Northwest regional mock advance level June 2021 further mathematics 1

Northwest regional mock advance level June 2021 further mathematics 1

Northwest regional mock advance level June 2021 further mathematics 1

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3
11. A continuous random variable X has a probability
density function /, where
0 A [1, 2 ] elsewhere
B [ 0,1]
C [–1, 0] 0
,
A k( l — x2 ) x < 0
0 < x < 1
The cumulative probability function F( x ) =

14. If f [ x ) =z 2 + x 2 – x3, then the equation
f [ x ) — Ohas a solution on the interval
0 < x < 1 x > 1 1
lc( x –*–)
B 0, 0 < x < 1
elsewhere D I .–2.– 1]

0, x < 0
0 < x < 1 x > 1
2sin|( )
c 1, –IT) 15. Given that f ( x ) = x x A 0
k
, x — 0
0
, x < 0
0 < x < 1 x > 1
is a continuous function at x = 0 , the value of k is
D *(*–£), A 0
0
B 1
2
12. A particle of mass m falls against a resistance of
magnitude to
^
where vis the velocity and A: is a positive
constant. The equation of motion is given by
CD
2
16. A force F = (3i — j 4– *2k )Ar acts on a particle giving
it a displacement of(3i 4– 4k) m. The work done by F is
A 15 J
B 5/l4 J
d v
A
= —rnkv
dl
dv
B
— = mg — kv
dt
dv C 5.1
D 17 J
C
— = mg –1– kv
dt
dv
D = —mg — kv 2