Express \(\frac{1}{x + 1}\) – \(\frac{1}{x – 2}\) as a single algebraic fraction
- A. \(\frac{-3}{(x + 1)(2 - x)}\)
- B. \(\frac{3}{(x + 1)(2 - x)}\)
- C. \(\frac{-1}{(x + 1)}\)
- D. \(\frac{1}{(x + 1)(x - 2)}\)
find the range of values of values of r which satisfies the following inequality, where a, b and c are positive \(\frac{r}{a}\) + \(\frac{r}{b}\) + \(\frac{r}{c}\) > 1
- A. r > \(\frac{abc}{bc + ac + ab}\)
- B. r < abc
- C. r > \(\frac{1}{a}\) + \(\frac{1}{b}\) + \(\frac{1}{c}\)
- D. . \(\frac{1}{abc}\)
What value of Q will make the expression 4x2 + 5x + Q a complete square?
- A. \(\frac{25}{16}\)
- B. \(\frac{25}{64}\)
- C. \(\frac{5}{8}\)
- D. \(\frac{5}{4}\)
Solve the pair of equation for x and y respectively \(2x^{-1} – 3y^{-1} = 4; 4x^{-1} + y^{-1} = 1\)
- A. -1, 2
- B. 1, 2
- C. 2, 1
- D. 2, -1
What are K and L respectively if \(\frac{1}{2}\)(3y – 4x)2 = (8x2 + kxy + Ly2)
- A. -12, \(\frac{9}{2}\)
- B. -6, 9
- C. 6, 9
- D. 12, \(\frac{9}{2}\)
Factorize 4a2 – 12ab – C2 + 9b2
- A. 4a(a - 3b) + (3b - c)2
- B. (2a + 3b - c)(2a + 3b + c)
- C. (2a - 3b + c)(2a - 3b - c)
- D. 4a(a - 3b) + (3b + c)
Factorize completely \(y^3 -4xy + xy^3 – 4y\)
- A. (y + xy)(y + 2)(y - 2)
- B. (y - xy)(y - 2)
- C. y(1 + x)(y + 2)(y -2)
- D. y(1 - x)(y + 2)(y - 2)
Simplify \(\frac{324 – 4x^2}{2x + 18}\)
- A. 2(x - 9)
- B. 2(9 + x)
- C. 81 - x2
- D. -2(x - 9)
Solve for a positive number x such that \(2^{(x^3 – x^2 – 2x)} = 1\)
- A. 4
- B. 3
- C. 2
- D. 1
If \(f(x) = 2x^2 – 5x + 3\), find f(x + 1).
- A. 2x2 - x
- B. 2x2 - x + 10
- C. 4x2 + 3x + 2
- D. 4x2 + 3x + 12
The cost of dinner for a group of students is partly constant and partly varies directly as the number of students. If the cost is N74.00 when the number of students is 20 and N96.00 when the number of students is 30, find the cost when there are 15 students
- A. N68.50
- B. N63.00
- C. N60.00
- D. N52.00
Make R the subject of the formula S = \(\sqrt{\frac{2R + T}{2RT}}\)
- A. R = \(\frac{T}{(TS^2 + 1)}\)
- B. R = \(\frac{T}{2(TS^2 - 1)}\)
- C. R = \(\frac{T}{2(TS^2 + 1)}\)
- D. R = \(\frac{R}{2(TS^2 + 1)}\)
What are the values of y which satisfy the equation \(9^{y} – 4 \times 3^{y} + 3 = 0\) ?
- A. -1 and 0
- B. -1 and 1
- C. 1 and 3
- D. 0 and 1
Find p in terms of q if \(\log_{3} p + 3\log_{3} q = 3\)
- A. (\(\frac{3}{q}\))3
- B. (\(\frac{q}{3}\))\(\frac{1}{3}\)
- C. (\(\frac{q}{3}\))3
- D. (\(\frac{3}{q}\))\(\frac{1}{3}\)
Simplify \(4 – \frac{1}{2 – \sqrt{3}}\)
- A. 2\(\sqrt{3}\)
- B. -2 - \(\sqrt{3}\)
- C. -2 + \(\sqrt{3}\)
- D. 2 - \(\sqrt{3}\)
If the surface area of a sphere increased by 44%, find the percentage increase in diameter
- A. 44
- B. 30
- C. 22
- D. 20
Oke deposited N800.00 in the bank at the rate of 12\(\frac{1}{2}\)% simple interest. After some time the total amount was one and half times the principal. For how many years was the money left in the bank?
- A. 2\(\frac{2}{3}\)
- B. 4
- C. 5\(\frac{1}{3}\)
- D. 8
If a : b = 5 : 8, x : y = 25 : 16; evaluate \(\frac{a}{x}\) : \(\frac{b}{y}\)
- A. 125 : 128
- B. 3 : 5
- C. 3 : 4
- D. 2 : 5
What is the different between 0.007685 correct to three significant figures and 0.007685 correct to four places of decimal?
- A. 10-5
- B. 7 x 10-4
- C. 8 x 10-5
- D. 10-6
Simplify \(\sqrt[3]{(64r^{-6})^{\frac{1}{2}}}\)
- A. \(\frac{r}{2}\)
- B. 2r
- C. \(\frac{1}{2r}\)
- D. \(\frac{2}{r}\)
If \(12_{e} = X_{7}\), where e = 12, find X.
- A. 20
- B. 15
- C. 14
- D. 12