if P and Q are fixed points and X is a point which moves so that XP = XQ, the locus of X is
- A. A straight line
- B. a circle
- C. the bisector of angle PXQ
- D. the perpendicular bisector of PQ
3y = 4x – 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.
- A. -4/3
- B. -3/4
- C. 3/4
- D. 4/3
An equilateral triangle of side โ3cm is inscribed in a circle. Find the radius of the circle.
- A. 2/3 cm
- B. 2 cm
- C. 1 cm
- D. 3 cm
P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and angle VUS = 50ยฐ, find angle UST.
- A. 310ยฐ
- B. 130ยฐ
- C. 80ยฐ
- D. 50ยฐ
A frustrum of pyramid with square base has its upper and lower sections as squares of sizes 2m and 5m respectively and the distance between them 6m. Find the height of the pyramid from which the frustrum was obtained.
- A. 8.0 m
- B. 8.4 m
- C. 9.0 m
- D. 10.0 m
If ฮฑ and ฮฒ are the roots of the equation 3x\(^2\) + 5x – 2 = 0, find the value of 1/ฮฑ + 1/ฮฒ
- A. -5/3
- B. -2/3
- C. 1/2
- D. 5/2
Solve the inequality 2 – x > x\(^2\).
- A. x < -2 or x > 1
- B. x > 2 or x< -1
- C. -1 < x < 2
- D. -2 < x < 1
A trader realizes 10x – x\(^2\) naira profit from the sale of x bags on corn. How many bags will give him the desired profit?
- A. 4
- B. 5
- C. 6
- D. 7
if (x – 1), (x + 1) and (x – 2) are factors of the polynomial ax\(^3\) + bx\(^2\) + cx – 1, find a, b, c in that order.
- A. -1/2, 1., 1/2
- B. 1/2, 1, 1/2
- C. 1/2, 1, -1/2
- D. 1/2, -1, 1/2
Evaluate (\(\frac{1}{2} – \frac{1}{4} + \frac{1}{8} – \frac{1}{16} + …) -1\)
- A. 2/3
- B. zero
- C. -2/3
- D. -1
Find the inverse of p under the binary operation * defined by p*q = p + q – pq, where p and q are real numbers and zero is the identity
- A. p
- B. p -1
- C. p/(p-1)
- D. p/(p+1)
The 3rd term of an A.P is 4x – 2y and the 9th term is 10x – 8y. Find the common difference.
- A. 19x - 17y
- B. 8x - 4y
- C. x - y
- D. 2x
A binary operation * is defined by a * b = a\(^b\). If a * 2 = 2 – a, find the possible values of a.
- A. 1, -1
- B. 1, 2
- C. 2, -2
- D. 1, -2
If \(P344_{6} – 23P2_{6} = 2PP2_{6}\), find the value of the digit P.
- A. 2
- B. 3
- C. 4
- D. 5
Simplify \(\frac{3(2^{n+1}) – 4(2^{n-1})}{2^{n+1} – 2^n}\)
- A. 2n+1
- B. 2n-1
- C. 4
- D. 1/4
If 314\(_{10}\) – 256\(_7\) = 340\(_x\), find x.
- A. 7
- B. 8
- C. 9
- D. 10
A man wishes to keep his money in a savings deposit at 25% compound interest so that after three years he can buy a car for N150,000. How much does he need to deposit?
- A. N112,000.50
- B. N96,000.00
- C. N85,714.28
- D. N76,800.00
Evaluate \(\frac{(2.813 \times 10^{-3} \times 1.063)}{(5.637 \times 10^{-2})}\) reducing each number to two significant figures and leaving your answer in two significant figures.
- A. 0.056
- B. 0.055
- C. 0.054
- D. 0.54
In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?
- A. 8
- B. 24
- C. 62
- D. 86
If \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})} = m +n\sqrt{6}\), find the values of m and n respectively.
- A. 1, -2
- B. -2, 1
- C. \(\frac{-2}{5}\), 1
- D. 2, 3/5
If the population of a town was 240,000 in January 1998 and it increased by 2% each year, what would be the population of the town in January, 2000?
- A. 480,000
- B. 249,696
- C. 249,600
- D. 244,800