Determine x + y if \(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix}\) \(\begin{pmatrix} x \\ y \end{pmatrix}\) = \(\begin{pmatrix}-1 \\ 8 \end{pmatrix}\)

• A. 3
• B. 4
• C. 7
• D. 12

A chord of length 30cm is 8cm away from the center of the circle. What is the radius of the circle. What is the perimeter of the sector? Take π = 22/7

• A. 16cm
• B. 17cm
• C. 18cm
• D. 20cm

(a) A body of mass 5 kg is placed on a smooth plane inclined at an angle 30° to the horizontal. Find the magnitude of the force: (i) acting parallel to the plane (ii) required to keep the body in equilibrium. [Take g = \(10 ms^{-2}\)].

(b) A uniform plank PQ of length 10m and mass m kg rests on two supports A and B, where |PA| = |BQ| = 1m. A load of mass 8 kg is placed on the plank at point C such that |AC| = 3.5 m. If the reaction at B is 100 N, calculate the (i) value of m (ii) reaction at A. [Take g = \(10 ms^{-2}\)].

Explanation

(i) Force parallel to plane = \(mg \sin 30\)

= \(5 \times 10 \times 0.5 \)

= \(25 N\)

(ii) Force required to keep the body in equilibrium

= \(mg \sin 30 - \mu R\)

= \(25 - \mu \times 5 \times \frac{5\sqrt{3}}{2}\)

= \(25(1 - \mu) \frac{\sqrt{3}}{2}\)

b)

Since the plank does not move, all forces and torques are balanced. Forces:

RA + RB - mCg - mpg=0,

torques (consider A as the pivot):

\(\frac{mp}{10}\)g ⋅ 0.5 − \(\frac{9}{10}\)mp?g⋅4.5 −mC?g⋅3.5+100⋅8=0

mp?=13 kg,

RA?=110 N.

If y = 2x³ + 6x² + 6x + 1, Find \(\frac{dy}{dx}\)

• A. 2
• B. \(\frac{1}{3}\)
• C. 1
• D. \(\frac{2}{3}\)

An arc subtends an angle of 72\(^o\) at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5 cm. [Take \(\pi = \frac{22}{7}\)]

• A. 6.6 cm
• B. 8.8 cm
• C. 4.4 cm
• D. 2.2 cm

Solve for k in the equation \(\frac{1}{8}^{k+2}\) = 1

• A. 2
• B. -4
• C. -2
• D. 4

Yomi was asked to label four seats S, R, P, Q. What is the probability he labelled them in alphabetical order?

• A. \(\frac{1}{24}\)
• B. \(\frac{1}{6}\)
• C. \(\frac{2}{13}\)
• D. \(\frac{1}{4}\)

Find the average of the first four prime numbers greater than 10

• A. 20
• B. 19
• C. 17
• D. 15

Out of 60 members of an Association, 15 are Doctors and 9 are Lawyers. If a member is selected at random from the Association, what is the probability that the member is neither a Doctor Nor a Lawyer

• A. \(\frac{3}{5}\)
• B. \(\frac{9}{10}\)
• C. \(\frac{3}{20}\)
• D. \(\frac{1}{4}\)

In the diagram, WXYZ is a rectangle with diamension 8cm by 6cm. P, Q, R and S are the midpoints of the rectangle as shown. Using this information calculate the area of the part of the rectangle that is not shaded

• A. 25cm²
• B. 24cm²
• C. 16cm²
• D. 12cm²