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In the diagram, PQR is a tangent to the circle QST at Q. If |QT| = |ST| and ∠SQR = 68°, find ∠PQT.
The angle of a sector of a circle radius 10.5cm is 120°. Find the perimeter of the sector [Take π = 22/7]
The area and a diagonal of a rhombus are 60 cm\(^2\) and 12 cm respectively. Calculate the length of the other diagonal.
A cone is 14cm deep and the base radius is 4\(\frac{1}{2}\)cm. Calculate the volume of water that is exactly half the volume of the cone.[Take π = \(\frac{22}{7}\)]
Calculate the total surface area of a cone of height 12cm and base radius 5cm. [Take π = 22/7]
A sector of a circle of radius 9cm subtends angle 120° at the centre of the circle. Find the area of the sector to the nearest cm\(^2\) [Take π = 22/7]
Solve the simultaneous equations y = 3x; 4y - 5x =14
Factorize 2x\(^2\) - 21x + 45
Write as a single fraction: \(\frac{5}{6r} - \frac{3}{4r}\)
Solve the equation x\(^2\) - 2x - 3 = 0
Factorize the expression 2s\(^2\) - 3st - 2t\(^2\).
Simplify: \(\frac{\log \sqrt{27}}{\log {81}}\)
Simplify: \(\frac{4^{-\frac{1}{2}} \times 16^{\frac{3}{4}}}{4^{\frac{1}{2}}}\)
The nth term of a sequence is given by (-1)\(^{n-2}\) x 2\(^{n-1}\). Find the sum of the second and third terms.
A stick of length 1.75m was measured by a boy as 1.80m. Find the percentage error in his measurement
Convert 89\(_{10}\) to a number in base two.
Solve the inequality: 3m + 3 > 9
Simplify: \(\frac{3}{4} \div 1\frac{1}{4} \times (1\frac{1}{2} - \frac{2}{3})\)
S = {1, 2, 3, 4, 5, 6}, T = {2,4,5,7} and R = {1,4, 5}, and (S∩T) ∪ R
The data below shows the number of worker?
employed in the various sections of a construction
company in Lagos.
Carpenters 24 Labourers 27
Plumbers 12 Plasterers 15
Painters 9 Messengers 3
Bricklayers 18