8 нұсқа.
1. m-нің қай мәнінде ( 2; -3 ) және ( m ; 5) векторлары перпендикуляр болады?
Жауаптары: А)-1; В) -7,5; С) 6; Д) 7,5
2. (3; -1) және (3; 2) векторларының скаляр көбейтіндісін табыңдар.
Жауаптары: А)-1; В) 11; С) 7; Д) -7.
3. (2;0) және (-1;4 ) векторларының арасындағы бұрыштың косинусын табыңдар.
Жауаптары: А)-17; В) ; С)- ; Д) 17.
4. {7;5} {-6;2} болса =3- векторын табыңыз
Жауаптары: А) {-27;-13}; В) {6;-1}; С) {27;13}; Д) {-6;13}
5.{7;5} {-6;2} болса =+ векторын табыңыз
Жауаптары: А) {-7;-1}; В) {7;-1}; С) {27;13}; Д) {1;7}
6.{1;4} {1;2} {7;2} болса, =3–2+ векторын табыңыз.
Жауаптары: А) {-8;-10}; В) {8;-10}; С) {27;13}; Д) {8;10}
7. = - векторының координаттарын жаз.
Жауаптары: А) {0;-10}; В) {8;0}; С) {0;-0,5}; Д) {0;0,5}
8. х шарттарын қанағаттандыратындай х пен у сандарын тап.
Жауаптары:А) х=1 В)х=-5 С) х=5 Д) х=5
у=-2 у=-2 у=-2 у=2
9. Егер болса, онда векторының координаттарын тап.
Жауаптары: А) {-8;-10}; В) {8;-10}; С) {5;7}; Д) {5;-7}
10. Төбелерінің координаталары: А(0;1), В(1;-4), С(5;2) болатын АВС үшбұрышының AN медианасын тап.
Жауаптары: А) 12 В) С) 13 Д) 5
9 нұсқа.
1. m-нің қай мәнінде ( 4; 5 ) және ( m ; -4) векторлары перпендикуляр болады?
Жауаптары: А)-1; В) -5; С) 6; Д) 5
2. (5; 4) және (3;-4) векторларының скаляр көбейтіндісін табыңдар.
Жауаптары: А)-1; В) -7,5; С) 6; Д) 7,5
3. векторларының ұзындықтарын тап.
Жауаптары: А)-1; В) -7,5; С) 5; Д) 7,5
4. . Егер ![](data:image/png;base64,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) болса, онда векторының координаттарын тап.
Жауаптары: А) {-8;-10}; В) {1;-1}; С) {27;13}; Д) {1;11}
5. -3 шарттарын қанағаттандыратындай х пен у сандарын тап.
Жауаптары:А) х=1 В)х=-3 С) х=3 Д) х=3
у=-2 у=7 у=-7 у=2
6. M(-1;-3) нүктесінен және координат басынан бірдей қашықтықта орналасқан ордината осіндегі нүктенінің координатасын табыңыз.
А) {-8;-10}; В) {1;0 }; С) {27;13}; Д) {0;-5/3}
7.A(1;2) B(7;10) АВ кесіндісін 1:3 қатынасында бөлетін нүктенінің координатасын табыңыз.
А) {2,5;-10}; В) {2,5;-4}; С) {2,5;4}; Д) {1;4 }
8. векторының координаттарын жаз.
Жауаптары: А) {-8;0}; В) {0;-8}; С) {8;0 }; Д) {1;8}
9. Егер а) болса, онда векторының координаттарын тап.
Жауаптары: А) {-1;-3}; В) {1;-3}; С) {7;13}; Д) {1;3}
10. Егер: А (2;3) және В(х;1) нүктелерінің ара қашықтығы 2-ге тең болса,онда х-ті тап.
Жауаптары: А) 2; В) 2,5; С) -2; Д) 7,5
10 нұсқа
1. m-нің қай мәнінде ( -5; m ) және ( 2 ; -4) векторлары перпендикуляр болады?
Жауаптары: А)-1; В) -2,5; С) 6; Д) 2,5
2. (3; 4) және (2;-5) векторларының скаляр көбейтіндісін табыңдар.
Жауаптары: А)-14; В) 14; С) 6; Д) 7,5
3. (6;-8) және (2; -1 ) векторларының арасындағы бұрыштың косинусын табыңдар.
Жауаптары: А)-17; В) ; С)- ; Д) 17
4. M нүктесі РК кесіндісінде жатыр, РМ:МК=2:1. Р(6;3) және М (14;9) болса, К нүктесінің координатасын табыңыз.
Жауаптары: А) (-18;-12); В) (18;2); С) (-18;-2); Д) (18;12)
5.А(1;2) және В(-1;0) нүктелері берілген вектордың координатасын табыңыз.
Жауаптары:А) (0;2) В) (2;2) С) (0;-2) Д) (-2;-2)
6. векторының координаттарын жаз.
Жауаптары:А) (0;2) В) (2;2) С) (0;-2) Д) (-2;-2)
7. х шарттарын қанағаттандыратындай х пен у сандарын тап.
Жауаптары:А) х=1 В)х=-4 С) х=-4 Д) х=4
у=-2 у=0 у=2 у=0
8. Егер болса, онда векторының координаттарын тап.
Жауаптары: А) {-1;0}; В) {1;0}; С) {27;13}; Д) {0;10}
9.Егер А (-1;х) және В(2х;3) нүктелерінің ара қашықтығы 7-ге тең болса,онда х-ті тап.
Жауаптары: А) -8 немесе -10; В) -3 немесе 2,6; С) 3 немесе -2,6;
Д) -3 немесе -2,6
10. Егер: М(1,1), N (6;1), Р (7;4), Q (2;4) болса, онда МNРQ төртбұрышының параллелограмм екенін дәлелдеңіз, оның диагональдарын табыңыз.
Жауаптары: А) 3 және 5; В) 3 және 7; С) 2 және 5; Д) 5 және 5
«Жазықтықтағы векторлар» тақырыбына арналған тесттер
А(-1;-2;4), В(-4;-2;0), С(3;-2;1) үшбұрышының төбелері болса,
А төбесіндегі үшбұрыштың бұрышын табыңыз.
А) B) C) D) E) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAMCAIAAADd4huNAAABD0lEQVR4nJWRvY5EUBTHl0xIaKgo9CJRTIEn8AQiEkpPIdHyAh5CMgoSiUqlpPHRiCmmm3ooJAphz2YlM5lmZ091Pn73f//33NO+71+fxelD7m/08Xjc73dRFA9UEITb7cZx3OVykSSpbVtd18FYkiRlWfI83/c9MD8oQE3T1HVt23bXda7r+r4/zzMkqqoyDANCB5rn+bquMMNxHMqqqqIogo7jOKZpQgkHnl4xDGNZNk1TyKdpIghi27ZxHAEFJwiCPNFlWYqisCzrer1SFAU3gCpN0zD65Q7UMIwwDEEYZKCUZTnLMqAVRXlf1jAMJEmCgSAIoPQ8T9M0FEXjOH5HYTuvrfP5DE/+9xe8xjcrHn/k2X5UoAAAAABJRU5ErkJggg==) ![](data:image/png;base64,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) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAMCAIAAADd4huNAAABIElEQVR4nGP5//8/A3GAhUh1hJW+f//+6dOnOjo6UKUfP35MTEzctWuXpKTk7du3L168GBISAnTY+vXrT548qa6ufv36dU1NTZDSsrIyaWnpV69eRUZGArnV1dWtra1fv34FMlxcXMTFxe/duwdVumnTpnPnznFxcW3cuBHIPXXq1KpVq/78+VNRUQHUDOQCNUAd8PbtW3Nz83fv3i1dutTf3x/oHqC2f//+ffjwAagU6BJGRkaoUiEhoSNHjnz+/NnX1xeoVEBAAGg70FRBQUGgLEQdVKmlpeXZs2eBrvnx4weQa2pqunXrVqBqMzMz9MBqb28HevnFixc9PT1AbktLS1BQEBMT07p169CVamhoXLlyBS5kYGAA9DLJUYAMAHl8hpjzmT8aAAAAAElFTkSuQmCC)
Шешуі: А(-1;-2;4), В(-4;-2;0), С(3;-2;1).
Жауабы:
![](data:image/png;base64,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) ![](data:image/png;base64,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)
2. векторлары өзара перпендикуляр.
скаляр көбейтіндісін табыңыз
А) B) C) D) E)
Шешуі: ; болса, ![](data:image/png;base64,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)
скаляр көбейтіндісін табамыз
3. Төбелері А(7;3;4), В(1;0;6), С(4;5;-2) нүктелерінде жатқан үшбұрыш ауданын тап.
А) 24 B) 23 C) 24,5 D) 23,5 E) 21
Төбелері А(7;3;4), В(1;0;6), С(4;5;-2) нүктелерінде
жатқан үшбұрыштың ауданын табамыз:
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADkAAAAYCAIAAADPisJBAAACS0lEQVR4nO2XPchxYRjH0eNjYDAwkHwMYhJZZDAJTymThdEiA4MdUQZKpEey2JQyGJBEYSKlsChRYrDIoBThvaJOp8PxUbw9b6//cLpd57qv+9f/vu775Ot4PBLuabfbkcnku2nv1tcjSb8BlIDHSiQSH/H7Eb2w1EO+/hJ9WN+jl7EmEgmXy5XP5/V6/bNze72e1WqF5/kniURCXh0OB2T8Mla73Z7JZMRi8bMTi8VioVAYDAboIBoR0St7YDgcCgSCZ2d9nwTbcjfzFms6nfb5fIvFQqVSVavV24VmsxmTyfR4PPF4PJvNarXay5xKpTKdTjFBo9HIZrMxQSi13W6VSmUqlUL2Cpe1VCqFQqFarTafz5PJ5G1QUL/fZzAYFovFYDA4HI5ut3uZQ6FQaDQaJojuzrMmkwmHw9lsNuAUtBZiEy4rgEYiEaFQ2Gg0ZDLZZWlMS8HJMJvNEolkvV6Px+OrNTUaDd5yaPH5fMLpYwmsXC4XieOydjodtVoNg3a7bTKZkPjVriecfLXZbDCo1+uwd1dzcrncaDTCBOEGQAOhBWuh9wGXFRyFs0mlUsvlMnQhXhqaFfwAd+Hmgpa9miMSieh0OiZ4GVEoFM1mc7/fBwIBnU53nzUYDEKe1+tdLpexWAym3WYFb6RSKfSZ3+9HL4CWXC6/DEaj0XA4DAMej+d2u51OJ+w+i8UCR+GA/vz83GeFe2S1WsEAfLpNeRZck4+kXcp5EjrSarWuZv6X39i/oA/re/RhfY+us77qH9JrS/1Lvv4BLpza0S5TkSEAAAAASUVORK5CYII=)
4. Егер және болса, онда табыңыз.
А) 15 B) 13 C) 16 D) 14 E) 12
Шешуі:
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC4AAAAYCAIAAAAK+FjQAAAB00lEQVR4nO2Wv8sBYRzA/Sr+gJNEFmU6Jhubk3ejznCLiZJuMyiLImUxMLCIxWKRxSQ3yWBgUVKyMclgugx4v3nq9N6P5+3eXs7gMzx9+95zz/fzPM/36ky32033Hpi0Fnjwlip6vR5zWfin/6yiOc9SmUwm6XR6tVoJGYPBIMTX6/VFKo1G43A4rNdrUV7W4LkqLMvCWCqVVL0lVtntdtlsdjQawQ5sNhvszGg0Sl/bbrfSTQMul8vr9aoykFc5nU6hUCiZTHY6nePxSNO0rAew2WyGw6E0HwwGMSoEQfA87/f7W62Wx+PBqVQqlVwuByq6+75JklRa9OuO0lMle6fTeT6fi8ViJpPhOA6n0u/3F4sFiufzuc/nU1UMj9vthtFsNoOKw+GQTvihAo1isVhQDE6xWExpXfhGqtWqNM8wDBwt3gm6UKiiqAJN1+v14vF4vV4fDAaFQkFpOfYOvqSIVCoFy14ul3K5HIlEflGBqdAoYFCr1eBS8/l8u91WVQ+RSCTG4zEEdrudoqhutwvxcrm0Wq1wHuFwuNlsopmBQGA6ncqoQCfu93sUR6PRP0ggUG0Rs9lMmhQ8xCra8lGR46Mix0MF/5P2gr/xtzwVzfkG4jyzLGseN6gAAAAASUVORK5CYII=)
Жауабы: 15
5. Егер және векторлар арасындағы бұрыш ,
әрі скаляр көбейтіндісі болса, онда осы
векторлар арқылы салынған параллелограмның ауданы қаншаға тең болады?
А) B) 2 C) D) 1 E)
Шешуі:
![](data:image/png;base64,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)
Жауабы: 1
Векторлар
ТЕСТ №1
І-нұсқа
1. Дұрыс тұжырым болуы үшін, толықтыру керек:
а)Нөльдік емес мен векторларының бағттары бірдей болса, онда
бұл векторларды ... деп атаймыз.
б) Егер ... , онда .
в) Егер ... , онда мен k векторлары қарама-қарсы бағытталған.
В) Егер ABCD параллелограмм болса, онда = ...
2.Тұжырымның ақиқаттығын анықтау керек:
а) мен айырмасы деп векторын айтады, мұндағы + =
б) Трапецияның орта сызығы табандарына параллель және
табандарының жарым қосындысына тең.
в) Нөльдік емес векторлар бірдей бағытталған болса, онда олар
коллинеар векторлар деп аталады.
3. ABCD –квадрат, AB = 5, онда І І
а) 10
б) 5
бв
4.Өрнекті ықшамдаңыз:
а)
б)
в)
5. ABCD- параллелограмында О –диагональдарының қиылысу нүктесі .
Егер = , = болса, онда ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAANCAIAAAAWvsgoAAABEklEQVR4nGP5//8/A3GAhUh1dFC6a9euioqK27dvW1lZzZ07V0ZGBij469cvY2PjoqKixMREqNKTJ09GR0cvXrzY2tq6qakpIyNjy5YtQPEFCxaEh4c/efIEYWpbWxtQhYeHB5BdW1sLMfL169eMjIw6Ojrbtm1DKD1y5MicOXMg7O/fv3NwcAAZ8+fPLygoOH/+/OPHjxFKgW7i4uKCsNeuXWtjY3Pt2rXq6mqg64Ei2traCKV2dnYdHR1AicOHD9fX12/dunXlypW/f/8GSv38+VNcXByhdPr06QkJCUAhZWVloOdOnTo1ZcqU4uJiPj6+lpaWT58+TZw4EapUTk5u3759yKGYk5MDYTSDAWlRAABjiXKeynZr0gAAAABJRU5ErkJggg==)
а) = ( + )
б) =- ( + )
в) = ( - )
6. ( өрнегін ықшамдаңдар:
а)
б) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAMCAIAAAAyIHCzAAABFklEQVR4nGP5//8/A9GAhXillKn+9euXsbFxUVFRYmIikBsQELBp0yYgQ0hIaN68eX5+fiiqFyxYEB4e/uTJEwi3qanp4cOH58+fv3DhgouLy5s3bxCqX79+zcjIqKOjs23bNojIxYsXDQwM/v79+/jxYyMjIxSXzJ8/v6CgAGgSUA4icunSpYVgIC4uvnXrVoTqa9euVVdXV1RUANna2tpws3ft2uXg4HDw4MHg4OD79+9DVa9cufL3799Axs+fP4Emwc3W09MDRsjXr1///PkDNXsKGBQXF/Px8bW0tHz69GnixInv379/9eqVhIQEMzOzqqrqrFmzoKpzwABiXjMYQNgNDQ1AC1lYWIC+Jyp2WFlZkbkAZK6DL5RzaI8AAAAASUVORK5CYII=)
в)
7. ABCD- трапеция, ВС АD, АВ CD. Бағыттас векторларды көрсетіңдер.
а)
б) ![](data:image/png;base64,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)
в)
8. ABCD- трапеция, ВС АD, АВ CD. Қарама-қарсы бағытталған векторларды
көрсетіңдер.
а) ![](data:image/png;base64,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)
б)
в) ![](data:image/png;base64,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)
9. ABCD- трапеция, ВС АD, АВ CD.
Ұзындықтары тең векторларды көрсетіңдер.
а) ![](data:image/png;base64,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)
б)
в) ![](data:image/png;base64,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)
10. ABCD-тіктөртбұрыш. АВ=4см, ВС=8см. -ның табыңдар.
а) 4см
б) 12см
в) 8см
ІІ-нұсқа
1. Дұрыс тұжырым болуы үшін, толықтыру керек:
а) Нөльдік емес мен векторлары қарама-қарсы бағытталған деп аталады, егер ...
б)Егер ... , онда = -
в) Егер ... , онда мен k векторлары бірдей бағытталған.
г) Егер ABCD – ромб болса, онда = …
2. Тұжырымның ақиқаттығын анықтау керек:
а) Нөльдік емес мен k санының көбейтіндісі деп векторын атайды,
б) Трапецияның орта сызығы оның қарама –қарсы қабырғаларының орталарын қосатын кеінді.
в) Кез келген М нүктесінен бастап. векторына тең жалғыз ғана векторды салуға болады.
3. Дұрыс жауапты таңдау керек:
ABCD –квадрат. АВ=4, онда
а) 8
б) 4
в)
4. Өрнекті ықшамдаңыз:
а)![](data:image/png;base64,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)
б)
в)![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAANCAIAAAAv2XlzAAABEElEQVR4nGP5//8/AymAhSTVdNYQEBCwadMmIENUVNTV1XXChAkiIiLz5s1raWl5/vy5sbHxkSNHUDQ0NTU9fPjw/PnzX7582b17d1ZWVkxMTF9f386dO9nY2HJzc9FtuHjxor6+PpDBw8NjZWWVnJz87t27rq4uVVVVoCDEchQNly5dgmgAAlZW1r9//169etXS0hKnH4A2eHh4QNh79uwBWnL48GFubm6cGoA26OjoAD2wb9++oqIioBvy8vKWLVsWFhaWnZ3t4+MTHByM0BAZGfnq1StJSUkWFhZDQ8P58+cbGRlNmTIlNjY2IyMD6NSGhgYUG5aDAdDdzMzMcDsNDAwuX76M00lAgKwaFwAAXwptGYsUv1MAAAAASUVORK5CYII=)
5. ABCD – параллелограмында О-диагональдарының қиылысу нүктесі. Егер = , =
болса, онда ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAANCAIAAAAv2XlzAAABMElEQVR4nGP5//8/AymAhSTVdNawa9euioqK27dvW1lZzZ07V0ZGJiAgYNOmTUApUVFRV1fXCRMmiIiIQDWcPHkyOjp68eLF1tbWTU1NGRkZW7ZsATIePnx4/vz5L1++7N69Oysra9WqVVANbW1tQGkPDw8gu7a2Fmg8kHHx4kV9fX0gg4eHB2htcnIywklHjhyZM2cOhP39+3cODg4g49KlSxANQMDKyvr371+Ehl+/fnFxcUHYa9eutbGxgdgAsRMI9uzZA7QEocHOzq6jowPo6cOHD9fX12/duhVig46ODtAD+/btKyoqggQAVMP06dMTEhLExcWVlZWBXjczM4uMjHz16pWkpCQLC4uhoeH8+fONjIwQGuTk5IDGIIf3cjAAupuZmRl7PGAFaKqBAAAQ9Hunj7tS0wAAAABJRU5ErkJggg==)
а) = ( - )
б) = - ( - )
в) = ( + )
6. өрнегін ықшамдаңдар.
а)
б) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAMCAIAAADgcHrrAAABO0lEQVR4nGP5//8/A+mAhQw91NAWFha2Zs2ap0+fSkpKArmTJk0qKChQVla+e/duTk4OkFtcXDxv3rxTp06pqqoitNXX11+7du3KlStAbT9+/Dhx4oS2tvaKFStiYmKAeh4/fiwmJnbz5k0giWLbxYsX7e3tL1++7OrqunnzZh0dHWZmZqCgnp7e8uXLP3/+XF5ejsWRQBWGhoZAbUCrODg4Hj58qK+vDxQEOuHkyZPHjx/H7jegCj8/vz179uzbt8/Ly6u7uzskJKS3t7erq+v8+fNAdwJ9gV2bhobGmzdv+Pn5gc67fv06xDaga01NTQ0MDEpKSri5uVG0RUdHv3z58sGDB87OztbW1sHBwW/fvrWxsQEK5uXlAf0GDOe4uLi1a9eiaFsKBkCGsbExkIRLw0FbWxt2v5EEADvXmB0mMw92AAAAAElFTkSuQmCC)
в)
7. ABCD- ромб. Бағыттас векторларды көрсетіңдер.
а)
б) ![](data:image/png;base64,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)
в)
8. ABCD- ромб, Қарама-қарсы бағытталған векторларды
көрсетіңдер.
а)
б) ![](data:image/png;base64,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)
в)
9. ABCD- ромб
Ұзындықтары тең векторларды көрсетіңдер.
а) ![](data:image/png;base64,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)
б)
в) ![](data:image/png;base64,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)
10.Ромбының диагональдары 6см, 18см. Диагональдарының қиылысу нүктесі- О.
-ні табыңдар. а) 3см ; б) 3см; в) см; г) 6см.
Достарыңызбен бөлісу: |