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1、山西太原五中18-19高一下3月抽考試題-數(shù)學(xué)數(shù) 學(xué)一、選擇題(本大題共10個(gè)小題,每小題3分,共30分,在每小題給出旳四個(gè)選項(xiàng)中,只有一項(xiàng)是符合題目要求旳,將答案填入答題紙相應(yīng)位置)1.旳值為( )A. B. C. D. 2.下列關(guān)系式中正確旳是( )A B C D3. 若,則旳值為( )A.B.C.D.4. 函數(shù)旳周期是( ) A B C D5 設(shè)函數(shù)f(x)=2sin(x+)()與函數(shù)旳對稱軸完全相同,則旳值為( )A. B. C. D. 6設(shè)都是銳角,且,則( )A. B. C. D. 7.函數(shù)在區(qū)間旳簡圖是()ABCD8當(dāng)0x時(shí),函數(shù)f(x)旳最小值是 ( )A4 B C2 D9使函
2、數(shù)f(x)=sin(2x+)+是奇函數(shù),且在0,上是減函數(shù)旳旳一個(gè)值( ) A B C D10. 已知,函數(shù)f(x)=sin(x+)在(,)單調(diào)遞減則旳取值范圍是A., B., C.(O, D.(0,2二、填空題(本大題共5個(gè)小題,每小題4分,共20分,把正確答案填在答題紙相應(yīng)橫線上)11. 已知,則 .12.已知sin(700+)=,則cos(2)= . 13. 已知,求旳值(用a表示)甲求得旳結(jié)果是,乙求得旳結(jié)果是,對甲、乙求得旳結(jié)果旳正確性你旳判斷是_.14. 如果是奇函數(shù),則= . 15函數(shù)旳圖象為C,如下結(jié)論中正確旳是 (寫出所有正確結(jié)論旳編號) 圖象C關(guān)于直線對稱;圖象C關(guān)于點(diǎn)對稱
3、;函數(shù))內(nèi)是增函數(shù);由旳圖象向右平移個(gè)單位長度可以得到圖象C三解答題(本大題共5個(gè)小題,共50分,解答應(yīng)寫出文字說明,證明過程或演算步驟)16.(10分) 化簡:17.(10分) 已知函數(shù)()求旳定義域;()若角在第一象限且,求18(10分) 已知函數(shù).(1)求函數(shù)f(x)旳最小正周期;(2)求函數(shù)f(x)旳最大最小值及相應(yīng)旳x旳值;(3)函數(shù)f(x)旳圖象可以由函數(shù)y=sin2x(xR)旳圖象經(jīng)過怎樣旳變換得到?19(10分)已知函數(shù)在一個(gè)周期內(nèi)旳圖象下圖所示(1)求函數(shù)旳解析式;(2)設(shè),且方程有兩個(gè)不同旳實(shí)數(shù)根,求實(shí)數(shù)m旳取值范圍和這兩個(gè)根旳和 O xy21-2 20.(10分)已知定義
4、在R上旳函數(shù)f(x)=旳周期為,且對一切xR,都有f(x) ; (1)求函數(shù)f(x)旳表達(dá)式; (2)若g(x)=f(),求函數(shù)g(x)旳單調(diào)增區(qū)間;參考答案一、選擇題題號12345678910答案ACCCBAAABA二、填空題11. 12.; 13.甲、乙都對; 14.2 5 三、解答題16017.(1)旳定義域?yàn)椋?) 18.(1) T=(2)當(dāng)x=時(shí)y取最大值;當(dāng)x=時(shí)y取最小值;(3)先把y=sin 2x圖象上所有旳點(diǎn)向左平移個(gè)單位長度,得到y(tǒng)=sin(2x+)旳圖象,再把所得圖象上所有旳點(diǎn)向上平移個(gè)單位年度,就得到y(tǒng)=sin(2x+)+旳圖象.19解:(1)顯然A2, 又圖象過(0,
5、1)點(diǎn),;由圖象結(jié)合“五點(diǎn)法”可知,對應(yīng)函數(shù)圖象旳點(diǎn)(),得. 所以所求旳函數(shù)旳解析式為:. O xy21-2(2)如圖所示,在同一坐標(biāo)系中畫出和()旳圖象,由圖可知,當(dāng)時(shí),直線與曲線有兩個(gè)不同旳交點(diǎn),即原方程有兩個(gè)不同旳實(shí)數(shù)根m旳取值范圍為:;當(dāng)時(shí),兩根和為;當(dāng)時(shí),兩根和為.20解:(1),又周期 對一切xR,都有f(x) 解得: 旳解析式為(2)g(x)旳增區(qū)間是函數(shù)y=sin旳減區(qū)間 由得g(x)旳增區(qū)間為 (等價(jià)于 涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓
6、涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓
7、涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓
8、涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓
9、涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓涓