JAMB UTME - Mathematics - 2001
Question 1 Report
Answer Details
Question 2 Report
If \(x = \frac{y}{2}\), evaluate \(\left(\frac{x^3}{y^3} + \frac{1}{2}\right) \div \left(\frac{1}{2} - \frac{x^2}{y^2}\right)\)
Answer Details
Question 3 Report
A sector of a circle of radius 7.2cm which subtends an angle of \(300^\circ\) at the centre is used to form a cone. What is the radius of the base of the cone?
Answer Details
Question 4 Report
The histogram above shows the distribution of passengers in taxis of a certain motor park. How many taxis have more than 4 passengers
Answer Details
Question 5 Report
Answer Details
A = P + I
I = (P.T.R)/100 = (P x 5 x 2)/100 = 10P/100 = P/10
But A = P + I,
=> 5500 = P + (P/10)
=> 55000 = 10P + P
=> 55000 = 11P
Thus P = 55000/11 = ₦5,000
Question 6 Report
Answer Details
Question 7 Report
Answer Details
This implies that Team P and Q wins
∴ P(P wins) = 1/2
P(Q wins) = 1/2
∴ P(game ends in a draw) = 1/2*1/2 = 1/4
Question 8 Report
Answer Details
Question 9 Report
The bar chart above shows different colours of passing a particular point of a certain street in two minutes. What fraction of the total number of cars
Answer Details
Question 10 Report
Answer Details
Question 11 Report
Answer Details
y = 4 - x2 and y = 2x + 1
=> 4 - x2 = 2x + 1
=> x2 + 2x - 3 = 0
(x+3)(x-1) = 0
thus x = -3 or x = 1.
Integrating x2 + 2x - 3 from (-3, to 1) w.r.t x will give 31/3 = 10(1/3)
Question 12 Report
The mean score is
Answer Details
(12 + 35 + 16 + 77 + 26 + 8)/20
174/20 = 8.7
Question 13 Report
Answer Details
Question 14 Report
Answer Details
Question 15 Report
Answer Details
Question 16 Report
Given that \(p = 1 + \sqrt{2}\) and \(q = 1 - \sqrt{2}\), evaluate \(\frac{(p^2 - q^2)}{2pq}\).
Answer Details
Question 17 Report
Answer Details
Question 18 Report
m2 + n2 = 29
m + n = 7
Answer Details
m + n = 7 ............(2)
From (2),
m = 7 - n
but m2 + n2 = 29, substituting;
(7-n)2 + n2 = 29
49 - 14n + n2 + n2 = 29
=> 2n2 -14n + 20 = 0
Thus n2 -7n + 10 = 0
Factorizing;
(n-5)(n-2) = 0
n - 5 = 0, => n = 5
n - 2 = 0, => n = 2.
When n = 5,
m + n = 7, => m = 2,
When n = 2,
m + n = 7, => m = 5.
Thus (m,n) = (5,2) and (2,5)
Question 19 Report
Answer Details
Question 20 Report
Answer Details
Question 21 Report
Find the value of \( \theta \) in the diagram
Answer Details
3t2 = 2t2 - 2t2 cos? = 2t2(1 - cos? )
1 - cos? = 3t22t2 = 32
cos = 1 - 32=?12
? = cos-1(-12 ) = 120? and 240?
N.B 0 ? ? 360
Question 22 Report
| ⊗ | k | l | m |
| k | l | m | k |
| l | m | k | l |
| m | k | l | m |
The identity element with respect to the multiplication shown in the table above is
Answer Details
Question 23 Report
Answer Details
Collect like terms: 4x2 + 20x + 25 - 9y2
(2x + 5)(2x + 5) - 9y2
(2x + 5)2 - (3y)2
(2x - 3y +5)(2x + 3y + 5)
Question 24 Report
Answer Details
Question 25 Report
In the figure above, PQR is a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, ?SQR is 75\(^{\circ}\) and ?QPT is 25\(^{\circ}\). Calculate the value of ?RST.
Answer Details
?PTQ = 25? (base ?s of isosceles ?)
In ? QSR,
?RQS = ?QPT + ?QTP
(Extr = sum of interior opposite ?s)
?RQS = 25 + 25
= 50?
Also in ? QSR,
75 + ?RQS + ?QSR = 180?
(sum of ?s of ?)
?75 + 50 + ?QSR = 180
125 + ?QSR = 180
?QSR = 180 - 125
?QSR = 55?
But ?QSR and ?RST are the same
?RST = 55?
Question 26 Report
The graph shows the cumulative frequency of the distribution of masses of fertilizer for 48 workers in one institution. Which of the following gives the inter-quartile range?
Answer Details
Question 27 Report
Answer Details
Question 28 Report
Answer Details
Question 29 Report
A cylindrical tank has a capacity of 3080 m3. What is the depth of the tank if the diameter of its base is 14 m?
(Take pi = 22/7)
Answer Details
Question 30 Report
The bar chart shows different colours of cars passing a particular point of a certain street in two minutes. What fraction of the cars is yellow
Answer Details
Thus, the fraction of the total numbers that are yellow is 325
Question 32 Report
Answer Details
To divide the given expression, we can use the long division method.
ax^2 - 26x + 156a - 216b
___________________________________
ax | ax^3 + 3x^2 - 26x^2 + 156ax - 216bx^2 - 24ax + 108
-ax^3
-----
3x^2 - 216bx^2
3x^2 - 3ax^2
--------------
-216bx^2 + 3ax^2
-216bx^2 + 36ax^2
------------------
-33ax^2 + 156a - 216bx^2 - 24ax + 108
-33ax^2 + 33bx^2
------------------
156a - 33ax^2 - 24ax + 108
156a - 33ax^2 - 156ax + 33ax
-------------------------
-24ax + 108
-24ax + 24bx
-------------
108 - 24bx
108 - 2ax
--------
2ax - 24bx + 108
Therefore, the quotient is ax - 2 with a remainder of 2ax - 24bx + 108.
Hence, the answer is ax - 2.
Question 33 Report
Answer Details
Square of 11 = 121
Question 34 Report
Answer Details
=0.14 x 0.275 = 0.0385 Approx. 0.039
Question 35 Report
Answer Details
Question 36 Report
Triangle SPT is the solution of the linear inequalities
Answer Details
2y - x - 2 ≤ 0
2y ≤ 2 + x
y ≤ 2/2 + x/2
y ≤ 1 + 1/2x
y + 2x + 2 ≥ 0,
y ≥ -2 -2x
∴ the solution of the inequalities
2y - x - 2 ≤ 0,
y + 2x + 2 ≥ 0
= -2 ≤ x ≤ -1
Question 37 Report
P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
Answer Details
Question 38 Report
Answer Details
Cos 30 = x/8
x = 8 cos 30 = 8√3cm
Question 39 Report
The distribution of colours of beads in a bowl is given above. What is the probability that a bead selected at random will be blue or white?
Answer Details
= 1+2+4+5+3
=15
Number of blue beads = 1
P(Blue beads) = 1/15
Numbers of white beads = 4
P(white beads) = 4/15
∴P(Blue of white beads)
= P(Blue) + P(White)
= 1/15 + 4/15
= 5/15
= 1/3
Question 40 Report
Answer Details
Question 41 Report
Answer Details
Question 42 Report
Answer Details
Question 43 Report
Answer Details
x cos 30 = 5, => x = 5√3
Coordinates of P = -5, 3, 0
Coordinates of Q = 0, 5
Gradient of PQ = (y2 - y1) (X2 - X1) = (5 - 0)/(0 -5√3)
= 5/5√3 = 1/√3
Equation of PQ = y - y1 = m (x -x1)
y - 0 = 1/√3 (x -(-5√3))
Thus: √3y = x + 5√3
Question 44 Report
Answer Details
Thus int. angle = 2x
But sum of int + ext = 180 (angle of a straight line).
2x + x = 180
3x = 180
x = 180/3 = 60
Each ext angle = 360/n
=> 60 = 360/n
n = 360/60 = 6
Question 45 Report
Answer Details
Question 46 Report
Answer Details
So that perimeter of square = 4p
4 x (p/4) = p.
Question 49 Report
Answer Details
Question 50 Report
Answer Details
