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Mathematics
UTME / JAMB 1999
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
If the standard deviation of the set of numbers 3, 6, x, 7, 5 is 2, find the least possible value of x.
A
2
B
3
C
4
D
6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Numbers: 3, 6, x, 7, 5
Mean = \(\frac{(21 + x)}{5}\)
Standard deviation = 2, so the sum of squared deviations = 20.
Solving:
2x² - 21x + 27 = 0
x = 9 or x = 1.5 ≈ 2
The **least possible value of x is 1.5
Source: Myschool Past Questions Archive (Record #10417)
Mathematics
UTME / JAMB 1999
Indices, Logarithms & Surds
Diagram
Solution
Find the value of l in the frustrum above
Attached Figure / Diagram
A
5cm
B
6cm
C
7cm
D
8cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\DeltaABE and \DeltaACD are similar
therefore \(\frac{ x}{ x + 4} = \frac{3}{6}\)
6x = 3(x+4)
6x = 3x + 12
3x = 12
x = 4
In \DeltaACD; \(L^2\) = \((4+4)^2 + 6^2\)
= \(8^2 + 6^2\)
= 64 + 36
= 100
L = \(\sqrt{100}\)
= 10cm
In ABE, \((AE)^2 = 4^2 + 3^2\)
= 16 + 9
= 25
AE = 5cm
∴L = 10 - 5
= 5cm
Source: Myschool Past Questions Archive (Record #10418)
Mathematics
UTME / JAMB 1999
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
The table above shows the frequency distribution of the ages (in years) of pupils in a certain secondary school. What percentage of the total number of pupils is over 15 years but less than 21 years?
Attached Figure / Diagram
A
35%
B
45%
C
50%
D
60%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
% of those above 15 but less than 21 years
age = \(\frac{25}{50}\) x \(\frac{100}{1}\)
= 50%
Source: Myschool Past Questions Archive (Record #10420)
Mathematics
UTME / JAMB 1999
Inequalities & Linear Programming
Diagram
the shaded portion in the graph is represented by
Attached Figure / Diagram
A
y + x - x \(\leq\) 0, y - x \(\leq\) 0
B
y - x + x, 3 \(\leq\) 0, y - x \(\geq\) 0
C
y + x - 3 \(\geq\) 0, y + x \(\leq\) 0
D
y - x + x3 \(\geq\) 0, y + x \(\leq\) 0
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #33084)
Mathematics
UTME / JAMB 1999
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG, and FH are chords. If < FHG = 42º and < EFH = 34º, calculate < HEG.
Attached Figure / Diagram
A
34o
B
42o
C
52o
D
76o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
< EFH = < EGH = 34º (angles n the same segment)
< GHF = < GEF = 42º(angles in the same segment)
< FOG = 42 + 34 = 76º (exterior angle)
< FOG = < EOH = 76º (vertically opposite angle)
< EDO = 90º, < DOE = \(\frac{76}{2}\) = 38º
< HEG = 90º - 38º = 52º
Source: Myschool Past Questions Archive (Record #33085)
Mathematics
UTME / JAMB 1999
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure, PQRS is a circle with ST||RQ. Find the value of x if PT = pS
Attached Figure / Diagram
A
70o
B
55o
C
40o
D
35o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
o (sum of o - 110o = 70o
in o
2x + 70 = 180o
2x = 180o - 70o = 110o
x = \(\frac{110^o}{2}\) = 55o
Source: Myschool Past Questions Archive (Record #33086)
Mathematics
UTME / JAMB 1999
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure, TZ is tangent to the circle QPZ. Find x if TZ = 6 units and PQ = 9 units
Attached Figure / Diagram
A
3
B
4
C
5
D
6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
In \(\bigtriangleup\)WOP, b2 = r2 - (4.502...........(i)
In \(\bigtriangleup\)WOT, b\(\bigtriangleup\) + (4.5 + x)2 = a2...........(ii)
In \(\bigtriangleup\)ZOT, a2 = 62 + r2 ..........(iii)
subst. equation (iii) and (i) in eqn (ii)
r2 - (4.5)2 + (4.5 + x)2 = 36 = 20.25
= (4.5 + x)2 = \(\sqrt{56.25}\) = (4.5 + x)
= 56.25
= 4.5 + x = 7.5
x = 3.0m
x =
Source: Myschool Past Questions Archive (Record #33087)
Mathematics
UTME / JAMB 1999
Fractions, Decimals, Percentages & Approximations
Solution
The sectoral allocations to various ministries in a state budget are as follows:
Agriculture - N25,000,000.00
Education - N20,000,000.00
Women affairs - N35,000,000.00
Commercial and Industries - N20,000,000.00
Use a pie chart to represent this information. The corresponding angle to Agriculture is
A
90\(^0\)
B
72\(^0\)
C
60\(^0\)
D
45\(^0\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Total allocation = ₦25m + ₦20m + ₦35m + ₦20m = ₦100,000,000
Fraction for Agriculture = ₦25,000,000 / ₦100,000,000 = 0.25 (or 25%)
Angle for Agriculture = 0.25 \times 360^\circ = 90^\circ
Other sectors:
- Education: (20/100) \times 360^\circ = 72^\circ
- Women Affairs: (35/100) \times 360^\circ = 126^\circ
- Commercial and Industries: (20/100) \times 360^\circ = 72^\circ
Source: Myschool Past Questions Archive (Record #33088)
Mathematics
UTME / JAMB 1999
Trigonometry, Elevation & Bearings
Diagram
Solution
find the length XZ in the triangle
Attached Figure / Diagram
A
\(\sqrt{7m}\)
B
\(\sqrt{6m}\)
C
\(\sqrt{5m}\)
D
\(\sqrt{3m}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
xz2 = xy2 + yx2 - 2(xy) (yz) cos 120o
= 22 + 12 - 2(2) (1) cos 1202
= 4 + 1 - 4x - cos 60 = 5 - 4x - \(\frac{1}{2}\)
5 + 2 = 7
xz = \(\sqrt{7}\)m
Source: Myschool Past Questions Archive (Record #33089)
Mathematics
UTME / JAMB 1999
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The grades of 36 students in a class test are as shown in the pie chart. How many student has excellent?
Attached Figure / Diagram
A
7
B
8
C
9
D
12
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
degree of excellent in the pie-chart = 360o - (90o + 120o + 80o) = 360o - 290o = 70o
= 360o = 36 students
70 = \(\frac{70^o}{360^o}\) x 36 = 7
Source: Myschool Past Questions Archive (Record #33090)
English Language
UTME / JAMB 1999
Oral English: Vowel & Consonant Sounds
Solution
Choose the word that does not have the same vowel sound as the others.
A
loot
B
boot
C
rout
D
route
medium Difficulty
Verified Correct Answer: Option C
Grammar & Contextual Explanation
loot - /luːt/
boot - /buːt/
rout - /raʊt/
route - /ruːt/
Source: Myschool Past Questions Archive (Record #11090)
English Language
UTME / JAMB 1999
Oral English: Vowel & Consonant Sounds
Choose the word that does not have the same vowel sound as the others?
A
deep
B
lease
C
meet
D
lace
medium Difficulty
Verified Correct Answer: Option D
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #11091)
English Language
UTME / JAMB 1999
Oral English: Vowel & Consonant Sounds
Choose from the options the word that has the same vowel sound as the one represented by the letter(s) underlined?
Plateau
A
wanted
B
below
C
holiday
D
haunted
medium Difficulty
Verified Correct Answer: Option B
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #11093)
English Language
UTME / JAMB 1999
Oral English: Vowel & Consonant Sounds
Choose from the options the word that has the same vowel sound as the one represented by the letter(s) underlined?
Rust
A
loud
B
touch
C
bought
D
march
medium Difficulty
Verified Correct Answer: Option B
Grammar & Contextual Explanation
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #11094)
English Language
UTME / JAMB 1999
Oral English: Vowel & Consonant Sounds
Solution
Choose from the options the word that has the same vowel sound as the one represented by the letter(s) underlined?
Research
A
disturb
B
comfort
C
affair
D
carry
medium Difficulty
Verified Correct Answer: Option A
Grammar & Contextual Explanation
Research /rɪˈsəːtʃ/
disturb /dɪˈstəːb/
Source: Myschool Past Questions Archive (Record #11095)