Question Library
Browse, filter, and study verified past examination questions with step-by-step mathematical reasoning.
Searching 18,000+ Questions...
Sifting topics, KaTeX formulas & verified solutions
Showing 5881–5895 of 14893 verified questions
Sort by:
Mathematics
UTME / JAMB 2009
Plane Geometry, Polygons & Circle Theorems
Solution
If \(p=\sqrt{\frac{rs^3}{t}}\), express r in terms of p, s and t?
A
\(\frac{p^2 t}{s^3}\)
B
\(\frac{p^3 t}{s^3}\)
C
\(\frac{p^3 t}{s^2}\)
D
\(\frac{p^ t}{s^3}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(p =\sqrt{\frac{rs^3}{t}}\)
= p\(^2 =\frac{rs^3}{t}\)
tp\(^2\) = rs\(^3\)
r = \(\frac{p^2 t}{s^3}\)
Source: Myschool Past Questions Archive (Record #9314)
Mathematics
UTME / JAMB 2009
Algebraic Expressions, Polynomials & Factorisation
Solution
A polynomial in x whose roots are 4/3 and -3/5 is?
A
15x2 - 11x – 12
B
15x2 + 11x – 12
C
12x2 - x – 12
D
12x2 + 11x – 15
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
If 4/3 and -3/5 are roots of a polynomial
Imply x = 4/3 and - 3/5
3x = 4 and 5x = -3
∴3x-4 = 0 and 5x+3 = 0 are factors
(3x-4)(5x+3) = 0 product of the factors
15x2 + 9x – 20x – 12 = 0 By expansion
15x2 - 11x – 12 = 0
Source: Myschool Past Questions Archive (Record #9315)
Mathematics
UTME / JAMB 2009
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
Which of the following equations represent the graph above?
Attached Figure / Diagram
A
y = 2+7x+4x2
B
y = 2-7x+4x2
C
y = 2+7x-4x2
D
y = 2-7x-4x2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x = -2 and x = 1/4
x = -2 and 4x = 1
x+2 and 4x-1
(x+2)(4x-1) = 0
4x2 - x + 8x -2 = 0
4x2 + 7x – 2 = 0 but y intercept is positive. Multiply the equation by -1
-4x2 - 7x + 2 = 0
∴y = 2 – 7x – 4x2
Source: Myschool Past Questions Archive (Record #9316)
Mathematics
UTME / JAMB 2009
Variations
Solution
W is directly proportional to U. If W = 5 when U = 3, find U when W = 2/7
A
6/35
B
10/21
C
21/10
D
35/6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
W ∝ U
W = KU
K = \(\frac{W}{U}\)
K = \(\frac{5}{3}\)
W = \(\frac{5}{3}U\)
\(\frac{2}{7} = \frac{5}{3}\)U
U = \(\frac{2}{7} \times \frac{3}{5}\)
U = \(\frac{6}{35}\)
Source: Myschool Past Questions Archive (Record #9317)
Mathematics
UTME / JAMB 2009
Linear, Simultaneous & Quadratic Equations
Solution
Determine the value of x for which (x\(^2\) - 1) > 0?
A
x 1
B
-1 < x < 1
C
x > 0
D
x < -1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x\(^2\) > 0
(x+1)(x-1) > 0
x = 1 or -1
x < -1 or x > 1
Source: Myschool Past Questions Archive (Record #9318)
Mathematics
UTME / JAMB 2009
Inequalities & Linear Programming
Solution
Find the range of values of x for which 3x - 7 \(\leq\) 0 and x + 5 > 0?
A
-5 < x < \(\frac{7}{3}\)
B
-5 \(\leq\) x \(\leq\) \(\frac{7}{3}\)
C
-5 < x \(\leq\) \(\frac{7}{3}\)
D
-5 \(\leq\) x < \(\frac{7}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3x - 7 \(\leq\) 0 and x + 5 > 0
3x \(\leq\) 7 and x > -5
x \(\leq\) \(\frac{7}{3}\)
∴ Range -5 < x \(\leq\) \(\frac{7}{3}\)
Source: Myschool Past Questions Archive (Record #9319)
Mathematics
UTME / JAMB 2009
Sequences & Series (AP & GP)
Solution
The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35, ... is?
A
n(3n - 0.5)
B
n(3n + 2)
C
n(3n + 2.5)
D
n(3n + 5)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
a = 5, d = 6, n = n
Sn = n/2(2a + (n-1)d)
= n/2(2(5) + (n-1)6)
= n/2(10 + 6n-6)
= n/2(6n+4)
= 6n2/2 + 4n/2
= 32 + 2n
= n(3n + 2)
Source: Myschool Past Questions Archive (Record #9320)
Mathematics
UTME / JAMB 2009
Sequences & Series (AP & GP)
Solution
Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3,.....\)
A
10
B
9
C
10/9
D
9/10
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
a = 1, r =\(\frac{9}{10}\)
S\(_n\) = \(\frac{a}{1 - r}\)
S\(_n\) = \(\frac{1}{1-\frac{9}{10}}\)
= 1\(\div \frac{1}{10}\)
=1\(\times \frac{10}{1}\) = 10
Source: Myschool Past Questions Archive (Record #9321)
Mathematics
UTME / JAMB 2009
Binary Operations, Matrices & Determinants
Solution
If m * n = n - (m+2) for any real number m and n find the value of 3*(-5)?
A
-6
B
-8
C
-10
D
-12
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
m * n = n - (m+2)
= -5 - (3+2)
= -5-5
= -10
Source: Myschool Past Questions Archive (Record #9322)
Mathematics
UTME / JAMB 2009
Binary Operations, Matrices & Determinants
Solution
A binary operation ⊗ defined on the set of integers is such that m⊗n = m + n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0?
A
-5/4
B
-5/6
C
zero
D
5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(m \otimes n = m + n + mn\)
Let the inverse of -5 be n.
\(\therefore -5 \otimes n = 0\)
\(-5 + n + (-5n) = 0\)
\(n - 5n = 5 \implies -4n = 5\)
\(n = -\frac{5}{4}\)
Source: Myschool Past Questions Archive (Record #9323)
Mathematics
UTME / JAMB 2009
Plane Geometry, Polygons & Circle Theorems
Solution
If Q is\( \left[ \begin{array}{cc}
9 & -2 \\
-7 & 4 \\
\end{array} \right]\) , then |Q| is?
A
-50
B
-22
C
22
D
50
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Q = \( \left[ \begin{array}{ccc}
9 & -2 \\
-7 & 4 \\
\end{array} \right]\)
|Q| = 9x4 - (-2 x -7)
= 36 - 14
= 22
Source: Myschool Past Questions Archive (Record #9324)
Mathematics
UTME / JAMB 2009
Plane Geometry, Polygons & Circle Theorems
Solution
If P \(=\left[\begin{array}{cc}x+3 & x+2\\
x+1 & x-1\end{array}\right]\) evaluate x if |P| = -10
A
-5
B
-2
C
2
D
5
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical 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
Source: Myschool Past Questions Archive (Record #9325)
Mathematics
UTME / JAMB 2009
Trigonometry, Elevation & Bearings
Solution
Find the acute angle between the straight lines y = x and y = √3x
A
15o
B
30o
C
45o
D
60o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
y = x, Gradient (m1) = 1
y = √3x gradient (m2) = √3
\(tan\theta = \frac{m_2 - m_1}{1+m_2 m_1}\\
tan\theta = \frac{\sqrt{3}-1}{1+\sqrt{3}\times 1}\\
=\frac{1.73 -1 }{1+1.73}=
\frac{0.73}{2.73}=0.268\)
θ = Tan-1 (0.268)
= 15o
Source: Myschool Past Questions Archive (Record #9326)
Mathematics
UTME / JAMB 2009
Plane Geometry, Polygons & Circle Theorems
Solution
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
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Sum 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
Source: Myschool Past Questions Archive (Record #9327)
Mathematics
UTME / JAMB 2009
Plane Geometry, Polygons & Circle Theorems
Solution
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
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Locus of a particle which moves in the first quadrant so that it is equidistant from the lines
X = 0 and Y = 0 are the x and y axes as the lines bisecting the angle between x and y axes.
Source: Myschool Past Questions Archive (Record #9332)