Neco further maths answers 2020

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(1) find the value of y for which 5^2x + 1 – 26(5^x + 3)

(2i) if x=x² and y=5/1, Find dy/dx

(2ii) find the value of y if

| y – 1 2|
| | = 4
| 4 3|

(3) A matrix M has the ability of transforming the vertices A(4,0), B(4,4) and C(0,4) of a triangle ABC to their image A(12,0), B(12,8) and C(0,8). Find:

(i) M
(ii) |M|
(iii) The area of triangle A‘B’ C, If the area of triangle ABC is 8 square units

(4a) Show that the point (–2, –1) lies on the circle x² + y² + 2x + 6y + 5 = 0.
Hence, Determine the equation of the tangent to the circle at the point (–2, –1)

(4b) Find the length of the tangent to a circle x² + y² + 6x – 2y – 4 = 0. From the point (4,3)

(5) Two lorries ofasses 50kg and 62kg are traveling on the same rate with speeds 6m/s and 4m/s respectively in the same direction. If there was a collision and the two hook, with one what speed do they move together? Correct your answer to 1 decimal place

(6a) The vertices P, Q, R and S of a quadrilateral have position vectors p, q, r and s respectively relative to the origin O where
p=2i + 3j, q=5i + 3j, r=5i + 6j and s=2i + 6j.
i and j being unit vectors along OX and OY axes respectively.

(i) Find the magnitude of the vectors:
(I) PS and QR
(II) PQ and SR

(ii) Find the area of the quadrilateral PQRS

(6b) Given that vectors a=2, b=3 and ab=3. Find the angle between a and b

(13ai)
Given: mass ,m =10kg
Force,F = 40N
Time, t = 0.5secs
Impulse, I = Ft = 40×0.5 = 20Ns

(13aii) Ft = m(v-u) where u= 0 (at rest)
20 = 10(v-0)
20 = 10v
V = 20/10 = 2m/s
Final speed = 2m/s

(13aiii)
Given: u=0 ; v=2m/s ; t=0.5secs

S= 1/2(u+v)t
S= 1/2(0+2)×0.5
S= 0.5 metres
Distance = 1/2 metre or 50cm