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Studyadz 3as-physique-c3-35-49

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1 1 10 2019 04 0 ‫ﺩ‬ 05 0 01 0 10 1 05 0 10 ( 14 04 ͳ‫ݑ‬ ൌ ͻ͵ͳǤͷ‫ܸ݁ܯ‬Ȁ‫ܥ‬ʹ Ǣܰ‫ܣ‬ ൌ ͸ǤͲʹ ൈ ͳͲʹ͵ ݉‫݈݋‬െͳ 14 13 ݉଴ ݉ 1 1 1 ( 13 1 - ܰ ଻ ଵଷ ଵ 2 ( ‫ܣ‬ ‫ݐ‬ ‫ܣ‬଴ ‫ܣ‬ λ 2 2 ‫ܣ‬଴ ‫ܣ‬ λ ‫ݐ‬భ మ 13 1 ݉଴ 3 ( 13 16 ܱ ଼ ଵ଺ ൅ ‫ܪ‬ ଵ ଵ ՜ ܺ ௓ ஺ ൅ ܰ ଻ ଵଷ - ܺ ௓ ஺ - - ܰ ଻ ଵଷ ܱ ଼ ଵ଺ ܺ ௓ ஺ ‫ܪ‬ ଵ ଵ ݊ ଴ ଵ ܺ ௓ ஺ ‫ܥ‬ ଺ ଵଷ ܰ ଻ ଵଷ ܱ ଼ ଵ଺ ͳǤͲͲ͹͵ ͳǤͲͲͺ͸ ͶǤͲͲͳͷ ͳ͵ǤͲͲͲͳ ͳ͵ǤͲͲͳͻ ͳͷǤͻͻͲͷ ݉ሺ‫ݑ‬ሻ 1 e n c y - e d u c a t i o n . c o m / e x a m s 14 14 04 ܰ‫ܣ‬ ‫ܣ‬ ൌ ൌ ͸ǤͲʹ Ͳʹ ൈ ͳ 14 14 ଵ ܺ ܺ ௓ ௓ ஺ ஺ o o o o Ͷ ͶǤͲͲͳͷ ͲͲͳ ͲͲͳ c n n n n c s m s s c y 1 3as.ency-education.com
2 2 10 2019 04 ሺܵሻ ݉ ൌ ʹͲͲ݃ ݉ ‫ܣ‬ ‫ܣ‬ Ƚ ‫ݒ‬஺ ‫ݒ‬ ሺܵሻ ሺ‫ܤܣ‬ሻ ݂ ൌ ͲǤͺܰ ݂ ‫ܤ‬ ‫ܦ‬ ‫ܦ‬ 2 2 ݃ ൌ ͻǤͺ݉Ȁ‫ݏ‬ଶ ‫ܤܣ‬ ൌ ͳǤʹ݉ ‫ܣ‬ 1 ( ሺ࡭࡮ሻ ሺ - ሺܵሻ - - ‫ݐ‬ ൌ Ͳ ሺܵሻ ‫ܣ‬ ‫ܣ‬ - ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ . 2 ( ࡮ ‫ݐ‬ ൌ Ͳ ‫ܤ‬ ‫ܤ‬ ሺܵሻ ሺ‫ݔܤ‬ǡ ‫ݕܤ‬ሻ 3 4 4 - ሺ‫ݔܤ‬ሻ ሺ‫ݕܤ‬ሻ - - ‫ݒ‬஻௫ ሺ‫ݔܤ‬ሻ ሺ ‫ݒ‬஻௬ ‫ݒ‬ ሺ‫ݕܤ‬ሻ Ƚ Ƚ ‫ݒ‬஻ ‫ܤ‬ - ‫ܦܣ‬ . 3 ( ܽ ܽ ሺܵሻ ሺ‫ܤܣ‬ሻ ‫ݒ‬஺ . 2 3 4 e n c c a t i o n . c o m / e x a m s ‫ܤ‬ 1 1 ( ( - ‫ݐ‬ ‫ݐ‬ ‫ݒ‬஻ ଶ ଶ െ െ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݒ‬ ଶ ൌ ʹܽ . ࡮ ࡮ 3as.ency-education.com
3 3 10 2019 06 5 - ‫ܧ‬ - ܴ ൌ ͳ݇ȳ . - ‫ܥ‬ଵ ‫ܥ‬ ‫ܥ‬ଶ - ‫ܮ‬ ‫ܮ‬ ‫ܭ‬ ‫ܭ‬ ‫ݐ‬ ൌ Ͳ ሺͳሻ ሺ ‫ݑ‬஼భ ሺ‫ݐ‬ሻ ‫ݑ‬ ‫ݑ‬஼మ ሺ‫ݐ‬ሻ ‫ݑ‬ 6 ଵ ஼೐ ൌ ଵ ஼భ ൅ ଵ ஼మ ‫ݍ‬ ൌ ‫ݍ‬ଵ ൌ ‫ݍ‬ଶ ‫ݍ‬ ‫ݍ‬ ‫ܥ‬௘ 1 ( ‫ݍ‬ ‫ݍ‬ ൌ ‫ܥܧ‬௘ ቀͳ െ ݁ି ೟ ഓቁ ‫ݑ‬஼భ ሺ‫ݐ‬ሻ ‫ݑ‬ ‫ݑ‬஼మ ሺ‫ݐ‬ሻ 2 ( 6 6 ߬ ‫ܧ‬ ‫ܥ‬௘ 3 ( ‫ܥ‬ଵ ‫ܥ‬ ‫ܥ‬ଶ ‫ܥ‬ 4 ( ‫ݑ‬஼భ ൌ ‫ݑ‬ோ ‫ݐ‬ ൌ ߬ ݈݊ ͵Ǥͷ 5 ( 5 6 e n c y - e d u c a t i o n . c o m / e x a m s - - - Ͳ ‫ݍ‬ ‫ݍ‬ ‫ݍ‬ ‫ݍ‬ a 3as.ency-education.com
4 4 10 2019 ሺʹሻ ሺ 1 ( ‫ݑ‬஼భ ‫ݑ‬ 2 ( ‫ݑ‬஼భ ൌ ‫ݑ‬ଵ …‘• ቀ ଶగ ்బ ‫ݐ‬ ൅ ߮ቁ ‫ݑ‬ ‫ݑ‬ଵ ‫ݑ‬ ‫ܥ‬ଵ ‫ܥ‬ ‫ݐ‬ ൒ ͳǤʹ‫ݏ‬ . . ܶ଴ 3 ( 6 ܶ଴ ܶ ‫ܮ‬ 6 6 I . ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ݉଴ ൌ ͲǤ͵݃ ݉ ͷͲͲ݉‫ܮ‬ ሺܵሻ . ܸ ௔ ൌ ʹͲ݉‫ܮ‬ ሺܵሻ ͺͲ݉‫ܮ‬ ሺܰܽା ൅ ‫ܱܪ‬ିሻ ‫ܥ‬௕ ൌ ͲǤͲͳ݉‫݈݋‬Ȁ‫ܮ‬ ʹͷԨ ʹ 1 ( 2 ( 3 ( ‫ܪ݌‬ ൌ ݂ሺܸ௕ሻ ‫݌‬ 4 ( 5 ( ‫ܥ‬௔ ሺܵሻ 6 ( ሺܵሻ ݉଴ ݉ 7 ( ‫ܽܭ݌‬ ሺ‫ܪܥ‬ଷ‫ܪܱܱܥ‬Ȁ‫ܪܥ‬ଷ‫ܱܱܥ‬ିሻ 8 ( 9 ( ‫ܪ݌‬ ‫݌‬ II . ͳͶͺ݃ ͳ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ͳʹͲ‰ ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ 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݌‬ e n c y - e d u c a t i o n . c o m / e x a m s ( 3 3 ( ( 6 6 6 ‫ܪܱܱܥ‬ ܱܱ‫ܪ‬ ͷͲͲ Ͳ݉‫ܮ‬ ݉‫ܮ‬ ܸ ௔ ௔ ܸ ൌ ൌ ʹͲ ʹͲ݉‫ܮ‬ ݉ ܸ ሺ ሺܰܽ ܰܽା ା ൅ ‫ܱܪ‬ ‫ܪ‬ ିሻ ‫ܥ‬ 19.5 19 19 9 18 8 n n n n n . o o n n 6 6.0 6 0 5.7 5.7 5.2 5. o o o n o n o n n n t t i o t i o t i o t i o o n o o n 3as.ency-education.com
5 5 10 2019 ( ( ‫ݔ‬௙ ( ( ( ( ( ( ( ( ͳͲ݃ ͵͹݃ ‫ܯ‬ሺ‫ܪ‬ሻ ൌ ͳ ݃ ݉‫݈݋‬ Τ ‫ܯ‬ ‫ܯ‬ሺܱሻ ൌ ͳ͸ ݃ ݉‫݈݋‬ Τ ‫ܯ‬ሺ‫ܥ‬ሻ ൌ ͳʹ ݃ ݉‫݈݋‬ Τ 8 e n c y - e d u c a t i o n . c o m / e x a m s ( ( ( ( ( ( ( ( ( ͳͲ ͳͲ݃ ͳ ͳ ݃ ‫ܯ‬ሺ ‫ܯ‬ ʹ ݃ ݉‫݈݋‬ ݉‫݈݋‬ Τ Τ 3as.ency-education.com
6 6 10 2019 05 0 6 0 0 10 1 10 1 10 ( 14 04 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 4 ( ‫ݑ‬ோሺ‫ݐ‬ሻ ௨಴ ௨ೃ ൌ ݁ ೟ ഓ െ ͳ 5 ( 2 2 3 3 ‫ܧ‬ ܴ ߬ ߬ ‫ܥ‬ ‫ܥ‬ 1 2 3 e n c y - e d u c 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
7 7 10 2019 ‫ݐ‬ ൌ Ͳ ሺʹሻ 4 4 1 ( 2 ( ‫ݍ‬ሺ‫ݐ‬ሻ ( ܶ ൎ ʹߨξ‫ܥܮ‬ ܶ ‫ܮ‬ ( ( ‫ݐ‬ ൌ ܶ ‫ݐ‬ ( ‫ܫ‬଴ 04 ܲ‫ݑ‬ ଽସ ଶଷଽ ൅ ݊ ଴ ଵ ՜ ‫݋ܯ‬ ସଶ ଵ଴ଶ ൅ ܶ݁ ହଶ ଵଷହ ൅ ͵ ݊ ଴ ଵ 1 - 2 - 3 - 4 - 5 - ο݉ଵ ο ο݉ଶ ο ο݉ଷ 5 4 e n c y - e d u c a t i o n . c o m ‫ݍ‬ሺ‫ݐ‬ ‫ݐ‬ሻ ሻ ܲ ଽସ ଶଷଽ ଶ x a m s 3as.ency-education.com
8 8 10 2019 - - ‫ܧ‬௟ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ܲ‫ݑ‬ ଽସ ଶଷଽ ଶ ܶ݁ ହଶ ଵଷହ . - ‫ܸ݁ܯ‬ - 5 - ܲ ൌ ͵ ൈ 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 6 ݇ ‫ܣ‬ ‫ܣ‬ Ƚ ൌ ͵Ͳι ሺܵሻ ‫ݔ‬଴ I . 1 ( ሺܵሻ 6 2 ( ‫ݔ‬଴ ‫ݔ‬ ‫ݔ‬଴ ൌ ௚௦௜௡ఈ ௞ ݉ 3 ( ሺܵሻ 300 225 150 75 ݉ሺ‰ሻ 6 4.5 3 1.5 ‫ݔ‬଴ሺܿ݉ሻ ( ‫ݔ‬଴ ൌ ݂ሺ݉ሻ . ( ( ݇ ݇ II . ሺܵሻ ݉଴ ሺܵሻ ܺ௠ ܺ ‫ݐ‬ ൌ Ͳ . 1 ( ‫ݔ‬ሺ‫ݐ‬ሻ 2 ( ‫ݔ‬ሺ‫ݐ‬ሻ ൌ ܺ௠ …‘•ሺ߱଴‫ݐ‬ ൅ ߮ሻ ߱଴ 6 e n c y - e d u c a t i o n . c o m / e x a m s 5 5 - - ܹ - ܶ݁ ݁ ହଶ ହଶ ൯ ൯ ൌ ൌ ͳͳʹ͸ ͳʹ Ǥͻ͸ 6 6 6 ‫ݔ‬ ‫ݔ‬଴ ଴ ൌ ൌ ௚௦௜௡ఈ ௚ a ‫ݔ‬ u u u 3as.ency-education.com
9 9 10 2019 ( ‫ܧ‬௉ா ሺܵሻ ሺ ‫ݐ‬ ‫ݐ‬ 7 7 ( ܶ଴ ܶ ߱଴ ‫ܧ‬௉ா೘ೌೣ ܺ௠ ܺ ݉଴ ( ‫ݔ‬ሺ‫ݐ‬ሻ ( ( ‫ݔ‬଴ ݃ ൌ ͳͲ݉Ȁ‫ݏ‬ଶ 6 6 I . ݉଴ ൌ ͲǤ͵݃ ‫݈ܣ‬ ‫ܣ‬ ܸ ൌ ʹͲͲ݉‫ܮ‬ ܸ ሺ‫ܪ‬ଷܱା ൅ ‫݈ܥ‬ିሻ ܿ ൌ ͲǤʹ ݉‫݈݋‬ ݈ Τ ܸுమ ൌ ݂ሺ‫ݐ‬ሻ ܸ ʹ‫݈ܣ‬ሺ௦ሻ ൅ ͸‫ܪ‬ଷܱା ሺ௔௤ሻ ൌ ʹ‫݈ܣ‬ଷା ሺ௔௤ሻ ൅ ͵‫ܪ‬ଶሺ௚ሻ ൅ ͸‫ܪ‬ଶܱሺ௟ሻ - ሺܱ‫ݔ‬ ܴ݁݀ Τ ሻ - ‫ݔ‬௠௔௫ ‫ܪ‬ଷܱା - - - ‫ݐ‬ଵ ଶ Τ 7 8 ૢ૙ ݉଴ ‫ݔ‬ ‫ݔ‬଴ ‫ݔ‬ ‫ݔ‬ ͳͲ݉Ȁ Ȁ‫ݏ‬ ‫ݏ‬ଶ ଶ ܿ ܿ ൌ ൌ Ͳ ͲǤʹ ʹ ݉‫݋‬ ʹ‫݈ܣ‬ ‫݈ܣ‬ሺ ሺ௦ሻ ൅ ൅ ͸‫ܪ‬ଷܱ 3as.ency-education.com
10 1 10 2019 - ‫ݐ‬ ‫ݐ‬ ‫ݒ‬ ൌ ଵ ଷ௏ಾ ൈ ௗ௏ಹమ ሺ௧ሻ ௗ௧ ‫ݐ‬ ൌ ͳͲ݉݅݊ II . ܸ ௔ ൌ ʹͲ݉‫ܮ‬ ሺܰܽା ൅ ‫ܱܪ‬ି ሻ ‫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 9 e n c y - e d u c a t i o n . c o m / e x a m s ൌ ʹͲ ʹͲ݉‫ܮ‬ ݉‫ܮ‬ ͲǤͲͳ Ͳͳ ݉‫݈݋‬ ݉‫݈݋‬ ‫ܮ‬ Τ Τ ܸ ܸெ ெ ܸ ܸ ܸ ൌ ʹ ܸ ܸ Ͳିଵସ ସ 3as.ency-education.com
11 1 10 04 4 ( α β γ γ 13 1 ߚା ߚ ‫݌‬ ଵ ଵ ՜ ݊ ଴ ଵ ൅ ݁ ାଵ ଴ ܰ ଻ ଵଷ ՜ ܺ ௓ ஺ ൅ ݁ ଵ ଴ ͳ͵ ൌ ‫ܣ‬ ͹ ൌ ܼ ൅ ͳ ֜ ܼ ൌ ͸ ܰ ଻ ଵଷ ՜ ‫ܥ‬ ଺ ଵଷ ൅ ݁ ାଵ ଴ 5 ( ‫ܣ‬ሺ‫ݐ‬ሻ ൌ ‫ܣ‬଴݁ିఒ௧ . Ž ‫ܣ‬ ൌ ܽ‫ݐ‬ ൅ ܾ ܽ ൌ ʹͳǤ͸ െ ͵ʹ ͳͷͲ െ Ͳ ൌ െͲǤͲ͸ͻ͵݉݅݊ିଵ ܾ ൌ ͵ʹ Ž ‫ܣ‬ ൌ െͲǤͲ͸ͻ͵‫ݐ‬ ൅ ͵ʹ ‫ܣ‬ሺ‫ݐ‬ሻ ൌ ‫ܣ‬଴݁ିఒ௧ ֜ Ž ‫ܣ‬ ൌ െߣ‫ݐ‬ ൅ Ž ‫ܣ‬଴ 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଺ ݃ 6 ( 13 16 ܱ ଼ ଵ଺ ൅ ‫ܪ‬ ଵ ଵ ՜ ܺ ௓ ஺ ൅ ܰ ଻ ଵଷ - ͳ͸ ൅ ͳ ൌ ‫ܣ‬ ൅ ͳ͵ ֜ ‫ܣ‬ ൌ Ͷ ͺ ൅ ͳ ൌ ܼ ൅ ͹ ֜ ܼ ൌ ʹ ܺ ௓ ஺ ௓ ஺ ‫݁ܪ‬ ଶ ସ - ܺ ௓ ஺ ܰ ଻ ଵଷ ܱ ଼ ଵ଺ ‫ܧ‬௟ ൌ ቀܼ݉௣ ൅ ሺ‫ܣ‬ െ ܼሻ݉௡ െ ݉ ௑ ೋ ಲ ቁ ‫ܥ‬ଶ ‫ܧ‬௟ሺ ܺ ௓ ஺ ሻ ൌ ሺʹ ൈ ͳǤͲͲ͹͵ ൅ ʹ ൈ ͳǤͲͲͺ͸ െ ͶǤͲͲͳͷሻ ൈ ͻ͵ͳǤͷ ൌ ʹͺǤʹʹ‫ܸ݁ܯ‬ ‫ܧ‬௟ሺ ܰ ଻ ଵଷ ሻ ൌ ሺ͹ ൈ ͳǤͲͲ͹͵ ൅ ͸ ൈ ͳǤͲͲͺ͸ െ ͳ͵ǤͲͲͳͻሻ ൈ ͻ͵ͳǤͷ ൌ ͻ͵Ǥͺͻ‫ܸ݁ܯ‬ ‫ܧ‬௟ሺ ܱ ଼ ଵ଺ ሻ ൌ ሺͺ ൈ ͳǤͲͲ͹͵ ൅ ͺ ൈ ͳǤͲͲͺ͸ െ ͳͷǤͻͻͲͷሻ ൈ ͻ͵ͳǤͷ ൌ ͳʹ͹Ǥ͵͵‫ܸ݁ܯ‬ e n c y - e d u c a t i o n . c o m / e x a m s ‫ܣ‬ ‫ܣ‬଴݁ି ିఒ ఒ௧ ௧ ͵݉݅݊ ݊ି ିଵ ଵ ͻ͵‫ݐ‬ ൅ ͵ʹ ͵ʹ ఒ௧ ֜ ֜ Ž Ž ‫ܣ‬ ‫ܣ‬ ൌ ൌ െߣ‫ݐ‬ ߣ ߣ ൌ ൌ െ െͲ ͲǤ ǤͲ͸ͻ͵ Ͳ͸ ‫ܣ‬଴ ൌ ͵ʹ ͵ʹ ֜ ֜ ‫ܣ‬ ‫ܣ‬଴ ଴ ൌ ݁ ߣ ݉ ݉଴ܰ ܰ஺ ஺ ܰ ܰ ‫ܯ‬ ‫ܯ‬ d u ֜ ֜ ݉ ݉଴ ൌ ‫ܣ‬ 3as.ency-education.com
12 1 10 ‫ܧ‬௟ ‫ܣ‬ ሺ ܺ ௓ ஺ ሻ ൌ ͹ǤͲͷ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ‫ܧ‬௟ ‫ܣ‬ ሺ ܰ ଻ ଵଷ ሻ ൌ ͹Ǥʹʹ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ‫ܧ‬௟ ‫ܣ‬ ሺ ܱ ଼ ଵ଺ ሻ ൌ ͹Ǥͻͷ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ܱ ଼ ଵ଺ 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 ֜ ‫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 - ‫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 2 e n c y - e d u c a t i o n . c o m / e x a m s 4 4 ( ( - ܲ ൅ ܴ ܴ ሬԦ ሬ ൅ ൅ ݂ ݂ Ԧ ൌ ൌ ݉ ݉ܽ Ԧ ֜ ܽ ܽ ൌ ൌ െ െ݃‫ߙ݊݅ݏ‬ ݃‫݊݅ݏ‬ െ ݂ ‫ݒ‬஺ ‫ݒ‬ ʹ ‫ݐ‬ଶ ൅ ൅ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݐ‬ ‫ݒ‬ ܽ‫ݐ‬ ‫ݐ‬ ൅ ൅ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݒ‬ ֜ ֜ ‫ݐ‬ ‫ݐ‬ ൌ ൌ ‫ݒ‬ െ o ൅ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݒ‬ ‫ݐ‬ ֜ ֜ ‫ݔ‬ ‫ݔ‬ ൌ ܽ ܽ ʹ ቀ ‫ݒ‬ െ ʹ‫ݒ‬ ‫ݒ‬‫ݒ‬ ‫ݒ‬஺ ‫ݒ‬ ܽଶ u c ൅ ൅ ‫ݒ‬ ‫ݒ‬‫ݒ‬ ‫ݒ‬஺ ‫ݒ‬ െ c ֜ ‫ݔ‬ ൌ ൌ ‫ݒ‬ ‫ݒ‬ଶ ଶ െ െ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݒ‬ ଶ ଶ ʹ ʹܽ d u ֜ 3as.ency-education.com
13 1 10 - ‫ܦܣ‬ ‫ܣ‬ ‫ܦܣ‬ ൌ ‫ߙ݊݅ݏܤܣ‬ ൅ ‫ݔ‬ ൌ ͳǤʹ ൈ ‫Ͳʹ݊݅ݏ‬ ൅ ͲǤͺ ൌ ͳǤʹͳ݉ 6 ( ܽ ܽ ሺܵሻ ሺ‫ܤܣ‬ሻ ‫ݒ‬஺ . ܽ ൌ െ݃‫ߙ݊݅ݏ‬ െ ݂ ݉ ൌ െͻǤͺ ൈ ‫Ͳʹ݊݅ݏ‬ െ ͲǤͺ ͲǤʹ ൌ െ͹Ǥ͵ͷ݉Ȁ‫ݏ‬ଶ ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ ֜ ‫ݒ‬஻ ଶ െ ʹܽ ൈ ‫ܤܣ‬ ൌ ‫ݒ‬஺ ଶ ֜ ‫ݒ‬஺ ଶ ൌ ʹǤͷଶ ൅ ʹ ൈ ͹Ǥ͵ͷ ൈ ͳǤʹ ֜ ‫ݒ‬஺ ൌ ͶǤͺͺ݉Ȁ‫ݏ‬ 06 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 ‫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 ( e n c y - e d u c a t i o n . c o m / e x a m s 6 ( ܴ ݀‫ݍ‬ ݀‫ݐ‬ ‫ݐ‬ x ൅ ൅ ‫ݍ‬ ‫ݍ‬ ͳ ͳ ‫ܥ‬ ‫ܥ‬௘ ௘ ‫ܥ‬ ‫ܥ‬ x a ൌ ൌ ‫ܧ‬ ൰ ݁ ௧ ఛ ௘ ߬ n ݁ ݁ି ௧ ఛ ఛ n ൅ ൅ ‫ܥܧ‬ ‫ܥ‬௘ ‫ܥ‬ ൬ ൬ͳ ௘ ௘ െ ‫ܧ‬ ‫ܧ‬‫ܥ‬ ‫ܥ‬௘ ‫ܥ‬ ݁ ݁ି ି ௧ ௧ ఛ ఛ o n ൌ ൌ ‫ܥܧ‬ ‫ݑ‬஼భ ൌ ൌ ‫ݍ‬ ‫ݍ‬ଵ ଵ ‫ܥ‬ ‫ܥ‬ଵ ଵ ‫ܥ‬ a t ൌ ൌ ‫ݍ‬ ‫ݍ‬ ‫ܥ‬ଵ ‫ܥ‬ t ൌ ‫ܧ‬ ‫ݑ‬ ‫ݑ‬஼ ஼మ మ ൌ ൌ ‫ݍ‬ ‫ݍ‬ଶ ‫ܥ‬ c ൌ 3as.ency-education.com
14 1 10 ‫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 ܶ଴ ൌ ʹߨξ‫ܥܮ‬ ֜ ܶ଴ ଶ ൌ Ͷߨଶ ‫ܥܮ‬ ֜ ‫ܮ‬ ൌ ܶ଴ ଶ Ͷߨଶ‫ܥ‬ ൌ ͲǤʹଶ Ͷߨଶ ൈ Ͷ ൈ ͳͲିସ ൌ ʹǤͷ͵‫ܪ‬ 10 ( ( 6 6 II . 10 ( ( ‫ܪ݌‬ ‫݌‬ - - 11 ( ( ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܱܪ‬ି ൌ ‫ܪܥ‬ଷ‫ܱܱܥ‬ି ൅ ‫ܪ‬ଶܱ ሺ ሺʹ ʹሻ ሻ ‫ݑ‬஼భ ֜ ‫ܮ‬ ݀ଶ ൫ ൫‫ݑ‬ ‫ݑ‬஼భ ‫ܥ‬ ‫ܥ‬ଵ ଵ ‫ܥ‬ ‫ܥ‬ ‫ܥ‬ ൯ ൯ ݀ ݀‫ݐ‬ ‫ݐ‬ଶ ଶ m ൅ ‫ݑ‬ ൅ ૚ ૚ ࡸ ࡸ࡯ ࡯૚ ૚ c o ࢛࡯૚ ૚ ൌ ૙ ‫ݑ‬஼భ ݀ ݀‫ݐ‬ ‫ݐ‬ଶ ଶ o n ൌ ൌ െ‫ݑ‬ ‫ݑ‬ଵ ଵ ൬ ൬ ʹ ʹߨ ܶ ൰ ଶ ൬ ߨ ܶ଴ ଴ ܶ t ൰ ൰ ଶ ଶ ‫ݑ‬ ‫ݑ‬஼ ஼భ భ ֜ ֜ ࢊ ࢊ૛ ૛ ࢛ ࢛࡯૚ ࢊ࢚૛ o ൬ ൬ ʹߨ ܶ ܶ଴ ܶ u c ൰ ൰ ଶ ଶ ൌ ͳ ൌ ʹߨ ߨξ ξ‫ܮ‬ ‫ܮ‬ ξ ξ ξ ‫ܥ‬ ‫ܥ‬ e d ֜ ֜ ܶ଴ ܶ ଶ 3as.ency-education.com
15 1 10 12 ( ( ‫ܪ݌‬ ൌ ݂ሺܸ௕ሻ 13 ( ( ‫ܪ݌‬ா ൌ ͺǢܸா ൌ ʹͲ݉‫ܮ‬ 14 (1 ( ‫ܥ‬௔ ሺܵሻ ሺ ‫ܥ‬௔ܸ ௔ ൌ ‫ܥ‬௕ܸா ֜ ‫ܥ‬௔ ൌ ‫ܥ‬௕ܸா ܸ ௔ ൌ ͲǤͲͳ ൈ ʹͲ ʹͲ ൌ ͲǤͲͳ݉‫݈݋‬Ȁ‫ܮ‬ 15 ( ( ሺܵሻ ݉ ൌ ‫ܯܸܥ‬ ൌ ͲǤͲͳ ൈ ͲǤͷ ൈ ͸Ͳ ൌ ͲǤ͵݃ - ݉଴ ൌ ݉ ݉ . - 16 ( ( ‫ܽܭ݌‬ ൌ ͶǤͺ 17 ( ( ‫ܪ݌‬ா ൐ ͹ ‫݌‬ 18 ( ( ‫ܪ݌‬ ‫݌‬ III . ( ‫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 e n c y - e d u c a t i o n . c o m / e x a m s ݉‫ܮ‬ ݉‫ܮ‬ ‫ܥ‬ ‫ܥ‬௔ ‫ܥ‬ ሻ ൌ ͲǤͲͳ Ͳͳ݉‫݈݋‬ ݉‫݈݋‬Ȁ Ȁ‫ܮ‬ ሺ ሺܵ ܵሻ ͷ ൈ ͸Ͳ Ͳ ൌ Ͳ ͲǤ Ǥ͵݃ ‫ܥ‬ ‫ܥ‬‫ܪ‬ ‫ܪ‬ଷ ଷ‫ܪܱܱܥ‬ ‫ܪܱܱܥ‬ ൅ ‫ܥ‬ ‫ܥ‬‫ܪ‬ ‫ܪ‬ଷ‫ܪܱܱܥ‬ ‫ܥ‬ y y - e y ݊଴ y y c y ݊ ݊଴ ଴ c y c y c y ݊ c y c y c y 3as.ency-education.com
16 1 10 ݇ ൌ ‫ݔ‬௙ ଶ ൫݊଴ െ ‫ݔ‬௙൯൫݊ଵ െ ‫ݔ‬௙൯ ֜ ʹǤʹͷ ൌ ͳǤʹଶ ሺʹ െ ͳǤʹሻሺ݊ଵ െ ͳǤʹሻ ֜ 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 ( ͸͹Ψ ( ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ ͳǤʹ ͳǤʹ ͲǤͺ ͲǤͺ ݊ ൌ ଵ଴ ଵ଼ ൌ ͲǤͷͷ ݊ ൌ ଷ଻ ଻ସ ൌ ͲǤͷ ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ ͳǤʹ ൅ ͲǤͷͷ ͳǤʹ ͲǤͺ ൅ ͲǤͷ ͲǤͺ ܳ‫ݎ‬௜ ൌ ͳǤʹ ൈ ͳǤ͹ͷ ͲǤͺ ൈ ͳǤ͵ ൌ ʹǤͲͳ ൏ ݇ e n c y - e d u c a t i o n . c o m / e x a m s ‫ܪ‬ଷ ൈ ൈ ͳͲͲ ͲͲ ൌ ൌ ͸ͲΨ ͸ͲΨ ͸͹Ψ ͸͹ ͸ ͸ ‫ܥ‬ ‫ܥ‬‫ܪ‬ ‫ܪ‬ଷ ଷ‫ܪܱܱܥ‬ ‫ܥ‬ ൅ - e y ͲǤͺ y y c y c y c y 3as.ency-education.com
17 1 10 14 04 ‫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 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
18 1 10 ߬ ൌ ܴ‫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 6 - 7 - 8 - 9 - - 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 - ܲ‫ݑ‬ ଽସ ଶଷଽ ଶ ܶ݁ ହଶ ଵଷହ . ‫ܧ‬௟ ‫ܣ‬ ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ൌ ͹Ǥͷͺ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ 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 3as.ency-education.com
19 1 10 ‫ܧ‬௟ ‫ܣ‬ ሺ ܶ݁ ହଶ ଵଷହ ሻ ൌ ͺǤ͵Ͷ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ܶ݁ ହଶ ଵଷହ - ‫ܸ݁ܯ‬ ‫ܧ‬௟௜௕ ൌ ο݉ଷ‫ܥ‬ଶ ൌ ͲǤʹͲͳ͵ͺ ൈ ͻ͵ͳǤͷ ൌ ͳͺ͹Ǥͷͺ‫ܸ݁ܯ‬ ൌ ͵ ൈ ͳͲିଵଵ ݆ - 10 - ‫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 6 4 ( σ ‫ܨ‬ Ԧ ൌ Ͳ ሬԦ֜ ܲ ሬԦ ൅ ܴ ሬԦ ൅ ‫ܨ‬ Ԧ ൌ Ͳ ሬԦ ݉݃‫ߙ݊݅ݏ‬ െ ݇‫ݔ‬଴ ൌ Ͳ ֜ ‫ݔ‬଴ ൌ ݃‫ߙ݊݅ݏ‬ ݇ ݉ 5 ( ( ‫ݔ‬଴ ൌ ݂ሺ݉ሻ . ( ݇ ݇ ‫ݔ‬଴ ൌ ܽ݉ ܽ ൌ ͲǤͲ͸ െ Ͳ ͲǤ͵ െ Ͳ ൌ ͲǤʹ ‫ݔ‬଴ ൌ ʹͲ݉ ݃‫ߙ݊݅ݏ‬ ݇ ൌ ʹͲ ֜ ݇ ൌ ݃‫ߙ݊݅ݏ‬ ʹͲ ൌ ͳͲ‫Ͳ͵݊݅ݏ‬ ͲǤʹ ൌ ʹͷܰȀ݉ III . 4 ( ‫ݔ‬ሺ‫ݐ‬ሻ σ ‫ܨ‬ Ԧ ൌ ݉ܽ Ԧ ֜ ܲ ሬԦ ൅ ܴ ሬԦ ൅ ‫ܨ‬ Ԧ ൌ ݉ܽ Ԧ ݉݃‫ߙ݊݅ݏ‬ െ ݇ሺ‫ݔ‬଴ ൅ ‫ݔ‬ሻ ൌ ݉ܽ ֜ ݉݃‫ߙ݊݅ݏ‬ െ ݇‫ݔ‬଴ െ ݇‫ݔ‬ ൌ ݉ܽ ֜ െ݇‫ݔ‬ ൌ ݉ܽ 0 1 2 3 4 5 6 7 0 100 200 300 400 e n c e n c y - e d u c c y - e d u c y - e d u n n c c y - e d d u c a t i o n . c o m / e x a m s - 10 10 - - - ͸ͲͲ ൈ ൈ ʹ͵ͻ ʹ͵ͻ ൈ ͵ ͵ ൈ ൈ ͳͲ ͳͲିଵଵ ଵଵ m / ൌ ͳͺ σ ‫ܨ‬ Ԧ ൌ Ͳ Ͳ ሬ ሬԦ ሬ ֜ ֜ ܲ ሬԦ ሬ ൅ ݉݃‫ߙ݊݅ݏ‬ ݉݃‫ߙ݊݅ݏ‬ െ ݇ 0 1 e n c y - e d u c 3as.ency-education.com
20 2 10 ֜ െ݇‫ݔ‬ ൌ ݉ ݀ଶ ‫ݔ‬ ݀‫ݐ‬ଶ ֜ ࢊ૛ ࢞ ࢊ࢚૛ ൅ ࢑ ࢓ ࢞ ൌ ૙ 5 ( ߱଴ ‫ݔ‬ሺ‫ݐ‬ሻ ൌ ܺ௠ …‘•ሺ߱଴‫ݐ‬ ൅ ߮ሻ ֜ ݀ଶ ‫ݔ‬ ݀‫ݐ‬ଶ ൌ െܺ௠ ߱଴ ଶ …‘•ሺ߱଴‫ݐ‬ ൅ ߮ሻ ֜ ࢊ૛ ࢞ ࢊ࢚૛ ൌ െ࣓૙ ૛ ࢞ ֜ ߱଴ ଶ ൌ ௞ ௠ ֜ ߱଴ ൌ ට ௞ ௠ 3 - ܶ଴ ൌ ͲǤͶ‫ݏ‬ ߱଴ ൌ ଶగ ்బ ൌ ͷߨ‫݀ܽݎ‬Ȁ݀ ‫ܧ‬௉ா೘ೌೣ ൌ ͳǤʹͷ݆ ܺ௠ ‫ܧ‬௉ா೘ೌೣ ൌ ଵ ଶ ݇ܺ௠ ଶ ֜ ܺ௠ ൌ ට ଶாುಶ೘ೌೣ ௞ ൌ ට ଶൈଵǤଶହ ଶହ ൌ ͲǤ͵ͳ͸݉ ݉଴ ߱଴ ଶ ൌ ݇ ݉ ֜ ݉ ൌ ݇ ߱଴ ଶ ൌ ʹͷ ሺͷߨሻଶ ൌ ͲǤͳ݇݃ ‫ݐ‬ ൌ Ͳ ֜ ‫ݔ‬ ൌ ܺ௠ ֜ ܿ‫߮ݏ݋‬ ൌ ͳ ֜ ߮ ൌ Ͳ ‫ݔ‬ሺ‫ݐ‬ሻ ൌ ܺ௠ …‘•ሺ߱଴‫ݐ‬ ൅ ߮ሻ ֜ ‫ݔ‬ሺ‫ݐ‬ሻ ൌ ͲǤ͵ͳ͸ …‘•ሺͷߨ‫ݐ‬ሻ ‫ݔ‬଴ ‫ݔ‬ ‫ݔ‬଴ ൌ ʹܿ݉ 6 6 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 e n c y - e d u c a t i o n . c o m / e x a m s 3 3 - ʹͷ݆ ͷ ܺ௠ ܺ ܺ ൌ ͲǤ͵ͳ͸ ͳ͸݉ ݉ ൌ ͲǤͳ ͳ݇݃ ݇݃ ֜ ܿ‫ݏ݋‬ ‫߮ݏ݋‬ ߮ ൌ ͳ ͳ ֜ ߮ ൅ ߮ሻ ֜ ֜ ‫ݔ‬ ‫ݔ‬ሺ‫ݐ‬ ‫ݐ‬ሻ ሻ ൌ ൌ Ͳ ͵ ‫ݔ‬଴ ʹ ʹ‫݈ܣ‬ ‫݈ܣ‬ሺ௦ሻ ൅ e y ݊ଵ y y - c y ݊ଵ ଵ െ c y c y c y ݊ c c c 3as.ency-education.com
21 2 10 ‫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 ‫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 - - ݉݅݊ ݊ m ൌ ͳͲ ͳͲ݉݅݊ ݉݅݊ ͷ ൈ ͳͲ ͳͲି ିହ ହ ݉‫݈݋‬ ݉‫݈݋‬Ȁ Ȁ݉݅ ሺ ሺܰܽ ܰܽା ା ൅ ൅ ‫ܱܪ‬ ‫ܱܪ‬ି ሻ ‫ܪ‬ ‫ܪ‬ଷ ଷܱ ܱା ା ൅ ൅ ‫ܱܪ‬ ‫ܱܪ‬ି ൌ ‫ܭ‬ ‫ܭ‬ ൌ ൌ ͳ ሾ ሾ‫ܪ‬ ‫ܪ‬ଷܱ c ݊ 3as.ency-education.com

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  • 1. 1 1 10 2019 04 0 ‫ﺩ‬ 05 0 01 0 10 1 05 0 10 ( 14 04 ͳ‫ݑ‬ ൌ ͻ͵ͳǤͷ‫ܸ݁ܯ‬Ȁ‫ܥ‬ʹ Ǣܰ‫ܣ‬ ൌ ͸ǤͲʹ ൈ ͳͲʹ͵ ݉‫݈݋‬െͳ 14 13 ݉଴ ݉ 1 1 1 ( 13 1 - ܰ ଻ ଵଷ ଵ 2 ( ‫ܣ‬ ‫ݐ‬ ‫ܣ‬଴ ‫ܣ‬ λ 2 2 ‫ܣ‬଴ ‫ܣ‬ λ ‫ݐ‬భ మ 13 1 ݉଴ 3 ( 13 16 ܱ ଼ ଵ଺ ൅ ‫ܪ‬ ଵ ଵ ՜ ܺ ௓ ஺ ൅ ܰ ଻ ଵଷ - ܺ ௓ ஺ - - ܰ ଻ ଵଷ ܱ ଼ ଵ଺ ܺ ௓ ஺ ‫ܪ‬ ଵ ଵ ݊ ଴ ଵ ܺ ௓ ஺ ‫ܥ‬ ଺ ଵଷ ܰ ଻ ଵଷ ܱ ଼ ଵ଺ ͳǤͲͲ͹͵ ͳǤͲͲͺ͸ ͶǤͲͲͳͷ ͳ͵ǤͲͲͲͳ ͳ͵ǤͲͲͳͻ ͳͷǤͻͻͲͷ ݉ሺ‫ݑ‬ሻ 1 e n c y - e d u c a t i o n . c o m / e x a m s 14 14 04 ܰ‫ܣ‬ ‫ܣ‬ ൌ ൌ ͸ǤͲʹ Ͳʹ ൈ ͳ 14 14 ଵ ܺ ܺ ௓ ௓ ஺ ஺ o o o o Ͷ ͶǤͲͲͳͷ ͲͲͳ ͲͲͳ c n n n n c s m s s c y 1 3as.ency-education.com
  • 2. 2 2 10 2019 04 ሺܵሻ ݉ ൌ ʹͲͲ݃ ݉ ‫ܣ‬ ‫ܣ‬ Ƚ ‫ݒ‬஺ ‫ݒ‬ ሺܵሻ ሺ‫ܤܣ‬ሻ ݂ ൌ ͲǤͺܰ ݂ ‫ܤ‬ ‫ܦ‬ ‫ܦ‬ 2 2 ݃ ൌ ͻǤͺ݉Ȁ‫ݏ‬ଶ ‫ܤܣ‬ ൌ ͳǤʹ݉ ‫ܣ‬ 1 ( ሺ࡭࡮ሻ ሺ - ሺܵሻ - - ‫ݐ‬ ൌ Ͳ ሺܵሻ ‫ܣ‬ ‫ܣ‬ - ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ . 2 ( ࡮ ‫ݐ‬ ൌ Ͳ ‫ܤ‬ ‫ܤ‬ ሺܵሻ ሺ‫ݔܤ‬ǡ ‫ݕܤ‬ሻ 3 4 4 - ሺ‫ݔܤ‬ሻ ሺ‫ݕܤ‬ሻ - - ‫ݒ‬஻௫ ሺ‫ݔܤ‬ሻ ሺ ‫ݒ‬஻௬ ‫ݒ‬ ሺ‫ݕܤ‬ሻ Ƚ Ƚ ‫ݒ‬஻ ‫ܤ‬ - ‫ܦܣ‬ . 3 ( ܽ ܽ ሺܵሻ ሺ‫ܤܣ‬ሻ ‫ݒ‬஺ . 2 3 4 e n c c a t i o n . c o m / e x a m s ‫ܤ‬ 1 1 ( ( - ‫ݐ‬ ‫ݐ‬ ‫ݒ‬஻ ଶ ଶ െ െ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݒ‬ ଶ ൌ ʹܽ . ࡮ ࡮ 3as.ency-education.com
  • 3. 3 3 10 2019 06 5 - ‫ܧ‬ - ܴ ൌ ͳ݇ȳ . - ‫ܥ‬ଵ ‫ܥ‬ ‫ܥ‬ଶ - ‫ܮ‬ ‫ܮ‬ ‫ܭ‬ ‫ܭ‬ ‫ݐ‬ ൌ Ͳ ሺͳሻ ሺ ‫ݑ‬஼భ ሺ‫ݐ‬ሻ ‫ݑ‬ ‫ݑ‬஼మ ሺ‫ݐ‬ሻ ‫ݑ‬ 6 ଵ ஼೐ ൌ ଵ ஼భ ൅ ଵ ஼మ ‫ݍ‬ ൌ ‫ݍ‬ଵ ൌ ‫ݍ‬ଶ ‫ݍ‬ ‫ݍ‬ ‫ܥ‬௘ 1 ( ‫ݍ‬ ‫ݍ‬ ൌ ‫ܥܧ‬௘ ቀͳ െ ݁ି ೟ ഓቁ ‫ݑ‬஼భ ሺ‫ݐ‬ሻ ‫ݑ‬ ‫ݑ‬஼మ ሺ‫ݐ‬ሻ 2 ( 6 6 ߬ ‫ܧ‬ ‫ܥ‬௘ 3 ( ‫ܥ‬ଵ ‫ܥ‬ ‫ܥ‬ଶ ‫ܥ‬ 4 ( ‫ݑ‬஼భ ൌ ‫ݑ‬ோ ‫ݐ‬ ൌ ߬ ݈݊ ͵Ǥͷ 5 ( 5 6 e n c y - e d u c a t i o n . c o m / e x a m s - - - Ͳ ‫ݍ‬ ‫ݍ‬ ‫ݍ‬ ‫ݍ‬ a 3as.ency-education.com
  • 4. 4 4 10 2019 ሺʹሻ ሺ 1 ( ‫ݑ‬஼భ ‫ݑ‬ 2 ( ‫ݑ‬஼భ ൌ ‫ݑ‬ଵ …‘• ቀ ଶగ ்బ ‫ݐ‬ ൅ ߮ቁ ‫ݑ‬ ‫ݑ‬ଵ ‫ݑ‬ ‫ܥ‬ଵ ‫ܥ‬ ‫ݐ‬ ൒ ͳǤʹ‫ݏ‬ . . ܶ଴ 3 ( 6 ܶ଴ ܶ ‫ܮ‬ 6 6 I . ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ݉଴ ൌ ͲǤ͵݃ ݉ ͷͲͲ݉‫ܮ‬ ሺܵሻ . ܸ ௔ ൌ ʹͲ݉‫ܮ‬ ሺܵሻ ͺͲ݉‫ܮ‬ ሺܰܽା ൅ ‫ܱܪ‬ିሻ ‫ܥ‬௕ ൌ ͲǤͲͳ݉‫݈݋‬Ȁ‫ܮ‬ ʹͷԨ ʹ 1 ( 2 ( 3 ( ‫ܪ݌‬ ൌ ݂ሺܸ௕ሻ ‫݌‬ 4 ( 5 ( ‫ܥ‬௔ ሺܵሻ 6 ( ሺܵሻ ݉଴ ݉ 7 ( ‫ܽܭ݌‬ ሺ‫ܪܥ‬ଷ‫ܪܱܱܥ‬Ȁ‫ܪܥ‬ଷ‫ܱܱܥ‬ିሻ 8 ( 9 ( ‫ܪ݌‬ ‫݌‬ II . ͳͶͺ݃ ͳ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ͳʹͲ‰ ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ 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݌‬ e n c y - e d u c a t i o n . c o m / e x a m s ( 3 3 ( ( 6 6 6 ‫ܪܱܱܥ‬ ܱܱ‫ܪ‬ ͷͲͲ Ͳ݉‫ܮ‬ ݉‫ܮ‬ ܸ ௔ ௔ ܸ ൌ ൌ ʹͲ ʹͲ݉‫ܮ‬ ݉ ܸ ሺ ሺܰܽ ܰܽା ା ൅ ‫ܱܪ‬ ‫ܪ‬ ିሻ ‫ܥ‬ 19.5 19 19 9 18 8 n n n n n . o o n n 6 6.0 6 0 5.7 5.7 5.2 5. o o o n o n o n n n t t i o t i o t i o t i o o n o o n 3as.ency-education.com
  • 5. 5 5 10 2019 ( ( ‫ݔ‬௙ ( ( ( ( ( ( ( ( ͳͲ݃ ͵͹݃ ‫ܯ‬ሺ‫ܪ‬ሻ ൌ ͳ ݃ ݉‫݈݋‬ Τ ‫ܯ‬ ‫ܯ‬ሺܱሻ ൌ ͳ͸ ݃ ݉‫݈݋‬ Τ ‫ܯ‬ሺ‫ܥ‬ሻ ൌ ͳʹ ݃ ݉‫݈݋‬ Τ 8 e n c y - e d u c a t i o n . c o m / e x a m s ( ( ( ( ( ( ( ( ( ͳͲ ͳͲ݃ ͳ ͳ ݃ ‫ܯ‬ሺ ‫ܯ‬ ʹ ݃ ݉‫݈݋‬ ݉‫݈݋‬ Τ Τ 3as.ency-education.com
  • 6. 6 6 10 2019 05 0 6 0 0 10 1 10 1 10 ( 14 04 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 4 ( ‫ݑ‬ோሺ‫ݐ‬ሻ ௨಴ ௨ೃ ൌ ݁ ೟ ഓ െ ͳ 5 ( 2 2 3 3 ‫ܧ‬ ܴ ߬ ߬ ‫ܥ‬ ‫ܥ‬ 1 2 3 e n c y - e d u c 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
  • 7. 7 7 10 2019 ‫ݐ‬ ൌ Ͳ ሺʹሻ 4 4 1 ( 2 ( ‫ݍ‬ሺ‫ݐ‬ሻ ( ܶ ൎ ʹߨξ‫ܥܮ‬ ܶ ‫ܮ‬ ( ( ‫ݐ‬ ൌ ܶ ‫ݐ‬ ( ‫ܫ‬଴ 04 ܲ‫ݑ‬ ଽସ ଶଷଽ ൅ ݊ ଴ ଵ ՜ ‫݋ܯ‬ ସଶ ଵ଴ଶ ൅ ܶ݁ ହଶ ଵଷହ ൅ ͵ ݊ ଴ ଵ 1 - 2 - 3 - 4 - 5 - ο݉ଵ ο ο݉ଶ ο ο݉ଷ 5 4 e n c y - e d u c a t i o n . c o m ‫ݍ‬ሺ‫ݐ‬ ‫ݐ‬ሻ ሻ ܲ ଽସ ଶଷଽ ଶ x a m s 3as.ency-education.com
  • 8. 8 8 10 2019 - - ‫ܧ‬௟ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ܲ‫ݑ‬ ଽସ ଶଷଽ ଶ ܶ݁ ହଶ ଵଷହ . - ‫ܸ݁ܯ‬ - 5 - ܲ ൌ ͵ ൈ 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 6 ݇ ‫ܣ‬ ‫ܣ‬ Ƚ ൌ ͵Ͳι ሺܵሻ ‫ݔ‬଴ I . 1 ( ሺܵሻ 6 2 ( ‫ݔ‬଴ ‫ݔ‬ ‫ݔ‬଴ ൌ ௚௦௜௡ఈ ௞ ݉ 3 ( ሺܵሻ 300 225 150 75 ݉ሺ‰ሻ 6 4.5 3 1.5 ‫ݔ‬଴ሺܿ݉ሻ ( ‫ݔ‬଴ ൌ ݂ሺ݉ሻ . ( ( ݇ ݇ II . ሺܵሻ ݉଴ ሺܵሻ ܺ௠ ܺ ‫ݐ‬ ൌ Ͳ . 1 ( ‫ݔ‬ሺ‫ݐ‬ሻ 2 ( ‫ݔ‬ሺ‫ݐ‬ሻ ൌ ܺ௠ …‘•ሺ߱଴‫ݐ‬ ൅ ߮ሻ ߱଴ 6 e n c y - e d u c a t i o n . c o m / e x a m s 5 5 - - ܹ - ܶ݁ ݁ ହଶ ହଶ ൯ ൯ ൌ ൌ ͳͳʹ͸ ͳʹ Ǥͻ͸ 6 6 6 ‫ݔ‬ ‫ݔ‬଴ ଴ ൌ ൌ ௚௦௜௡ఈ ௚ a ‫ݔ‬ u u u 3as.ency-education.com
  • 9. 9 9 10 2019 ( ‫ܧ‬௉ா ሺܵሻ ሺ ‫ݐ‬ ‫ݐ‬ 7 7 ( ܶ଴ ܶ ߱଴ ‫ܧ‬௉ா೘ೌೣ ܺ௠ ܺ ݉଴ ( ‫ݔ‬ሺ‫ݐ‬ሻ ( ( ‫ݔ‬଴ ݃ ൌ ͳͲ݉Ȁ‫ݏ‬ଶ 6 6 I . ݉଴ ൌ ͲǤ͵݃ ‫݈ܣ‬ ‫ܣ‬ ܸ ൌ ʹͲͲ݉‫ܮ‬ ܸ ሺ‫ܪ‬ଷܱା ൅ ‫݈ܥ‬ିሻ ܿ ൌ ͲǤʹ ݉‫݈݋‬ ݈ Τ ܸுమ ൌ ݂ሺ‫ݐ‬ሻ ܸ ʹ‫݈ܣ‬ሺ௦ሻ ൅ ͸‫ܪ‬ଷܱା ሺ௔௤ሻ ൌ ʹ‫݈ܣ‬ଷା ሺ௔௤ሻ ൅ ͵‫ܪ‬ଶሺ௚ሻ ൅ ͸‫ܪ‬ଶܱሺ௟ሻ - ሺܱ‫ݔ‬ ܴ݁݀ Τ ሻ - ‫ݔ‬௠௔௫ ‫ܪ‬ଷܱା - - - ‫ݐ‬ଵ ଶ Τ 7 8 ૢ૙ ݉଴ ‫ݔ‬ ‫ݔ‬଴ ‫ݔ‬ ‫ݔ‬ ͳͲ݉Ȁ Ȁ‫ݏ‬ ‫ݏ‬ଶ ଶ ܿ ܿ ൌ ൌ Ͳ ͲǤʹ ʹ ݉‫݋‬ ʹ‫݈ܣ‬ ‫݈ܣ‬ሺ ሺ௦ሻ ൅ ൅ ͸‫ܪ‬ଷܱ 3as.ency-education.com
  • 10. 10 1 10 2019 - ‫ݐ‬ ‫ݐ‬ ‫ݒ‬ ൌ ଵ ଷ௏ಾ ൈ ௗ௏ಹమ ሺ௧ሻ ௗ௧ ‫ݐ‬ ൌ ͳͲ݉݅݊ II . ܸ ௔ ൌ ʹͲ݉‫ܮ‬ ሺܰܽା ൅ ‫ܱܪ‬ି ሻ ‫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 9 e n c y - e d u c a t i o n . c o m / e x a m s ൌ ʹͲ ʹͲ݉‫ܮ‬ ݉‫ܮ‬ ͲǤͲͳ Ͳͳ ݉‫݈݋‬ ݉‫݈݋‬ ‫ܮ‬ Τ Τ ܸ ܸெ ெ ܸ ܸ ܸ ൌ ʹ ܸ ܸ Ͳିଵସ ସ 3as.ency-education.com
  • 11. 11 1 10 04 4 ( α β γ γ 13 1 ߚା ߚ ‫݌‬ ଵ ଵ ՜ ݊ ଴ ଵ ൅ ݁ ାଵ ଴ ܰ ଻ ଵଷ ՜ ܺ ௓ ஺ ൅ ݁ ଵ ଴ ͳ͵ ൌ ‫ܣ‬ ͹ ൌ ܼ ൅ ͳ ֜ ܼ ൌ ͸ ܰ ଻ ଵଷ ՜ ‫ܥ‬ ଺ ଵଷ ൅ ݁ ାଵ ଴ 5 ( ‫ܣ‬ሺ‫ݐ‬ሻ ൌ ‫ܣ‬଴݁ିఒ௧ . Ž ‫ܣ‬ ൌ ܽ‫ݐ‬ ൅ ܾ ܽ ൌ ʹͳǤ͸ െ ͵ʹ ͳͷͲ െ Ͳ ൌ െͲǤͲ͸ͻ͵݉݅݊ିଵ ܾ ൌ ͵ʹ Ž ‫ܣ‬ ൌ െͲǤͲ͸ͻ͵‫ݐ‬ ൅ ͵ʹ ‫ܣ‬ሺ‫ݐ‬ሻ ൌ ‫ܣ‬଴݁ିఒ௧ ֜ Ž ‫ܣ‬ ൌ െߣ‫ݐ‬ ൅ Ž ‫ܣ‬଴ 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଺ ݃ 6 ( 13 16 ܱ ଼ ଵ଺ ൅ ‫ܪ‬ ଵ ଵ ՜ ܺ ௓ ஺ ൅ ܰ ଻ ଵଷ - ͳ͸ ൅ ͳ ൌ ‫ܣ‬ ൅ ͳ͵ ֜ ‫ܣ‬ ൌ Ͷ ͺ ൅ ͳ ൌ ܼ ൅ ͹ ֜ ܼ ൌ ʹ ܺ ௓ ஺ ௓ ஺ ‫݁ܪ‬ ଶ ସ - ܺ ௓ ஺ ܰ ଻ ଵଷ ܱ ଼ ଵ଺ ‫ܧ‬௟ ൌ ቀܼ݉௣ ൅ ሺ‫ܣ‬ െ ܼሻ݉௡ െ ݉ ௑ ೋ ಲ ቁ ‫ܥ‬ଶ ‫ܧ‬௟ሺ ܺ ௓ ஺ ሻ ൌ ሺʹ ൈ ͳǤͲͲ͹͵ ൅ ʹ ൈ ͳǤͲͲͺ͸ െ ͶǤͲͲͳͷሻ ൈ ͻ͵ͳǤͷ ൌ ʹͺǤʹʹ‫ܸ݁ܯ‬ ‫ܧ‬௟ሺ ܰ ଻ ଵଷ ሻ ൌ ሺ͹ ൈ ͳǤͲͲ͹͵ ൅ ͸ ൈ ͳǤͲͲͺ͸ െ ͳ͵ǤͲͲͳͻሻ ൈ ͻ͵ͳǤͷ ൌ ͻ͵Ǥͺͻ‫ܸ݁ܯ‬ ‫ܧ‬௟ሺ ܱ ଼ ଵ଺ ሻ ൌ ሺͺ ൈ ͳǤͲͲ͹͵ ൅ ͺ ൈ ͳǤͲͲͺ͸ െ ͳͷǤͻͻͲͷሻ ൈ ͻ͵ͳǤͷ ൌ ͳʹ͹Ǥ͵͵‫ܸ݁ܯ‬ e n c y - e d u c a t i o n . c o m / e x a m s ‫ܣ‬ ‫ܣ‬଴݁ି ିఒ ఒ௧ ௧ ͵݉݅݊ ݊ି ିଵ ଵ ͻ͵‫ݐ‬ ൅ ͵ʹ ͵ʹ ఒ௧ ֜ ֜ Ž Ž ‫ܣ‬ ‫ܣ‬ ൌ ൌ െߣ‫ݐ‬ ߣ ߣ ൌ ൌ െ െͲ ͲǤ ǤͲ͸ͻ͵ Ͳ͸ ‫ܣ‬଴ ൌ ͵ʹ ͵ʹ ֜ ֜ ‫ܣ‬ ‫ܣ‬଴ ଴ ൌ ݁ ߣ ݉ ݉଴ܰ ܰ஺ ஺ ܰ ܰ ‫ܯ‬ ‫ܯ‬ d u ֜ ֜ ݉ ݉଴ ൌ ‫ܣ‬ 3as.ency-education.com
  • 12. 12 1 10 ‫ܧ‬௟ ‫ܣ‬ ሺ ܺ ௓ ஺ ሻ ൌ ͹ǤͲͷ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ‫ܧ‬௟ ‫ܣ‬ ሺ ܰ ଻ ଵଷ ሻ ൌ ͹Ǥʹʹ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ‫ܧ‬௟ ‫ܣ‬ ሺ ܱ ଼ ଵ଺ ሻ ൌ ͹Ǥͻͷ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ܱ ଼ ଵ଺ 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 ֜ ‫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 - ‫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 2 e n c y - e d u c a t i o n . c o m / e x a m s 4 4 ( ( - ܲ ൅ ܴ ܴ ሬԦ ሬ ൅ ൅ ݂ ݂ Ԧ ൌ ൌ ݉ ݉ܽ Ԧ ֜ ܽ ܽ ൌ ൌ െ െ݃‫ߙ݊݅ݏ‬ ݃‫݊݅ݏ‬ െ ݂ ‫ݒ‬஺ ‫ݒ‬ ʹ ‫ݐ‬ଶ ൅ ൅ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݐ‬ ‫ݒ‬ ܽ‫ݐ‬ ‫ݐ‬ ൅ ൅ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݒ‬ ֜ ֜ ‫ݐ‬ ‫ݐ‬ ൌ ൌ ‫ݒ‬ െ o ൅ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݒ‬ ‫ݐ‬ ֜ ֜ ‫ݔ‬ ‫ݔ‬ ൌ ܽ ܽ ʹ ቀ ‫ݒ‬ െ ʹ‫ݒ‬ ‫ݒ‬‫ݒ‬ ‫ݒ‬஺ ‫ݒ‬ ܽଶ u c ൅ ൅ ‫ݒ‬ ‫ݒ‬‫ݒ‬ ‫ݒ‬஺ ‫ݒ‬ െ c ֜ ‫ݔ‬ ൌ ൌ ‫ݒ‬ ‫ݒ‬ଶ ଶ െ െ ‫ݒ‬ ‫ݒ‬஺ ஺ ‫ݒ‬ ‫ݒ‬ ଶ ଶ ʹ ʹܽ d u ֜ 3as.ency-education.com
  • 13. 13 1 10 - ‫ܦܣ‬ ‫ܣ‬ ‫ܦܣ‬ ൌ ‫ߙ݊݅ݏܤܣ‬ ൅ ‫ݔ‬ ൌ ͳǤʹ ൈ ‫Ͳʹ݊݅ݏ‬ ൅ ͲǤͺ ൌ ͳǤʹͳ݉ 6 ( ܽ ܽ ሺܵሻ ሺ‫ܤܣ‬ሻ ‫ݒ‬஺ . ܽ ൌ െ݃‫ߙ݊݅ݏ‬ െ ݂ ݉ ൌ െͻǤͺ ൈ ‫Ͳʹ݊݅ݏ‬ െ ͲǤͺ ͲǤʹ ൌ െ͹Ǥ͵ͷ݉Ȁ‫ݏ‬ଶ ‫ݒ‬஻ ଶ െ ‫ݒ‬஺ ଶ ൌ ʹܽ ൈ ‫ܤܣ‬ ֜ ‫ݒ‬஻ ଶ െ ʹܽ ൈ ‫ܤܣ‬ ൌ ‫ݒ‬஺ ଶ ֜ ‫ݒ‬஺ ଶ ൌ ʹǤͷଶ ൅ ʹ ൈ ͹Ǥ͵ͷ ൈ ͳǤʹ ֜ ‫ݒ‬஺ ൌ ͶǤͺͺ݉Ȁ‫ݏ‬ 06 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 ‫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 ( e n c y - e d u c a t i o n . c o m / e x a m s 6 ( ܴ ݀‫ݍ‬ ݀‫ݐ‬ ‫ݐ‬ x ൅ ൅ ‫ݍ‬ ‫ݍ‬ ͳ ͳ ‫ܥ‬ ‫ܥ‬௘ ௘ ‫ܥ‬ ‫ܥ‬ x a ൌ ൌ ‫ܧ‬ ൰ ݁ ௧ ఛ ௘ ߬ n ݁ ݁ି ௧ ఛ ఛ n ൅ ൅ ‫ܥܧ‬ ‫ܥ‬௘ ‫ܥ‬ ൬ ൬ͳ ௘ ௘ െ ‫ܧ‬ ‫ܧ‬‫ܥ‬ ‫ܥ‬௘ ‫ܥ‬ ݁ ݁ି ି ௧ ௧ ఛ ఛ o n ൌ ൌ ‫ܥܧ‬ ‫ݑ‬஼భ ൌ ൌ ‫ݍ‬ ‫ݍ‬ଵ ଵ ‫ܥ‬ ‫ܥ‬ଵ ଵ ‫ܥ‬ a t ൌ ൌ ‫ݍ‬ ‫ݍ‬ ‫ܥ‬ଵ ‫ܥ‬ t ൌ ‫ܧ‬ ‫ݑ‬ ‫ݑ‬஼ ஼మ మ ൌ ൌ ‫ݍ‬ ‫ݍ‬ଶ ‫ܥ‬ c ൌ 3as.ency-education.com
  • 14. 14 1 10 ‫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 ܶ଴ ൌ ʹߨξ‫ܥܮ‬ ֜ ܶ଴ ଶ ൌ Ͷߨଶ ‫ܥܮ‬ ֜ ‫ܮ‬ ൌ ܶ଴ ଶ Ͷߨଶ‫ܥ‬ ൌ ͲǤʹଶ Ͷߨଶ ൈ Ͷ ൈ ͳͲିସ ൌ ʹǤͷ͵‫ܪ‬ 10 ( ( 6 6 II . 10 ( ( ‫ܪ݌‬ ‫݌‬ - - 11 ( ( ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܱܪ‬ି ൌ ‫ܪܥ‬ଷ‫ܱܱܥ‬ି ൅ ‫ܪ‬ଶܱ ሺ ሺʹ ʹሻ ሻ ‫ݑ‬஼భ ֜ ‫ܮ‬ ݀ଶ ൫ ൫‫ݑ‬ ‫ݑ‬஼భ ‫ܥ‬ ‫ܥ‬ଵ ଵ ‫ܥ‬ ‫ܥ‬ ‫ܥ‬ ൯ ൯ ݀ ݀‫ݐ‬ ‫ݐ‬ଶ ଶ m ൅ ‫ݑ‬ ൅ ૚ ૚ ࡸ ࡸ࡯ ࡯૚ ૚ c o ࢛࡯૚ ૚ ൌ ૙ ‫ݑ‬஼భ ݀ ݀‫ݐ‬ ‫ݐ‬ଶ ଶ o n ൌ ൌ െ‫ݑ‬ ‫ݑ‬ଵ ଵ ൬ ൬ ʹ ʹߨ ܶ ൰ ଶ ൬ ߨ ܶ଴ ଴ ܶ t ൰ ൰ ଶ ଶ ‫ݑ‬ ‫ݑ‬஼ ஼భ భ ֜ ֜ ࢊ ࢊ૛ ૛ ࢛ ࢛࡯૚ ࢊ࢚૛ o ൬ ൬ ʹߨ ܶ ܶ଴ ܶ u c ൰ ൰ ଶ ଶ ൌ ͳ ൌ ʹߨ ߨξ ξ‫ܮ‬ ‫ܮ‬ ξ ξ ξ ‫ܥ‬ ‫ܥ‬ e d ֜ ֜ ܶ଴ ܶ ଶ 3as.ency-education.com
  • 15. 15 1 10 12 ( ( ‫ܪ݌‬ ൌ ݂ሺܸ௕ሻ 13 ( ( ‫ܪ݌‬ா ൌ ͺǢܸா ൌ ʹͲ݉‫ܮ‬ 14 (1 ( ‫ܥ‬௔ ሺܵሻ ሺ ‫ܥ‬௔ܸ ௔ ൌ ‫ܥ‬௕ܸா ֜ ‫ܥ‬௔ ൌ ‫ܥ‬௕ܸா ܸ ௔ ൌ ͲǤͲͳ ൈ ʹͲ ʹͲ ൌ ͲǤͲͳ݉‫݈݋‬Ȁ‫ܮ‬ 15 ( ( ሺܵሻ ݉ ൌ ‫ܯܸܥ‬ ൌ ͲǤͲͳ ൈ ͲǤͷ ൈ ͸Ͳ ൌ ͲǤ͵݃ - ݉଴ ൌ ݉ ݉ . - 16 ( ( ‫ܽܭ݌‬ ൌ ͶǤͺ 17 ( ( ‫ܪ݌‬ா ൐ ͹ ‫݌‬ 18 ( ( ‫ܪ݌‬ ‫݌‬ III . ( ‫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 e n c y - e d u c a t i o n . c o m / e x a m s ݉‫ܮ‬ ݉‫ܮ‬ ‫ܥ‬ ‫ܥ‬௔ ‫ܥ‬ ሻ ൌ ͲǤͲͳ Ͳͳ݉‫݈݋‬ ݉‫݈݋‬Ȁ Ȁ‫ܮ‬ ሺ ሺܵ ܵሻ ͷ ൈ ͸Ͳ Ͳ ൌ Ͳ ͲǤ Ǥ͵݃ ‫ܥ‬ ‫ܥ‬‫ܪ‬ ‫ܪ‬ଷ ଷ‫ܪܱܱܥ‬ ‫ܪܱܱܥ‬ ൅ ‫ܥ‬ ‫ܥ‬‫ܪ‬ ‫ܪ‬ଷ‫ܪܱܱܥ‬ ‫ܥ‬ y y - e y ݊଴ y y c y ݊ ݊଴ ଴ c y c y c y ݊ c y c y c y 3as.ency-education.com
  • 16. 16 1 10 ݇ ൌ ‫ݔ‬௙ ଶ ൫݊଴ െ ‫ݔ‬௙൯൫݊ଵ െ ‫ݔ‬௙൯ ֜ ʹǤʹͷ ൌ ͳǤʹଶ ሺʹ െ ͳǤʹሻሺ݊ଵ െ ͳǤʹሻ ֜ 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 ( ͸͹Ψ ( ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ ͳǤʹ ͳǤʹ ͲǤͺ ͲǤͺ ݊ ൌ ଵ଴ ଵ଼ ൌ ͲǤͷͷ ݊ ൌ ଷ଻ ଻ସ ൌ ͲǤͷ ‫ܪܥ‬ଷ‫ܪܱܱܥ‬ ൅ ‫ܥ‬௡‫ܪ‬ଶ௡ାଵܱ‫ܪ‬ ൌ ‫ܪܥ‬ଷ‫ܥܱܱܥ‬௡‫ܪ‬ଶ௡ାଵ ൅ ‫ܪ‬ଶܱ ͳǤʹ ൅ ͲǤͷͷ ͳǤʹ ͲǤͺ ൅ ͲǤͷ ͲǤͺ ܳ‫ݎ‬௜ ൌ ͳǤʹ ൈ ͳǤ͹ͷ ͲǤͺ ൈ ͳǤ͵ ൌ ʹǤͲͳ ൏ ݇ e n c y - e d u c a t i o n . c o m / e x a m s ‫ܪ‬ଷ ൈ ൈ ͳͲͲ ͲͲ ൌ ൌ ͸ͲΨ ͸ͲΨ ͸͹Ψ ͸͹ ͸ ͸ ‫ܥ‬ ‫ܥ‬‫ܪ‬ ‫ܪ‬ଷ ଷ‫ܪܱܱܥ‬ ‫ܥ‬ ൅ - e y ͲǤͺ y y c y c y c y 3as.ency-education.com
  • 17. 17 1 10 14 04 ‫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 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
  • 18. 18 1 10 ߬ ൌ ܴ‫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 6 - 7 - 8 - 9 - - 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 - ܲ‫ݑ‬ ଽସ ଶଷଽ ଶ ܶ݁ ହଶ ଵଷହ . ‫ܧ‬௟ ‫ܣ‬ ሺ ܲ‫ݑ‬ ଽସ ଶଷଽ ሻ ൌ ͹Ǥͷͺ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ 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 3as.ency-education.com
  • 19. 19 1 10 ‫ܧ‬௟ ‫ܣ‬ ሺ ܶ݁ ହଶ ଵଷହ ሻ ൌ ͺǤ͵Ͷ‫ܸ݁ܯ‬Ȁ݊‫ܿݑ‬ ܶ݁ ହଶ ଵଷହ - ‫ܸ݁ܯ‬ ‫ܧ‬௟௜௕ ൌ ο݉ଷ‫ܥ‬ଶ ൌ ͲǤʹͲͳ͵ͺ ൈ ͻ͵ͳǤͷ ൌ ͳͺ͹Ǥͷͺ‫ܸ݁ܯ‬ ൌ ͵ ൈ ͳͲିଵଵ ݆ - 10 - ‫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 6 4 ( σ ‫ܨ‬ Ԧ ൌ Ͳ ሬԦ֜ ܲ ሬԦ ൅ ܴ ሬԦ ൅ ‫ܨ‬ Ԧ ൌ Ͳ ሬԦ ݉݃‫ߙ݊݅ݏ‬ െ ݇‫ݔ‬଴ ൌ Ͳ ֜ ‫ݔ‬଴ ൌ ݃‫ߙ݊݅ݏ‬ ݇ ݉ 5 ( ( ‫ݔ‬଴ ൌ ݂ሺ݉ሻ . ( ݇ ݇ ‫ݔ‬଴ ൌ ܽ݉ ܽ ൌ ͲǤͲ͸ െ Ͳ ͲǤ͵ െ Ͳ ൌ ͲǤʹ ‫ݔ‬଴ ൌ ʹͲ݉ ݃‫ߙ݊݅ݏ‬ ݇ ൌ ʹͲ ֜ ݇ ൌ ݃‫ߙ݊݅ݏ‬ ʹͲ ൌ ͳͲ‫Ͳ͵݊݅ݏ‬ ͲǤʹ ൌ ʹͷܰȀ݉ III . 4 ( ‫ݔ‬ሺ‫ݐ‬ሻ σ ‫ܨ‬ Ԧ ൌ ݉ܽ Ԧ ֜ ܲ ሬԦ ൅ ܴ ሬԦ ൅ ‫ܨ‬ Ԧ ൌ ݉ܽ Ԧ ݉݃‫ߙ݊݅ݏ‬ െ ݇ሺ‫ݔ‬଴ ൅ ‫ݔ‬ሻ ൌ ݉ܽ ֜ ݉݃‫ߙ݊݅ݏ‬ െ ݇‫ݔ‬଴ െ ݇‫ݔ‬ ൌ ݉ܽ ֜ െ݇‫ݔ‬ ൌ ݉ܽ 0 1 2 3 4 5 6 7 0 100 200 300 400 e n c e n c y - e d u c c y - e d u c y - e d u n n c c y - e d d u c a t i o n . c o m / e x a m s - 10 10 - - - ͸ͲͲ ൈ ൈ ʹ͵ͻ ʹ͵ͻ ൈ ͵ ͵ ൈ ൈ ͳͲ ͳͲିଵଵ ଵଵ m / ൌ ͳͺ σ ‫ܨ‬ Ԧ ൌ Ͳ Ͳ ሬ ሬԦ ሬ ֜ ֜ ܲ ሬԦ ሬ ൅ ݉݃‫ߙ݊݅ݏ‬ ݉݃‫ߙ݊݅ݏ‬ െ ݇ 0 1 e n c y - e d u c 3as.ency-education.com
  • 20. 20 2 10 ֜ െ݇‫ݔ‬ ൌ ݉ ݀ଶ ‫ݔ‬ ݀‫ݐ‬ଶ ֜ ࢊ૛ ࢞ ࢊ࢚૛ ൅ ࢑ ࢓ ࢞ ൌ ૙ 5 ( ߱଴ ‫ݔ‬ሺ‫ݐ‬ሻ ൌ ܺ௠ …‘•ሺ߱଴‫ݐ‬ ൅ ߮ሻ ֜ ݀ଶ ‫ݔ‬ ݀‫ݐ‬ଶ ൌ െܺ௠ ߱଴ ଶ …‘•ሺ߱଴‫ݐ‬ ൅ ߮ሻ ֜ ࢊ૛ ࢞ ࢊ࢚૛ ൌ െ࣓૙ ૛ ࢞ ֜ ߱଴ ଶ ൌ ௞ ௠ ֜ ߱଴ ൌ ට ௞ ௠ 3 - ܶ଴ ൌ ͲǤͶ‫ݏ‬ ߱଴ ൌ ଶగ ்బ ൌ ͷߨ‫݀ܽݎ‬Ȁ݀ ‫ܧ‬௉ா೘ೌೣ ൌ ͳǤʹͷ݆ ܺ௠ ‫ܧ‬௉ா೘ೌೣ ൌ ଵ ଶ ݇ܺ௠ ଶ ֜ ܺ௠ ൌ ට ଶாುಶ೘ೌೣ ௞ ൌ ට ଶൈଵǤଶହ ଶହ ൌ ͲǤ͵ͳ͸݉ ݉଴ ߱଴ ଶ ൌ ݇ ݉ ֜ ݉ ൌ ݇ ߱଴ ଶ ൌ ʹͷ ሺͷߨሻଶ ൌ ͲǤͳ݇݃ ‫ݐ‬ ൌ Ͳ ֜ ‫ݔ‬ ൌ ܺ௠ ֜ ܿ‫߮ݏ݋‬ ൌ ͳ ֜ ߮ ൌ Ͳ ‫ݔ‬ሺ‫ݐ‬ሻ ൌ ܺ௠ …‘•ሺ߱଴‫ݐ‬ ൅ ߮ሻ ֜ ‫ݔ‬ሺ‫ݐ‬ሻ ൌ ͲǤ͵ͳ͸ …‘•ሺͷߨ‫ݐ‬ሻ ‫ݔ‬଴ ‫ݔ‬ ‫ݔ‬଴ ൌ ʹܿ݉ 6 6 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 e n c y - e d u c a t i o n . c o m / e x a m s 3 3 - ʹͷ݆ ͷ ܺ௠ ܺ ܺ ൌ ͲǤ͵ͳ͸ ͳ͸݉ ݉ ൌ ͲǤͳ ͳ݇݃ ݇݃ ֜ ܿ‫ݏ݋‬ ‫߮ݏ݋‬ ߮ ൌ ͳ ͳ ֜ ߮ ൅ ߮ሻ ֜ ֜ ‫ݔ‬ ‫ݔ‬ሺ‫ݐ‬ ‫ݐ‬ሻ ሻ ൌ ൌ Ͳ ͵ ‫ݔ‬଴ ʹ ʹ‫݈ܣ‬ ‫݈ܣ‬ሺ௦ሻ ൅ e y ݊ଵ y y - c y ݊ଵ ଵ െ c y c y c y ݊ c c c 3as.ency-education.com
  • 21. 21 2 10 ‫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 ‫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 - - ݉݅݊ ݊ m ൌ ͳͲ ͳͲ݉݅݊ ݉݅݊ ͷ ൈ ͳͲ ͳͲି ିହ ହ ݉‫݈݋‬ ݉‫݈݋‬Ȁ Ȁ݉݅ ሺ ሺܰܽ ܰܽା ା ൅ ൅ ‫ܱܪ‬ ‫ܱܪ‬ି ሻ ‫ܪ‬ ‫ܪ‬ଷ ଷܱ ܱା ା ൅ ൅ ‫ܱܪ‬ ‫ܱܪ‬ି ൌ ‫ܭ‬ ‫ܭ‬ ൌ ൌ ͳ ሾ ሾ‫ܪ‬ ‫ܪ‬ଷܱ c ݊ 3as.ency-education.com