A man sells different brands of an items. \(^1/_9\) of the items he has in his shop are from Brand A, \(^5/_8\) of the remainder are from Brand B and the rest are from Brand C. If the total number of Brand C items in the man’s shop is 81, how many more Brand B items than Brand C does the shop has?
- A. 243
- B. 108
- C. 54
- D. 135
A rectangular plot of land has sides with lengths of 38 m and 52 m corrected to the nearest m. Find the range of the possible values of the area of the rectangle
- A. 1931.25 m\(^2\) ≤ A < 2021.25 m\(^2\)
- B. 1950 m\(^2\) ≤ A < 2002 m\(^2\)
- C. 1957 m\(^2\) ≤ A < 1995 m\(^2\)
- D. 1931.25 m\(^2\) ≥ A > 2021.25 m\(^2\)
Calculate, correct to three significant figures, the length of the arc AB in the diagram above.
[Take \(\pi = ^{22}/_7\)]
- A. 32.4 cm
- B. 30.6 cm
- C. 28.8 cm
- D. 30.5 cm
An article when sold for ₦230.00 makes a 15% profit. Find the profit or loss % if it was sold for ₦180.00
- A. 10% gain
- B. 10% loss
- C. 12% loss
- D. 12% gain
Calculate, correct to three significant figures, the length AB in the diagram above.
- A. 36.4 cm
- B. 36.1 cm
- C. 36.2 cm
- D. 36.3 cm
The angle of elevation and depression of the top and bottom of another building, measured from the top of a 24 m tall building, is 30° and 60°, respectively. Determine the second building’s height.
- A. 24 m
- B. 32\(\sqrt3\) m
- C. 24\(\sqrt3\)
- D. 32 m
Two numbers are respectively 35% and 80% more than a third number. The ratio of the two numbers is
- A. 7 : 16
- B. 3 : 4
- C. 16 : 7
- D. 4 : 3
The locus of a point equidistant from two intersecting lines is
- A. where the sum of the distances of two focal points is fixed
- B. the collection of points that are equally distant from a fixed point and a line
- C. the perpendicular bisector of the lines
- D. pair of bisectors of the angles between the two lines
What is the general term of the sequence 3, 8, 13, 18, …?
- A. 5n - 2
- B. 5n + 2
- C. 5
- D. 5n
Solve the following quadratic inequality: \(x^2 – x\) – 4 ≤ 2
- A. \(-3 < x < 2\)
- B. \(-2 ≤ x ≤ 3\)
- C. \(x ≤ -2, x ≤ 3\)
- D. \(-2 < x < 3\)
Let a binary operation ‘*’ be defined on a set A. The operation will be commutative if
- A. a*b = b*a
- B. (a*b)*c = a*(b*c)
- C. (b ο c)*a = (b*a) ο (c*a)
- D. None of the above
If \(-2x^3 + 6x^2 + 17x\) – 21 is divided by \((x + 1)\), then the remainder is
- A. 32
- B. 30
- C. -30
- D. -32
Find the matrix A
A \(\begin {bmatrix} 0 & 1\\2 & -1 \end {bmatrix}\) = \(\begin {bmatrix} 2 & -1\\1 & 0 \end {bmatrix}\)
- A. \(\begin {bmatrix} 2 & 1\\-^1/_2 & -^1/_2 \end {bmatrix}\)
- B. \(\begin {bmatrix} 0 & 1\\^1/_2 & ^1/_2 \end {bmatrix}\)
- C. \(\begin {bmatrix} 2 & 1\\0 & -1 \end {bmatrix}\)
- D. \(\begin {bmatrix} 2 & 1\\^1/_2 & -2 \end {bmatrix}\)
The ages of students in a small primary school were recorded in the table below.
| Age | 5-6 | 7-8 | 9-10 |
| Frequency | 29 | 40 | 38 |
Estimate the median.
- A. 7.725
- B. 6.225
- C. 7.5
- D. 6.5
A bag contains 8 red balls and some white balls. If the probability of drawing a white ball is half of the probability of drawing a red ball then find the probability of drawing a red ball and a white ball if the balls are drawn without replacement.
- A. \(\frac {1}{3}\)
- B. \(\frac {2}{9}\)
- C. \(\frac {2}{3}\)
- D. \(\frac {8}{33}\)
If A = { 1, 2, 3, 4, 5, 6}, B = { 2, 4, 6, 8 }. Find (A – B) ⋃ (B – A).
- A. {1, 3, 5, 8}
- B. {8}
- C. {1, 2, 3, 4, 5, 6, 8}
- D. {1, 3, 5}
Factorize: \(16x^4 – y^4\)
- A. \((2x - y)(2x + y)(4x^2 + y^2)\)
- B. \((2x + y)(2x + y)(4x^2 + y^2)\)
- C. \((2x - y)(2x - y)(4x^2 + y^2)\)
- D. \((2x - y)(2x + y)(4x^2 - y^2)\)
In a group of 500 people, 350 people can speak English, and 400 people can speak French. Find how many people can speak both languages.
- A. 750
- B. 850
- C. 250
- D. 150
Find the value of y, if log (y + 8) + log (y – 8) = 2log 3 + 2log 5
- A. y = ±5
- B. y = ±10
- C. y = ±17
- D. y = ±13