山东省青岛市格兰德中学2012-2013学年高一下学期模块检测数学试题(中美三,四班)无答案

1、青岛格兰德中学 2012 2013学年度第二学期高一年级中英班数学学科模块检测考试时间：90分钟；命题人：数学组3x2 _x _21. (a) Simplify 2x -13x2-x-21(b) Hence, or otherwise, express 2as a single fraction in itsx -1x(x + 1)simplest form.2. Express2x2 +3x-6(2x 3)(x-2) x2-x-2as a single fraction in its simplest form.3. The function f(x) is define by-2(1)2E

2、xE1f(x)=、(x+1)(2_x)_1 ex 兰2a. Sketch the graph of f(x)b. Write down the range of fc. Find the values of x for which f(x) 0.(a) Find the temperature of the ball as it enters the liquid.(b) Find the value of t for which T = 300, giving your answer to 3 significant figures.(c) Find the rate at which th

3、e temperature of the ball is decreasing at the instant when t = 50. Give your answer in C per minute to 3 significant figures.(d) From the equation for temperature T in terms of t, given above, explain why thetemperature of the ball can never fall to 20 C.35. f(x) = 2x -x -4.(a) Show that the equati

4、on f(x) = 0 can be written as3The equation 2x -x -4 = 0 has a root between 1.35 and 1.4.(b) Use the iteration formulawith x0 = 1.35, to find, to 2 decimal places, the value ofx1, X2 and X3.The only real root of f(x) = 0 is :.(c) By choosing a suitable interval, prove that- = 1.392, to 3 decimal plac

5、es.6. The functions f and g are defined byf :x 一 2x + In 2,x 三?, 2x g:x e ,x 三?.(a) Prove that the composite function gf isgf:x 4e4x,x 三?.(b) Sketch the curve with equation y = gf(x), and show the coordinates of the point where the curve cuts they-axis.(c) Write down the range of gf.7. The function

6、f is defined by5x +13f: x 2, x 1.x +x2x+22(a) Show that f(x) =, x 1.x 1(b) Find f-(x).The function g is defined by2g: x_x + 5,?.1(c) Solve fgx) = 4 .8. A particular species of orchid is being studied. The population p at time t years after the study started is assumed to be0.2t2800aep = 02, where a is a constant.1 +aeGiven that there were 300 orchids when the study started,(a) show that a = 0.12,(b) use the equation with a = 0.12 to predict the number of years before the population of o