Find the value of x if \(\frac{\sqrt{2}}{x + \sqrt{2}}\) = \(\frac{1}{x - \sqrt{2}}\)

• A. 3\(\sqrt{2}\) + 4
• B. 3\(\sqrt{2}\) - 4
• C. 3 - 2\(\sqrt{2}\)
• D. 4 + 2\(\sqrt{2}\)

The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group.

• A. 7
• B. 9
• C. 15
• D. 42

A binary operation x is defined by a x b = a^b. If a x 2 = 2 - a, find the possible values of a?

• A. 1, -2
• B. 2, -1
• C. 2, -2
• D. 1, -1

Three consecutive terms of a geometric progression are give as n - 2, n and n + 3. Find the common ratio

• A. 3/2
• B. 2/3
• C. 1/2
• D. 1/4

Four boys and ten girls can cut a field first in 5 hours. If the boys work at 5/4 the rate at which the girls work, how many boys will be needed to cut the field in 3 hours?

• A. 180
• B. 60
• C. 25
• D. 20

The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST

• A. \(\frac{\pi r}{3}\)
• B. \(\frac{\pi r}{2}\)
• C. \(\frac{\pi r}{12}\)
• D. \(\frac{\pi r}{6}\)

Factorise (4a + 3)² - (3a - 2)²

• A. (a + 1)(a + 5)
• B. (a - 5)(7a - 1)
• C. (a + 5)(7a + 1)
• D. a(7a + 1)

A cylindrical tank has a capacity of 3080m³. What is the depth of the tank if the diameter of its base is 14m?

• A. 25m
• B. 23m
• C. 22m
• D. 20m

Express the product of 0.0014 and 0.011 in standard form

• A. 1.54 x 10⁻²
• B. 1.54 x 10⁻³
• C. 1.54 x 10⁻²
• D. 1.54 x 10⁻⁵

A surveyor walks 500m up a hill which slopes at an angle of 30°. Calculate the vertical height through which he rises

• A. 252m
• B. 500m
• C. 250m
• D. 255m