Year :
2009
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
21 - 30 of 50 Questions
| # | Question | Ans |
|---|---|---|
| 21. |
If P \(=\left[\begin{array}{cc}x+3 & x+2\\ A. -5 B. -2 C. 2 D. 5 Detailed Solution\(P=\left[\begin{array}{cc}x+3 & x+2\\x+1 & x-1\end{array}\right]\) evaluate x if |P| = -10 (x+3)(x-1) - {(x+1)(x+2)} = -10 x2 - x + 3x - 3 - {x2 + 2x + x + 2} = -10 x2 + 2x - 3 - {x2 + 3x + 2} = -10 -x - 5 = -10 -5 + 10 = x 5 = x ∴x = 5 There is an explanation video available below. |
|
| 22. |
Find the acute angle between the straight lines y = x and y = √3x A. 15o B. 30o C. 45o D. 60o |
|
| 23. |
A regular polygon has 150º as the size of each interior angle. How many sides does it have? A. 12 B. 10 C. 9 D. 8 Detailed SolutionSum of interior angles of a polygon = each interior ∠ x n(n-2)180 = 150 x n 180n - 360 = 150n 180n-150n = 360 30n = 360 n = 360/30 n = 12 sides There is an explanation video available below. |
|
| 24. |
 In the figure above , TS//XY and XY = TY, ∠STZ = 34°, ∠TXY = 47°, find the angle marked n? A. 47o B. 52o C. 56o D. 99o Detailed Solution
XY = TY ∴y =47° base ∠s of ISCΔ But y+x+34+47 = 180 interior opposite ∠s are supplementary 47 + x + 34 + 47 = 180 x + 128= 180 x = 180- 128 x = 52° There is an explanation video available below. |
|
| 25. |
If the hypotenuse of a right-angled isosceles triangle is 2cm. What is the area of the triangle? A. 1/√2 cm2 B. 1 cm2 C. √2 cm2 D. 2√2 cm2 Detailed Solution
2x\(^2\) = 4 x\(^2\) = 4/2 x\(^2\) = 2 x = +/-√2 Area of Δ = 1/2bh = 1/2 x √2 x √2 = 2/2 = 1 cm\(^2\) There is an explanation video available below. |
|
| 26. |
A chord drawn 5 cm away from the center of a circle of radius 13 cm. Calculate the length of the chord? A. 7cm B. 9cm C. 12cm D. 24cm Detailed Solution
x\(^2\) + 25 = 169 x\(^2\) = 144 x = √ 144 = 12 Length of the chord AB = 2x 2\(\times\)12= 24cm There is an explanation video available below. |
|
| 27. |
Find the radius of a sphere whose surface area is 154 cm\(^2\)? A. 7.00 cm B. 3.50 cm C. 3.00 cm D. 1.75 cm |
|
| 28. |
Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x = 0 and y = 0 (where k is a constant)? A. x + y = 0 B. x - y = 0 C. x + y + k = 0 D. x - y - k = 0 Detailed Solution
X = 0 and Y = 0 are the x and y axes as the lines bisecting the angle between x and y axes. There is an explanation video available below. |
|
| 29. |
What is the locus of the mid-point of all the chords of length 6cm with circle of radius 5cm and with center O? A. A circle of radius 4 cm and the center 0 B. The perpendicular bisector of the chords C. A straight line passing through 0 D. A circle of radius 6 cm and with center 0 Detailed Solution
x\(^2\) + 9 = 25 x\(^2\) = 25 – 9 x\(^2\) = 16 x = √ 16 = 4 cm ∴ The locus is a circle of radius 4 cm with the center O There is an explanation video available below. |
|
| 30. |
What is the value of p if the gradient of the line joining (-1,p) and (p, 4) is \(\frac{2}{3}\)? A. -2 B. -1 C. 1 D. 2 |
| 21. |
If P \(=\left[\begin{array}{cc}x+3 & x+2\\ A. -5 B. -2 C. 2 D. 5 Detailed Solution\(P=\left[\begin{array}{cc}x+3 & x+2\\x+1 & x-1\end{array}\right]\) evaluate x if |P| = -10 (x+3)(x-1) - {(x+1)(x+2)} = -10 x2 - x + 3x - 3 - {x2 + 2x + x + 2} = -10 x2 + 2x - 3 - {x2 + 3x + 2} = -10 -x - 5 = -10 -5 + 10 = x 5 = x ∴x = 5 There is an explanation video available below. |
|
| 22. |
Find the acute angle between the straight lines y = x and y = √3x A. 15o B. 30o C. 45o D. 60o |
|
| 23. |
A regular polygon has 150º as the size of each interior angle. How many sides does it have? A. 12 B. 10 C. 9 D. 8 Detailed SolutionSum of interior angles of a polygon = each interior ∠ x n(n-2)180 = 150 x n 180n - 360 = 150n 180n-150n = 360 30n = 360 n = 360/30 n = 12 sides There is an explanation video available below. |
|
| 24. |
In the figure above , TS//XY and XY = TY, ∠STZ = 34°, ∠TXY = 47°, find the angle marked n? A. 47o B. 52o C. 56o D. 99o Detailed Solution
XY = TY ∴y =47° base ∠s of ISCΔ But y+x+34+47 = 180 interior opposite ∠s are supplementary 47 + x + 34 + 47 = 180 x + 128= 180 x = 180- 128 x = 52° There is an explanation video available below. |
|
| 25. |
If the hypotenuse of a right-angled isosceles triangle is 2cm. What is the area of the triangle? A. 1/√2 cm2 B. 1 cm2 C. √2 cm2 D. 2√2 cm2 Detailed Solution
2x\(^2\) = 4 x\(^2\) = 4/2 x\(^2\) = 2 x = +/-√2 Area of Δ = 1/2bh = 1/2 x √2 x √2 = 2/2 = 1 cm\(^2\) There is an explanation video available below. |
| 26. |
A chord drawn 5 cm away from the center of a circle of radius 13 cm. Calculate the length of the chord? A. 7cm B. 9cm C. 12cm D. 24cm Detailed Solution
x\(^2\) + 25 = 169 x\(^2\) = 144 x = √ 144 = 12 Length of the chord AB = 2x 2\(\times\)12= 24cm There is an explanation video available below. |
|
| 27. |
Find the radius of a sphere whose surface area is 154 cm\(^2\)? A. 7.00 cm B. 3.50 cm C. 3.00 cm D. 1.75 cm |
|
| 28. |
Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x = 0 and y = 0 (where k is a constant)? A. x + y = 0 B. x - y = 0 C. x + y + k = 0 D. x - y - k = 0 Detailed Solution
X = 0 and Y = 0 are the x and y axes as the lines bisecting the angle between x and y axes. There is an explanation video available below. |
|
| 29. |
What is the locus of the mid-point of all the chords of length 6cm with circle of radius 5cm and with center O? A. A circle of radius 4 cm and the center 0 B. The perpendicular bisector of the chords C. A straight line passing through 0 D. A circle of radius 6 cm and with center 0 Detailed Solution
x\(^2\) + 9 = 25 x\(^2\) = 25 – 9 x\(^2\) = 16 x = √ 16 = 4 cm ∴ The locus is a circle of radius 4 cm with the center O There is an explanation video available below. |
|
| 30. |
What is the value of p if the gradient of the line joining (-1,p) and (p, 4) is \(\frac{2}{3}\)? A. -2 B. -1 C. 1 D. 2 |