Find the equation of the tangent at the point (2, 0) to the curve y = x² - 2x

• A. y = 2x - 4
• B. y = 2x + 4
• C. y = 2x - 2
• D. y = 2x + 2

\(\begin{array}{c|c} x & 1 & 4 & p \\ \hline y & 0.5 & 1 & 2.5\end{array}\). The table below satisfies the relation y - k\(\sqrt{x}\), where k is a positive constant. Find the value of P,

• A. 2
• B. 4
• C. 10
• D. 25

Two forces \(F_{1} = (7i + 8j)N\) and \(F_{2} = (3i + 4j)N\) act on a particle. Find the magnitude and direction of \(F_{1} - F_{2}\).

• A. \((4\sqrt{2} N, 000
• B. \((4\sqrt{2} N, 045
• C. \((4\sqrt{2} N, 090
• D. \((4\sqrt{2} N, 180

Which of the following is a singular matrix?

• A. \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)
• B. \(\begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}\)
• C. \(\begin{pmatrix} 3 & 8 \\ 5 & 16 \end{pmatrix}\)
• D. \(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\)

On a pie chart there are six sectors of which four angles are 30°, 45°, 60°, 90° and the remaining two angles are in the ratio 2:1. Find the smallest angles of the remaining two angles.

• A. 15°
• B. 30°
• C. 45°
• D. 60°

(a) In the diagram, /PQ/ = 6 cm, /QR/ = 13 cm, /RS/ = 5 cm and < RSQ is a right- angled triangle. Calculate, correct to one decimal place, /PS/.

(b) The diagram show a wooden structure in the form of a cone mounted on a hemispherical base. The vertical height of the cone is 24 cm and the base radius 7 cm. Calculate, correct to 3 significant figures, the surface area of the structure. [Take \(\pi = \frac{22}{7}\)].

Simplify \(\sqrt{50} + \frac{10}{\sqrt{2}}\)

• A. 10
• B. 10\(\sqrt{2}\)
• C. 20
• D. 20\(\sqrt{2}\)

A binary operation ⊗ defined on the set of integers is such that m⊗n = m + n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0?

• A. -5/4
• B. -5/6
• C. zero
• D. 5

A notebook of length 15 cm was measured to be 16.8 cm, calculate, correct to two d.p, the percentage error in the measurement.

• A. 12.00%
• B. 11.71%
• C. 10.71%
• D. 11.21%

Simplify 3 log₆9 + log₆12 + log₆64 - log₆72

• A. 5
• B. 777
• C. log₆31
• D. (7776)₆