山东省青岛市格兰德中学2020学年高一数学上学期学段评估测试试题（中英班）（无答案）

青岛格兰德中学2020学年度第一学期高一年级数学五班（中英班）期终考试 测试卷注意：本试卷分测试卷和答题卷两部分，共6页。满分100分，考试用时90分钟。考试结束后，只交答题卷，测试卷请自主保存。 请用0.5毫米签字笔做答。. 1. Factorise completelyx3 4x2 + 3x. 2. The curve C has equation y = x3 4x2 + 8x + 3. The point P has coordinates (3, 0). (a)Show that P lies on C.(b)Find the equation of the tangent to C at P, giving your answer in the form y = mx + c, where m and c are constants. Another point Q also lies on C. The tangent to C at Q is parallel to the tangent to C at P. (c)Find the coordinates of Q.(d) Find the equation of the normal at point Q.3.a. expand (X2/3-1)(X-1/2+1)b. a curve has equation y= (X2/3-1)(X-1/2+1),X0,find . 4.the fifth term of an arithmetic series is 14 and the sum of the first three term of the series is -3.a.use algebra to show that the first term of the series is -6,and calculate the common difference of the series.b. given that the nth term of the series is greater than 282,find the least possible value of n. 5.given that y=3X2+4,X0,find a. b. c. 6.a set of curves,that each pass through the origin,have equatioons y=f1(x),y=f2(x), y=f3(x).where fn(x)=fn-1(x),and f1(x)=x2.a. find f2(x), f3(x).b. Suggest an expression for fn(x).7. 7. Figure 1O(1, 0)(4, 0)(0, 3)xy Figure 1 shows a sketch of the curve with equation y = f(x). The curve passes through the points (0, 3) and (4, 0) and touches the x-axis at the point (1, 0).On separate diagrams, sketch the curve with equation(a)y = f(x + 1), （d）y = f(2x) (b)y = 2f(x), (e)y = f(-x)+2(c)y = -f(x).On each diagram show clearly the coordinates of all the points at which the curve meets the axes.8 。(a)Write down the value of . (b) Find the value of . 9. make an objective appraisal on homework, Perfarmance in math class,attitude and so on .(将你本学期的表现做客观的评价，可以包括作业完成情况、数学课堂上的表现、态度、笔记等方面均可。描述时可用中文或英文或者两者夹杂。)青岛格兰德中学2020学年度第一学期高一年级数学五班（中英）期末考试 答题卷注意：本试卷分测试卷和答题卷两部分，共4页。满分100分，考试用时90分钟。考