ൌ ൌ Ͳ Ͳ ֜ ֜ Ͳ Ͳ ൌ ‫ܣ‬ ‫ݑ‬ ‫ݑ‬ோ ோ ൅ ൅ ‫ݑ‬ ‫ݑ‬஼ ൌ ‫ܧ‬ ֜ 3as.ency-education.com
  • 15. 15 1 8 ߬ ൌ ܴ‫ܥ‬ ֜ ‫ܥ‬ ൌ ߬ ܴ ൌ ͲǤͲͶ ͳͲͲͲ ൌ Ͷ ൈ ͳͲିହ ‫ܨ‬ ሺʹሻ 1 ( 2 ( ‫ݍ‬ሺ‫ݐ‬ሻ ‫ݑ‬௕ ൅ ‫ݑ‬஼ ൌ Ͳ ֜ ‫ܮ‬ ݀݅ ݀‫ݐ‬ ൅ ‫݅ݎ‬ ൅ ‫ݍ‬ ‫ܥ‬ ൌ Ͳ ֜ ‫ܮ‬ ݀ଶ ‫ݍ‬ ݀‫ݐ‬ଶ ൅ ‫ݎ‬ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ‫ܥ‬ ൌ Ͳ ֜ ݀ଶ ‫ݍ‬ ݀‫ݐ‬ଶ ൅ ‫ݎ‬ ‫ܮ‬ ݀‫ݍ‬ ݀‫ݐ‬ ൅ ‫ݍ‬ ‫ܮܥ‬ ൌ Ͳ ( ܶ ൌ ͲǤͲͶ‫ݏ‬ ܶ ൎ ʹߨξ‫ܥܮ‬ ֜ ܶଶ ൌ Ͷߨଶ ‫ܥܮ‬ ֜ ‫ܮ‬ ൌ ܶଶ Ͷߨଶ‫ܥ‬ ൌ ͲǤͲͶଶ Ͷߨଶ ൈ Ͷ ൈ ͳͲିହ ൌ ͳ‫ܪ‬ ( ‫ܿܧ‬௠௔௫ ൌ ͳ ʹ ‫ܧܥ‬ଶ ൌ ͲǤͷ ൈ Ͷ ൈ ͳͲିହ ൈ ͳʹଶ ൌ ʹǤͺͺ ൈ ͳͲିଷ ݆ ( ‫ݐ‬ ൌ ܶ ‫ݐ‬ ο‫ܧ‬ ൌ ‫ܿܧ‬௠௔௫ െ ‫ܿܧ‬ሺ‫ݐ‬ሻ ൌ ‫ܿܧ‬௠௔௫ െ ͳ ʹ ൈ ‫ݍ‬ଶ ‫ܥ‬ ൌ ʹǤͺͺ ൈ ͳͲିଷ െ ͲǤͷ ൈ ሺ͵ǤͺͶ ൈ ͳͲିସሻଶ Ͷ ൈ ͳͲିହ ൌ ͳǤͲ͵ ൈ ͳͲିଷ ݆ ( ‫ܫ‬଴ ‫ܿܧ‬௠௔௫ ൌ ‫ܧ‬௅೘ೌೣ ֜ ‫ܿܧ‬௠௔௫ ൌ ͳ ʹ ‫ܫܮ‬଴ ଶ ֜ ‫ܫ‬଴ ൌ ඨ ʹ‫ܿܧ‬௠௔௫ ‫ܮ‬ ൌ ඨ ʹ ൈ ʹǤͺͺ ൈ ͳͲିଷ ͳ ൌ ͲǤͲ͹ͷ‫ܣ‬ 04 4 ( ሺ࡭࡮ሻ ሺ - ሺܵሻ σ ‫ܨ‬ Ԧ ൌ ݉ܽ Ԧ ֜ ܲ ሬԦ ൅ ܴ ሬԦ ൅ ݂ Ԧ ൌ ݉ܽ Ԧ ֜ െ݉݃‫ߙ݊݅ݏ‬ െ ݂ ൌ ݉ܽ ֜ ܽ ൌ െ݃‫ߙ݊݅ݏ‬ െ ݂ ݉ ‫ݒ‬ ൌ ܽ‫ݐ‬ ൅ ‫ݒ‬஺ ‫ݔ‬ ൌ ܽ ʹ ‫ݐ‬ଶ ൅ ‫ݒ‬஺‫ݐ‬ ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ ‫ݒ‬ ൌ ܽ‫ݐ‬ ൅ ‫ݒ‬஺ ֜ ‫ݐ‬ ൌ ‫ݒ‬ െ ‫ݒ‬஺ ܽ ‫ݔ‬ ൌ ܽ ʹ ‫ݐ‬ଶ ൅ ‫ݒ‬஺‫ݐ‬ ֜ ‫ݔ‬ ൌ ܽ ʹ ቀ ‫ݒ‬ െ ‫ݒ‬஺ ܽ ቁ ଶ ൅ ‫ݒ‬஺ ቀ ‫ݒ‬ െ ‫ݒ‬஺ ܽ ቁ ֜ ‫ݔ‬ ൌ ܽ ʹ ‫ݒ‬ଶ ൅ ‫ݒ‬஺ ଶ െ ʹ‫ݒݒ‬஺ ܽଶ ൅ ‫ݒݒ‬஺ െ ‫ݒ‬஺ ଶ ܽ ֜ ‫ݔ‬ ൌ ‫ݒ‬ଶ ൅ ‫ݒ‬஺ ଶ െ ʹ‫ݒݒ‬஺ ʹܽ ൅ ʹ‫ݒݒ‬஺ െ ʹ‫ݒ‬஺ ଶ ʹܽ 2 e n c y - e d u c a t i o n . c o m / e x a m s ( ( ( ‫ܪ‬ ͳͲ Ͳି ିଷ ݆ ݆ ͲǤͷ ͷ ൈ ൈ ሺ ሺ͵ ͵Ǥ ǤͺͶ Ͷ ൈ ൈ ͳͲି Ͷ Ͷ ൈ ͳ o m ൌ ඨ ඨ ʹ‫ܿܧ‬ ‫ܿܧ‬௠௔௫ ௠ ‫ܮ‬ n c ൌ ൌ ඨ ඨ ʹ ൈ c c y - e d u c 3as.ency-education.com
  • 16. 16 1 8 ֜ ‫ݔ‬ ൌ ‫ݒ‬ଶ െ ‫ݒ‬஺ ଶ ʹܽ ֜ ʹܽ‫ݔ‬ ൌ ‫ݒ‬ଶ െ ‫ݒ‬஺ ଶ ֜ ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ 5 ( ࡮ ࡮ - ሺ‫ݔܤ‬ሻ ሺ‫ݕܤ‬ሻ ሺ‫ݔܤ‬ሻ ሺ ሺ‫ݕܤ‬ሻ ሺ Ͳ ൑ ‫ݐ‬ ൑ ͺͷ݉‫ݏ‬ ͺͷ݉‫ݏ‬ ൑ ‫ݐ‬ ൑ ͵ͶͲ݉‫ݏ‬ σ ‫ܨ‬ Ԧ ൌ ݉ܽ Ԧ ֜ ܲ ሬԦ ൌ ݉ܽ Ԧ ֜ ݃ Ԧ ൌ ܽ Ԧ ֜ ൜ ܽ௫ ൌ Ͳ ܽ௬ ൌ െ݃ ֜ ൜ ‫ݒ‬௫ ൌ ‫ݒ‬஻ …‘• ߙ ‫ݒ‬௬ ൌ െ݃‫ݐ‬ ൅ ‫ݒ‬஻ •‹ ߙ ֜ ൝ ‫ݔ‬ ൌ ‫ݒ‬஻ …‘• ߙ ‫ݐ‬ ‫ݕ‬ ൌ െ ͳ ʹ ݃‫ݐ‬ଶ ൅ ‫ݒ‬஻ •‹ ߙ ‫ݐ‬ ‫ݐ‬ ൌ ௫ ௩ಳ ୡ୭ୱ ఈ ‫ݔ‬ ൌ ‫ݒ‬஻ …‘• ߙ ‫ݐ‬ ֜ ‫ݕ‬ ൌ െ ͳ ʹ ݃ ൬ ‫ݔ‬ ‫ݒ‬஻ …‘• ߙ ൰ ଶ ൅ ‫ݒ‬଴ •‹ ߙ ൬ ‫ݔ‬ ‫ݒ‬஻ …‘• ߙ ൰ ֜ ‫ݕ‬ ൌ െ ݃‫ݔ‬ଶ ʹ‫ݒ‬஻ ଶܿ‫ݏ݋‬ଶߙ ൅ ‫݊ܽݐ‬ ߙ ‫ݔ‬ - ‫ݒ‬஻௫ ൌ ο௫ ο௧ ൌ ଴Ǥସି଴ ଴Ǥଵ଻ି଴ ൌ ʹǤ͵ͷ݉Ȁ‫ݏ‬ ‫ݒ‬஻௬ ൌ ͲǤͺͷͷ݉Ȁ‫ݏ‬ –ƒ ߙ ൌ ‫ݒ‬஻௬ ‫ݒ‬஻௫ ൌ ͲǤͺͷͷ ʹǤ͵ͷ ൌ ͲǤ͵͸͵ ֜ ߙ ൌ ͳͻǤͻ͸ ൎ ʹͲι ‫ݒ‬஻ ൌ ඥ‫ݒ‬஻௫ ଶ ൅ ‫ݒ‬஻௬ ଶ ൌ ξʹǤ͵ͷଶ ൅ ͲǤͺͷͷଶ ൌ ʹǤͷ݉Ȁ‫ݏ‬ - ‫ܦܣ‬ ‫ܣ‬ ‫ܦܣ‬ ൌ ‫ߙ݊݅ݏܤܣ‬ ൅ ‫ݔ‬ ൌ ͳǤʹ ൈ ‫Ͳʹ݊݅ݏ‬ ൅ ͲǤͺ ൌ ͳǤʹͳ݉ ‫ݕ‬ ൌ ͲǤͲͺͷ ൈ ͲǤͺͷͷ ʹ ൅ ͳǤʹ‫Ͳʹ݊݅ݏ‬ ൌ ͲǤͶͶ݉ 6 ( ܽ ܽ ሺܵሻ ሺ‫ܤܣ‬ሻ ‫ݒ‬஺ . ܽ ൌ െ݃‫ߙ݊݅ݏ‬ െ ݂ ݉ ൌ െͻǤͺ ൈ ‫Ͳʹ݊݅ݏ‬ െ ͲǤͺ ͲǤʹ ൌ െ͹Ǥ͵ͷ݉Ȁ‫ݏ‬ଶ ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ ֜ ‫ݒ‬஻ ଶ െ ʹܽ ൈ ‫ܤܣ‬ ൌ ‫ݒ‬஺ ଶ e n c y - e d u c a t i o n . c o m / e x a m s ൅ ‫ݒ‬஻ •‹ ߙ ߙ ‫ݐ‬ ‫ݐ‬ ‫ݐ‬ ‫ݐ‬ ൌ ൌ ௫ ௩ …‘• ‘• ߙ ‫ݐ‬ ‫ݐ‬ ֜ ֜ ൬ ‫ݔ‬ ‫ݒ‬஻ ஻ …‘• …‘• ߙ ߙ a t i ൰ ൰ ଶ ଶ ൅ ൅ ‫ݒ‬଴ • ֜ ‫ݕ‬ ‫ݕ‬ ൌ െ െ ݃‫ݔ‬ଶ ʹ‫ݒ‬஻ ଶ c a –ƒ –ƒ ߙ ߙ ൌ ‫ݒ‬஻ ‫ݒ‬஻ ൌ 3as.ency-education.com
  • 17. 17 1 8 ֜ ‫ݒ‬஺ ଶ ൌ ʹǤͷଶ ൅ ʹ ൈ ͹Ǥ͵ͷ ൈ ͳǤʹ ֜ ‫ݒ‬஺ ൌ ͶǤͺͺ݉Ȁ‫ݏ‬ 7 II . - ሺܱ‫ݔ‬ ܴ݁݀ Τ ሻ ‫݈ܣ‬ଷା ‫݈ܣ‬ Τ ‫ܣ‬ ‫ܪ‬ଷܱା ‫ܪ‬ଶ Τ ‫ܪ‬ - ʹ‫݈ܣ‬ሺ௦ሻ ൅ ͸‫ܪ‬ଷܱା ሺ௔௤ሻ ൌ ʹ‫݈ܣ‬ଷା ሺ௔௤ሻ ൅ ͵‫ܪ‬ଶሺ௚ሻ ൅ ͸‫ܪ‬ଶܱሺ௟ሻ Ͳ Ͳ ݊ଶ ݊ଵ ͵‫ݔ‬ ʹ‫ݔ‬ ݊ଶ െ ͸‫ݔ‬ ݊ଵ െ ʹ‫ݔ‬ ͵‫ݔ‬௙ ʹ‫ݔ‬௙ ݊ଶ െ ͸‫ݔ‬௙ ݊ଵ െ ʹ‫ݔ‬௙ ‫ݔ‬௠௔௫ ܸுమ ܸெ ൌ ͵‫ݔ‬௙ ֜ ‫ݔ‬௙ ൌ ܸுమ ͵ܸெ ൌ ͲǤ͵͸ ͵ ൈ ʹͶ ൌ ͷ ൈ ͳͲିଷ ݉‫݈݋‬ ‫ܪ‬ଷܱା ݊ଶ െ ͸‫ݔ‬௙ ൌ ܸܿ െ ͸‫ݔ‬௙ ൌ ͲǤʹ ൈ ͲǤʹ െ ͸ ൈ ͷ ൈ ͳͲିଷ ൌ ͲǤͲͳ ് Ͳ ‫ܪ‬ଷܱା - ݊ଵ െ ʹ‫ݔ‬௙ ൌ Ͳ ֜ ݊ଵ ൌ ʹ‫ݔ‬௙ ൌ ʹ ൈ ͷ ൈ ͳͲିଷ ൌ ͲǤͲͳ݉‫݈݋‬ ݊ଵ ൌ ݉ ‫ܯ‬ ֜ ݉ ൌ ݊‫ܯ‬ ൌ ͲǤͲͳ ൈ ʹ͹ ൌ ͲǤʹ͹݃ - ܲ ൌ ݉ ݉଴ ൈ ͳͲͲ ൌ ͲǤʹ͹ ͲǤ͵ ൈ ͳͲͲ ൌ ͻͲΨ - ‫ݐ‬ଵ ଶ Τ ൌ ͵Ǥͷ݉݅݊ - ‫ݒ‬ ൌ ݀‫ݔ‬ ݀‫ݐ‬ ൌ ݀ ൬ ܸுమ ͵ܸெ ൰ ݀‫ݐ‬ ൌ ͳ ͵ܸெ ൈ ܸ݀ுమ ሺ‫ݐ‬ሻ ݀‫ݐ‬ ‫ݐ‬ ൌ ͳͲ݉݅݊ ‫ݐ‬ ‫ݒ‬ ൌ ͳ ͵ܸெ ൈ ܸ݀ுమ ሺ‫ݐ‬ሻ ݀‫ݐ‬ ൌ ͸Ǥʹͷ ൈ ͳͲିହ ݉‫݈݋‬Ȁ݉݅݊ III . 6 ( 7 ( ሺ‫ܪ‬ଷܱା ൅ ‫݈ܥ‬ିሻ ሺ ሺܰܽା ൅ ‫ܱܪ‬ି ሻ ‫ܪ‬ଷܱା ൅ ‫ܱܪ‬ି ൌ ‫ܪ‬ଶܱ e n c y - e d u c a t i o n . c o m / e x a m s - - e e e ‫ݔ‬௠௔௫ ௠௔ ͳͲିଷ ଷ ݉‫݈݋‬ ݉‫݈݋‬ ͸ ൈ ͷ ͷ ൈ ൈ ͳͲି ିଷ ଷ ൌ Ͳ ʹ‫ݔ‬௙ ௙ ‫ݔ‬ ൌ ൌ ʹ ʹ ൈ ൈ ͷ ͷ ൈ ͳͲ ݉ ‫ܯ‬ a ֜ ֜ ݉ ݉ ൌ ൌ ݊‫ܯ‬ ݊‫ܯ‬ ൌ ܲ ܲ ൌ ൌ ݉ ݉ ݉ ݉଴ u c ൈ ͳ 3as.ency-education.com
  • 18. 18 1 8 ‫ܭ‬ ൌ ͳ ሾ‫ܪ‬ଷܱାሿሾ‫ܱܪ‬ିሿ ൌ ͳ ‫݁ܭ‬ ൌ ͳͲଵସ 8 ( ‫ܪ݌‬ ൌ ͹Ǣܸா ൌ ʹͲ݉‫ܮ‬ 9 ( ‫ܥ‬௔ ‫ܥ‬௔ܸ ௔ ൌ ‫ܥ‬௕ܸா ֜ ‫ܥ‬௔ ൌ ͲǤͲͳ ൈ ʹͲ ʹͲ ൌ ͲǤͲͳ݉‫݈݋‬Ȁ‫ܮ‬ 10 ( ‫ݔ‬௠௔௫ ‫ݔ‬ ݊௙ ൌ ݊ଶ െ ͸‫ݔ‬௠௔௫ ֜ ‫ݔ‬௠௔௫ ൌ ݊ଶ െ ݊௙ ͸ ൌ ܸܿ െ ͷ‫ܥ‬௔ܸ ͸ ൌ ͲǤʹ ൈ ͲǤʹ െ ͷ ൈ ͲǤͲͳ ൈ ͲǤʹ ͸ ֜ ‫ݔ‬௠௔௫ ൌ ͷ ൈ ͳͲିଷ ݉‫݈݋‬ ‫ݔ‬௠௔௫ ‫ݔ‬ e n c y - e d u c a t i o n . c o m / e x a m s 8 ( 9 9 ( ( ௔ ( ͷ ൈ ͲǤͲͳ Ͳͳ ൈ ൈ Ͳ ͲǤ Ǥʹ ʹ ͸ e x 3as.ency-education.com