Solve for x if \(25^{x} + 3(5^{x}) = 4\)

The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number

Evaluate \(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} -1 + \frac{3}{4})]\)

Evaluate \(\frac{0.36 \times 5.4 \times 0.63}{4.2 \times 9.0 \times 2.4}\)

Evaluate \(\frac{log_5 (0.04)}{log_3 18 - log_3 2}\)

Without using table, solve the equation 8x^-2 = \(\frac{2}{25}\)

Simplify \(\sqrt{48}\) - \(\frac{9}{\sqrt{3}}\) + \(\sqrt{75}\)

Given that \(\sqrt{2} = 1.414\), find without using tables, the value of \(\frac{1}{\sqrt{2}}\)

Given that for sets A and B, in a universal set E, A \(\subseteq\) B then A \(\cap\)(A \(\cap\) B)' is

Simplify \(\frac{(2m - u)^2 - (m - 2u)^2}{5m^2 - 5u^2}\)

Factorize a2x - b2y - b2x + a2y

Find the values of p and q such that (x - 1)and (x - 3) are factors of px3 + qx2 + 11x - 6

If a = 1, b = 3, solve for x in the equation \(\frac{a}{a - x}\) = \(\frac{b}{x - b}\)

Solve for r in the following equation \(\frac{1}{r - 1}\) + \(\frac{2}{r + 1}\) = \(\frac{3}{r}\)

Find P if \(\frac{x - 3}{(1 - x)(x + 2)}\) = \(\frac{p}{1 - x}\) + \(\frac{Q}{x + 2}\)

Find the range of values of x for which \(\frac{1}{x}\) > 2 is true

If the 6th term of an arithmetic progression is 11 and the first term is 1, find the common difference.

Find the value of log₁₀ r + log₁₀ r² + log₁₀ r⁴ + log₁₀ r⁸ + log₁₀ r¹⁶ + log₁₀ r³² = 63

Find the nth term of the sequence 3, 6, 10, 15, 21.....

A binary operation \(\oplus\) is defines on the set of all positive integers by a \(\oplus\) b = ab for all positive integers a, b. Which of the following properties does NOT hold?

\(\begin{array}{c|c} \oplus mod 10 & 2 & 4 & 6 & 8 \\ \hline 2 & 4 & 8 & 2 & 6 \\4 & 8 & 6 & 4 & 2\\ 4 & 8 & 6 & 4 & 2\\ 6 & 2 & 4 & 6 & 8\\ 8 & 6 & 2 & 8 & 4\end{array}\)
The multiplication table above has modulo 10 on the set S = (2, 4, 6, 8). Find the inverse of 2

Solve for x and y \(\begin{pmatrix} 1 & 1 \\ 3 & y \end{pmatrix}\)\(\begin{pmatrix} x \\ 1 \end{pmatrix}\) = \(\begin{pmatrix} 4 \\ 1\end{pmatrix}\)

The determination of the matrix \(\begin{pmatrix} 1 & 3 & 3 \\ 4 & 5 & 6\\ 2 & 0 & 1 \end{pmatrix}\) is

\(\begin{array}{c|c} \text{Age in years} & 10 & 11 & 12 \\ \hline \text{Number of pupils} & 6 & 27 & 7\end{array}\)
The table above shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?

If three angles of a quadrilateral are (3y - x - z)^o, 3x^o, (2z - 2y - x)^o find the fourth angle in terms of x, y and z

An open rectangular box is made of wood 2cm thick. If the internal dimensions of the box are 50cm long, 36cm wide and 20cm deep, the box volume of wood in the box is

Calculate the perimeter, in cm, of a sector of a circle of radius 8cm and angle 45^o

What is the locus of a point P which moves on one side of a straight line XY, so that the angle XPY is always equal to 90^o?

If M(4, q) is the mid-point of the line joining L(p, -2) and N(q, p). Find the values of p and q

The angle of depression of a boat from the top of a cliff 10m high is 30. How far is the boat from the foot of the cliff?

What is the value of sin(-690)?

If y = 3t³ + 2t² - 7t + 3, find \(\frac{dy}{dt}\) at t = -1

Find the point (x, y) on the Euclidean plane where the curve y = 2x² - 2x + 3 has 2 as gradient

Evaluate \(\int^{1}_{-1}(2x + 1)^2 \mathrm d x\)

\(\begin{array}{c|c} x & 1 & 2 & 3 & 4 & 5 \\ \hline f & y + 2 & y - 1 & 2y - 3 & y + 4 & 3y - 4\end{array}\)
This table shows the frequency distribution of a data if the mean is \(\frac{43}{14}\), find y

Find the mean deviation of the set of numbers 4, 5, 9

Class interval	1 - 5	6 - 10	11 - 15	16 - 20	21 - 25
Frequency	6	15	20	7	2

Estimate the median of the frequency distribution above

\(\begin{array}{c|c} x & 1 & 2 & 3 & 4 & 5 \\ \hline f & 2 & 1 & 2 & 1 & 2\end{array}\)
Find the variance of the frequency distribution above

In a survey, it was observed that 20 students read newspapers and 35 read novels. If 40 of the students read either newspapers or novels, what is the probability of the students who read both newspapers and novels?

The equation of the graph is

Find the inequality which represents the shaded portion in the diagram

In the diagram, O is the centre of the circle. If SOQ is a diameter and < PRS is 38^o, what is the value of < PSQ

In the diagram, PTS is a tangent to the circle TQR at T. Calculate < RTS