Mathematics数学-附答案(1)

2024年3月13日发(作者：镇雄2021中考数学试卷)

Mathematics数学-附答案（1）

Mathematics

Answer all questions

that 2x+y= 16 and In (2x–y) = ? In 5, find the value of x and of y, leaving your

answers in surd form. [8]

X=(4+√5)/3 Y=(8-√5)/3

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. [5]

a=-6 b=8

ons 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 [4]

(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]

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. [4]

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]

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]

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

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] all the angles between 0° and 360° inclusive which satisfy

sinxsec2x– 2tan x = 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, [4]

(b)The acceleration when t = 4, Answer:75

[3]