2003 - JAMB Mathematics Past Questions and Answers - page 2

y = 3 sin(-4x)

dy/dx = 3x - 4 cos (-4x)

= -12 cos (-4x)

y = 3x² - x³

dy/dx = 6x - 3x²

as dy/dx = 0

6x - 3x² = 0

3x (2 - x) = 0

this implies that 2 -x = 0 and 3x = 0

x = 2 (or) 0

But = dy/dx = 6x - 3x²

d²y/dx² = 6 - 6x at x = 2

= 6 - 6(2)

= -6

y = 3x² - x³

= 3(2)² - 2³

= 12 - 8

= 4

(Mean = \frac{30+56+31+55+43+44}{6}=\frac{259}{6}=43.167\Median = 30,31,43,44,55,56=\frac{43+44}{2}=\frac{87}{2}=43.5\Median-mean = 43.3-43.17=0.33)

Range = (Highest - Lowest) items

= 27 - 3

= 24

(Mean = \frac{(0 \times 1) + (1 \times 2) + (2 \times 2) + (3 \times 1) + (4 \times 9)}{1 + 2 + 2 + 1 + 9}=\frac{(0 + 2 + 4 + 3 + 36)}{15}=\frac{45}{15}=3)

Let the 4th angle be = x

∴ x + 45 + 90 + 135 = 360

x + 270 = 360

x = 360 - 270

x = 90

∴ smallest angle = 45^o

45^o = N28.00

1^o = 28.00/45

135^o = (28.00/45) * (135/1)

= N84.00

(^{n}P_3 - 6(^{n}C_{4})=0\frac{n!}{(n-3)!}-6\left( \frac{n!}{(n-4)!4!}\right)=0\frac{n!}{(n-3)!}=6\left(\frac{n!}{(n-4)!4!}\right)\n!((n-4)!4!)=6n!(n-3)!((n-4)!4!)=6(n-3)!\frac{(n-4)!}{(n-3)!}=\frac{6}{4!}\frac{(n-4)!}{(n-3)(n-4)!}=\frac{6}{4 \times 3\times 2\times 1}\frac{1}{(n-3)}=]\frac{1}{4}\n-3=4\n=4+3\n=7)

(^{4}C_2 \times ^{3}C_1 = \left(\frac{4!}{(4-2)!2!}\right)\times\left(\frac{3!}{(3-1)!1!}\right)=\frac{4!}{2!2!}\times \frac{3!}{2!}=\frac{4 \times 3 \times 2!}{2 \times 1 \times 2!} \times \frac{3 \times 2!}{2!}=18)

Black balls = 5

Red balls = 3/8

P(B) = 5/8, P(R) = 3/8

P( a Black and a Red) = BR + RB

= (5/8) * (3/7) * (3/8) * (5/7)

= (15/56) + (15/56)

= 30/56

= 15/28

12 + 20 + x + 21 + x-1 +28 = 120

2x + 80 = 120

2x = 120 - 80

2x = 40

x = 20