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Mathematics
UTME / JAMB 1986
Fractions, Decimals, Percentages & Approximations
Solution
An open rectangular box externally measures 4m x 3m x 4m. Find the total cost of painting the box externally if it costs N2.00 to paint one square meter
A
N96.00
B
N112.00
C
N136.00
D
N160.00
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total surface area(s) = 2(4 x 3) + 2(4 x 4)
= 2(12) + 2(16)
= 24 + 32
= 56cm2
1m2 costs N2.00
∴ 56m∴ will cost 56 x N2.00
= N112.00
Source: Myschool Past Questions Archive (Record #32172)
Mathematics
UTME / JAMB 1986
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Of the nine hundred students admitted in a university in 1979, the following was the distribution by state: Anambrs 185, Imo 135, Kaduna 90, Kwara 110, Ondo 155, Oyo 225. In a pie chart drawn to represent this distribution, The angle subtended at the centre by anambra is
A
50o
B
65o
C
74o
D
88o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Anambra = \(\frac{185}{900}\) x \(\frac{360}{1}\)
= 74o
Source: Myschool Past Questions Archive (Record #32173)
Mathematics
UTME / JAMB 1986
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119
A
131
B
125
C
123
D
120
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Arrange in ascending order
89, 100, 108, 119, |120, 130|, 131, 131, 141, 161
Median = \(\frac{120 + 130}{2}\)
= 125
Source: Myschool Past Questions Archive (Record #32174)
Mathematics
UTME / JAMB 1986
Permutations, Combinations & Probability
Solution
A man kept 6 black, 5 brown and 7 purple shirts in a drawer. What is the probability of his picking a purple shirt with his eyes closed?
A
\(\frac{1}{7}\)
B
\(\frac{11}{18}\)
C
\(\frac{7}{18}\)
D
\(\frac{7}{11}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Prob. of purple shirt is \(\frac{7}{18}\)
Source: Myschool Past Questions Archive (Record #32177)
Mathematics
UTME / JAMB 1986
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The table below gives the scores of a group of students in a Mathematical test.
\(\begin{array}{c|c} Scores & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline Frequency & 2 & 4 & 7 & 14 & 12 & 6 & 4 & 1\end{array}\)
If the mode in m and the number of students who scored 4 or less is s. What is (s, m)?
A
(27, 4)
B
(14,4)
C
(13,4)
D
(4,4)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
M = mode = the number having the highest frequency = 4
S = Number of students with 4 or less marks
= 14 + 7 + 4 + 2
= 27
∴ (M,S) = (27, 4)
Source: Myschool Past Questions Archive (Record #32178)
Mathematics
UTME / JAMB 1986
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PQ and RS are chords of a circle centre O which meet at T outside the circle. If TP = 24cm. TQ = 8cm and TS = 12cm, find TR.
Attached Figure / Diagram
A
16cm
B
14cm
C
12cm
D
8cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
PT x QT = TR x TS
24 x 8 = TR x 12
TR = \(\frac{24 \times 8}{12}\)
= = 16cm
Source: Myschool Past Questions Archive (Record #32833)
Mathematics
UTME / JAMB 1986
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The figure is a solid with the trapezium PQRS as its uniform cross-section. Find its volume
Attached Figure / Diagram
A
120m2
B
576m3
C
816m3
D
1056m3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of solid = cross section x H
Since the cross section is a trapezium
= \(\frac{1}{2} (6 + 11) \times 12 \times 8\)
= 6 x 17 x 8 = 816m3
Source: Myschool Past Questions Archive (Record #32835)
Mathematics
UTME / JAMB 1986
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
PQ and PR are tangents from P to a circle centre O as shown in the figure. If QRP = 34o, find the angle marked x
Attached Figure / Diagram
A
34o
B
56o
C
68o
D
112o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
From the circle centre 0, if PQ & PR are tangents from P and QRP = 34o
Then the angle marked x i.e. QOP
34o x 2 = 68o
Source: Myschool Past Questions Archive (Record #32836)
Mathematics
UTME / JAMB 1986
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure, \(\bigtriangleup\)PQT is isosceles. PQ = QT, SRQ = 35o, TPQ = 20o and PQR is a straight line.Calculate TSR
Attached Figure / Diagram
A
20o
B
55o
C
75o
D
140o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Given \(\bigtriangleup\) isosceles PQ = QT, SRQ = 35o
TPQ = 20o
PQR = is a straight line
Since PQ = QT, angle P = angle T = 20o
Angle PQR = 180o - (20 + 20) = 140o
TQR = 180o - 140o = 40o < on a straight line
QSR = 180o - (40 + 35)o = 105o
TSR = 180o - 105o
= 75o
Source: Myschool Past Questions Archive (Record #32838)
Mathematics
UTME / JAMB 1986
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
in the figure, PQ||ST, RS||UV. If PQR = 35o and QRS = 65o, find STV
Attached Figure / Diagram
A
30o
B
35o
C
55o
D
65o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Draw a line WX through R and parallel to \(\overline{PQ}\) and \(\overline{ST}\) as shown in the diagram above
X\(\widehat{R}\)Q = P\(\widehat{Q}\)R = 35º
X\(\widehat{R}\)Q + X\(\widehat{R}\)S = 65º
35 + x = 65
x = 65 - 35 = 30º
R\(\widehat{S}\)T = 30º (Alternative angle)
S\(\widehat{T}\)V = 30º (Alternative angle)
Source: Myschool Past Questions Archive (Record #32841)
Mathematics
UTME / JAMB 1986
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The people in a city with a population of 0.9 million were grouped according to their ages. Use the diagram to determine the number of people in the 15 - 29 years group
Attached Figure / Diagram
A
29 x 104
B
26 x 104
C
16 x 104
D
13 x 104
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
15 - 29 years is represented by 104o
Number of people in the group is \(\frac{104}{360}\) x 0.9m
= 260000 = 26 x 104
Source: Myschool Past Questions Archive (Record #32845)
Mathematics
UTME / JAMB 1986
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In \(\bigtriangleup\)XYZ, determine the cosine of angle Z.
Attached Figure / Diagram
A
\(\frac{3}{39}\)
B
\(\frac{29}{36}\)
C
\(\frac{14}{5}\)
D
\(\frac{7}{5}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
cos z = \(\frac{y^2 + x^2 -z^2}{2yx}\)
= \(\frac{9 + 36 - 16}{2(3)(6)}\)
= \(\frac{29}{36}\)
Source: Myschool Past Questions Archive (Record #32859)
Mathematics
UTME / JAMB 1985
Indices, Logarithms & Surds
Solution
Find x if log\(_9\)x = 1.5
A
72.0
B
27.0
C
36.0
D
3.5
E
24.5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If log\(_9\)x = 1.5,
9\(^1.5\) = x
9^\(\frac{3}{2}\) = x
(\sqrt9)\(^3\) = 3
∴ x = 27
Source: WAEC / JAMB / NECO Classroom Archive (Record #32213)
Mathematics
UTME / JAMB 1985
Fractions, Decimals, Percentages & Approximations
Solution
Solve the following equation \(\frac{2}{2r - 1}\) - \(\frac{5}{3}\) = \(\frac{1}{r + 2}\)
A
(\(\frac{5}{2}\), 1)
B
(5, -4)
C
(2, 1)
D
(1, \(\frac{-5}{2}\))
E
(1,-2)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{2}{2r - 1}\) - \(\frac{5}{3}\) = \(\frac{1}{r + 2}\)
\(\frac{2}{2r - 1}\) - \(\frac{1}{r + 2}\) = \(\frac{5}{3}\)
\(\frac{2r + 4 - 2r + 1}{2r - 1 (r + 2)}\) = \(\frac{5}{3}\)
\(\frac{5}{(2r + 1)(r + 2)}\) = \(\frac{5}{3}\)
5(2r - 1)(r + 2) = 15
(10r - 5)(r + 2) = 15
\(10r^2\) + 20r - 5r - 10 = 15
\(10r^2\) + 15r = 25
\(10r^2\) + 15r - 25 = 0
\(2r^2\) + 3r - 5 = 0
(\(2r^2 + 5r)\)(2r + 5) = r(2r + 5) - 1(2r + 5)
(r - 1)(2r + 5) = 0
r = 1 or \(\frac{-5}{2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #32229)
Mathematics
UTME / JAMB 1985
Linear, Simultaneous & Quadratic Equations
Solution
Solve the simultaneous equations 2x - 3y + 10, 10x - 6y = - 5
A
x = 2\(\frac{1}{2}\), y = 5
B
x = \(\frac{1}{2}\), y = \(\frac{3}{2}\)
C
x = 2\(\frac{1}{4}\), y = 3\(\frac{1}{2}\)
D
x = 2\(\frac{1}{3}\), y = 3\(\frac{1}{2}\)
E
x = 2\(\frac{1}{3}\), y = 2\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
2x - 3y = - 10; 10x - 6y = -5
2x - 3y = -10 x 2
10x - 6y = -5
4x - 6y = -20 .......(i)
10x - 6y = -5.......(ii)
eqn(ii) - eqn(1)
6x = 15
x = \(\frac{15}{6}\)
= \(\frac{5}{2}\)
x = 2\(\frac{1}{2}\)
Sub. for x in equ.(ii) 10(\(\frac{5}{2}\)) - 6y = -5
6y = 25 + 5 → 30
y = \(\frac{30}{6}\)
y = 5
Source: WAEC / JAMB / NECO Classroom Archive (Record #32230)