Mathematics
Answer all questions
1. Given that 2x+y = 16 and In (2x– y) = ? In 5, find the value of x and of y, leaving your answers in surd form.
X=(4+√5)/3 Y=(8-√5)/3
2. Given that A = {x:-5 < 2x-3 ≤ 15}, B = {x: -4 ≤ x + 1 < 7} and A U B = {x: a ≤ x -1≤ b}, find the value of a and of b.
a=-6 b=8
3. Functions f, g and h are defined by
f:x → 2 + x g:x → -|x-1| h:x → -x2 + 2
(a) Find the values of gh(-2) and f-1gh(-2).-3and-1
(b) Find in similar form, gf, fg and gh. gf=-|x+1| fg=2-|x-1| gh=-|-x2+1|
[3]
(c) Find the values of x such that fg(x) = -1 x=4 or x=-2
[3]
(d) Show that hg(x) = 1 + 2x- x2. ∵hg(x)=h(-|x-1|)=-(-|x-1|)2+2=-(x-1)2+2
=-x2+2x+1
[4]
4. Three points have coordinates A(5, -3), B(-2,1) and C(a , 5).
(a) Find, in terms of a, the coordinates of M, which is the midpoint of BC. The midpoint of BC is ((a-2)/2,3)
(b) Find the value of a for which AM is perpendicular to AB a=132/7.
[6]
[8]
[5]
[4]
[4]
5. Find the fifth and sixth terms of binomial expansion of ( 2- ? x2 )9 . Hence find the coefficient of x10 in ( 2- ? x2 )9 (3x2 +5 ) . 5th:(-19/3)9 6th:( -10) 9
[8]
6. Find the coordinates of the points of intersection of the line x + y = 3 and the curve x2 – 2x +2y2 = 3.
[6]
x=3, y=0 or x=3/5,y=12/5
7. Find the range of values of k for which the equation x2 – 6x + k2 – 7 = 0 has real roots. 36-4×1×（k2-7）≥0 the result is -4≤k≤4
[6]
8. Find all the angles between 0° and 360° inclusive which satisfy
sinxsec2x – 2tanx = 0
x=60°
[6]
9. A body moves in a straight line so that its displacement, S m, from a point O at time t sec, is given by S = 5 + 15t2 – 5t3. Find
(a) The time when the body is instantaneously at rest, (b) The acceleration when t = 4, Answer:75
[3]
[6] [4]
[4]
(c) The total distance moved by the body in 9 seconds, (d) The average speed of the moving body.
10.
PQ
A10 cmOB
A semicircle of centre O and radius 10 cm has diameter AB. The chord AQ is 10 cm and the ratio of arc AP to arc AQ is 2 : 3.
(a) Show that ∠AOP is 2?9 π radians.
∵AO=QO=AQ=10 cm ∴∠AOQ=60° and∵the ratio of arc AP to arc AQ is 2 : 3. ∴∠AOP=40°
[6]
(40°/360°)×2л=2л/9
(b) Calculate the area of segment AQP. the area of segment AQP is (50л/3)-25√3
[4]
11. If x2 – 2x – 3 is a factor of the expression x4 + px3 + qx – 81, find the value of p and of q. With these of p and q, factorize the expression completely.
[10]
数学
回答以下所有问题
1. 已知2x+y和ln（2x-y）= ? In 5 求x和y的值，保留根号。
[8]
2. 已知A = {x:-5 < 2x-3 ≤ 15}, B = {x: -4 ≤ x + 1 < 7} 且A U B = {x: a ≤ x -1≤ b}, 求a 和b的值。 3. 已知函数f, g 和 h 分别是
f:x → 2 + x g:x → -|x-1| h:x → -x2 + 2
[5]
(a) 求gh(-2) 和 f-1gh(-2)的值. (b) 找出函数方程gf, fg 和gh.
[3]
[4] [4] [3]
(c) 当fg(x) = -1时，求x的值 (d) 证明 hg(x) = 1 + 2x- x2.
4. 已知坐标轴上有三点分别是A(5, -3), B(-2,1) 和 C(a , 5).
(a) 已知a为常数，且M为BC连线的中点，求出M的坐标。 [4] (b) 若AM垂直于AB,求出a的值。
[6]
5. 找出二项式 ( 2- ? x2 )9 的第五项和第六项，并求出( 2- ? x2 )9 (3x2 +5 )中 x10 的系数
[8]
6. 已知直线L：x + y = 3 与曲线M：x2 – 2x +2y2 = 3相交，求交点坐标 [6]
7. 已知方程 x2 – 6x + k2 – 7 = 0 有真根，求k的范围 [6] 8. 已知sinxsec2x – 2tanx = 0，（0°≤x≤ 360°）求x的值 [6]
9. 一人在t秒时从O点出发，沿直线走了S m, 若S = 5 + 15t2 – 5t3. 求：
(a) 当此人停下来时，求此时的瞬时时间。 (b) 当t = 4时,求加速度
[4] [3]
(c) 9秒后，求此人移动的总路程, (d) 求该人的平均速度
[6] [4]
相关推荐：
loading