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Mathematics
UTME / JAMB 1983
Number and Numeration
Solution
Correct each of the numbers 59.81798 and 0.0746829 to three significant figures and multiply them, giving your answer to three significant figures
A
4.46
B
4.48
C
4.47
D
4.49
E
4.50
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
59.81798 = 59.8(3 s.f)
0.0746829 = 0.0747
59.8 x 0.0747 = 4.46706
= 4.47(3s.f)
Source: Myschool Past Questions Archive (Record #32467)
Mathematics
UTME / JAMB 1983
Number and Numeration
Solution
If a rod of length 250cm is measured as 255cm long in error, what is the percentage error in the measurement?
A
55
B
10
C
5
D
4
E
2
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
% error = \(\frac{\text{Actual error}}{\text{real value}}\) x 100
= \(\frac{5}{250}\) x 100
= 2%
Source: Myschool Past Questions Archive (Record #32468)
Mathematics
UTME / JAMB 1983
Number and Numeration
Solution
In a sample survey of a University Community, the following table shows the percentage distribution of the number of members per house hold
\(\begin{array}{c|c} \text{No. of members per household} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & \text{Total} \\ \hline \text{No. of households} & 3 & 12 & 15 & 28 & 21 & 10 & 7 & 4 & 100\end{array}\)
What is the median?
A
4
B
3
C
5
D
4.5
E
None
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} x & f \\\hline 1 & 3\\ 2 & 13\\3 & 15\\ 4 & 28\\ 5 & 21\\ 6 & 10\\ 7 & 7\\ 8 & 4\end{array}\)
Median is half of total frequency = 50th term
4 falls in the range = 4
Source: Myschool Past Questions Archive (Record #32474)
Mathematics
UTME / JAMB 1983
Number and Numeration
Solution
On a square paper of length 2.524375cm is inscribed square diagram of length 0.524375cm. Find the area of the paper not covered by the diagram. correct to 3 significant figures.
A
6.00cm2
B
6.10cm2
C
6cmv
D
6.09cm2
E
4.00cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area of the paper = area of square = L x B or S2
where s = S x k
Area of the paper = (2.524)2
area of the diagram = (0.524)2
area not covered = (2.524)2 - (0.524)2
= 6.370576 - 0.274576
= 6.096
= 6.10cm2 (2 s.f)
Source: Myschool Past Questions Archive (Record #32475)
Mathematics
UTME / JAMB 1983
Number and Numeration
Solution
Simplify \(\sqrt[3]{\frac{27a^{-9}}{8}}\).
A
\(\frac{9a^2}{2a^3}\)
B
\(\frac{3}{2a^3}\)
C
\(\frac{2}{3a^2}\)
D
\(\frac{3a^2}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\sqrt[3]{\frac{27a ^{-9}}{8}}\) = \(\frac{3a^{-3}}{2}\)
= \(\frac{3}{2}\) x \(\frac{1}{a^3}\)
= \(\frac{3}{2a^3}\)
Source: Myschool Past Questions Archive (Record #32476)
Mathematics
UTME / JAMB 1983
Number and Numeration
Diagram
Solution
In a class of 60 pupils, the statistical distribution of the numbers of pupils offering Biology, History, French, Geography and Additional mathematics is as shown in the pie chart. How many pupils offer Additional Mathematics?
Attached Figure / Diagram
A
15
B
10
C
18
D
12
E
20
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(2x - 24)^\circ + (3x - 18)^\circ + (2x + 12)^\circ + (x + 12)^\circ + x^\circ = 360^\circ
9x = 360^\circ + 18^\circ
x = \(\frac{378}{9}\)
= 42^\circ, if x = 42^\circ, then add maths = \(\frac{2x - 42}{360}\) x 60
= \(\frac{2 \times 42 - 24}{360}\) x 60
= \(\frac{84 - 24}{6}\)
= 10
Source: Myschool Past Questions Archive (Record #32765)
Mathematics
UTME / JAMB 1983
Number and Numeration
Diagram
Solution
PQRS isa cyclic quadrilateral which PQ = PS. PT is a tangent to the circle and PQ makes an angle of 50o with the tangent as shown in the figure. What is the size of QRS?
Attached Figure / Diagram
A
50o
B
40o
C
110o
D
80o
E
100o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
< PSQ = < QPT = 50º
In \(\triangle\) PQS, PS = PQ (given) base angles of an isosceles triangle.
< QRS = 180º - < SPQ (opp
Source: Myschool Past Questions Archive (Record #32771)
Mathematics
UTME / JAMB 1983
Number and Numeration
Diagram
Solution
In the figure, PQR is a straight line. Find the values of x and y
Attached Figure / Diagram
A
x = 22.5o, y = 33.75o
B
x = 15o, y = 52.5o
C
x = 22.5o, y = 45.0o
D
x = 56.25o, y = 11.5o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{3}{2}\)x + 3y + 45^\circ = 180^\circ
3x + 6y + 90^\circ = 360^\circ
3x + 6y = 270.......(i) x 2,
5x + y + y = 180^\circ
5x + 2y = 180^\circ ... (ii) x 6
6x + 12y = 540 ... (iii)
30x + 12y = 1080 ... (iv)
eqn(iv) - eqn(iii)
24x = 540
x = 22.5^\circ and y = 33.75^\circ
Source: Myschool Past Questions Archive (Record #32773)
Mathematics
UTME / JAMB 1983
Number and Numeration
Diagram
Solution
In the diagram, if PS = SR and PQ||SQ, what is the size of PQR?
Attached Figure / Diagram
A
25o
B
50o
C
55o
D
65o
E
75o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
o = 180
o
Source: Myschool Past Questions Archive (Record #32774)
Mathematics
UTME / JAMB 1982
Number and Numeration
Solution
Rationalize the expression \(\frac{1}{\sqrt{2} + \sqrt{5}}\)
A
\(\frac{1}{3}\)(\(\sqrt{5} - \sqrt{2}\)
B
\(\frac{\sqrt{2}}{3}\) + \(\frac{\sqrt{5}}{5}\)
C
\(\sqrt{2} - \sqrt{5}\)
D
5(\(\sqrt{2} - \sqrt{5}\)
E
\(\frac{1}{3}\)(\(\sqrt{2} - \sqrt{5}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{1}{\sqrt{2} + \sqrt{5}}\)
\(\frac{1}{\sqrt{2} + \sqrt{5}} \times \frac{(\sqrt{2} - \sqrt{5})}{(\sqrt{2} - \sqrt{5})}\)
= \(\frac{\sqrt{2} - \sqrt{5}}{2 - 5}\)
= \(\frac{\sqrt{2} - \sqrt{5}}{-3}\)
= \(\frac{1}{3} (\sqrt{5} - \sqrt{2})\)
Source: Myschool Past Questions Archive (Record #32481)
Mathematics
UTME / JAMB 1982
Number and Numeration
Solution
Simplify 3 - 2 \(\div\) \(\frac{4}{5}\) + \(\frac{1}{2}\)
A
1\(\frac{3}{4}\)
B
-1
C
1\(\frac{3}{10}\)
D
1
E
1\(\frac{9}{10}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
3 - 2 \(\div\) (\(\frac{4}{5}\)) + \(\frac{1}{2}\)
3 - (2 x \(\frac{5}{4}\)) + \(\frac{1}{2}\) = 3 - \(\frac{10}{4}\) + \(\frac{1}{2}\)
= 3 - \(\frac{5}{2}\) + \(\frac{1}{2}\)
= \(\frac{6 - 5 + 1}{2}\)
= \(\frac{2}{2}\)
= 1
Source: Myschool Past Questions Archive (Record #32482)
Mathematics
UTME / JAMB 1982
Number and Numeration
Solution
If N560.70 is shared in the ratio 7 : 2 : 1, what is the smallest share?
A
N392.49
B
N56.70
C
N113.40
D
N112.14
E
N56.07
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
7 + 2 + 1 = 10
\(\frac{1}{10}\) x 560.70
= N56.07
Source: Myschool Past Questions Archive (Record #32483)
Mathematics
UTME / JAMB 1982
Number and Numeration
Solution
The factors of 6x - 5 - x2 are
A
-(x + 3)(x + 2)
B
(x + 5)(x + 1)
C
(x - 5)(1 - x)
D
(x + 1)(x + 5)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
6x - 5 - x2 = (-1)(-x2 - 5 + 6x)
= x2 - 6x + 5
= (x - 5)(x - 1)
-(x - 1) = 1 - x
= (x - 5)(1 - x)
Source: Myschool Past Questions Archive (Record #32485)
Mathematics
UTME / JAMB 1982
Number and Numeration
Solution
Write the equation 2 log2x - x log2(1 + y) = 3 in a form not involving logarithms
A
2x(1 + y) = 3
B
2x - x(1 + y) = 8
C
x2 = 8(1 + y)x
D
x2 - x(1 + y) = 8
E
x2 - (1 + y)2 = 8
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2log2 x - x log2 (1 + y) = 3
log2 \(\frac{x^2}{(1 + y)^x}\) = 3
= \(\frac{x^2}{(1 + y)^x}\)
= 23
= 8
= x2 = 8(1 + y)x
Source: Myschool Past Questions Archive (Record #32488)
Mathematics
UTME / JAMB 1982
Number and Numeration
Solution
Find \(\alpha\) and \(\beta\) such that x\(\frac{3}{8}\) x y\(\frac{-6}{7}\) x (\(\frac{y^{\frac{9}{7}}}{x^{\frac{45}{8}}}\))\(\frac{1}{9}\) = \(\frac{x^{\alpha}}{y^{\beta}}\)
A
\(\alpha\) = 1, \(\beta\) = \(\frac{5}{7}\)
B
\(\alpha\)= 1, \(\beta\) = -\(\frac{5}{7}\)
C
\(\alpha\)= \(\frac{3}{5}\), \(\beta\) = -6
D
\(\alpha\)= 1, \(\beta\) = -\(\frac{3}{5}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x\(\frac{3}{8}\) x y\(\frac{-6}{7}\) x (\(\frac{y^{\frac{9}{7}}}{x^{\frac{45}{8}}}\))\(\frac{1}{9}\) = \(\frac{y^{\alpha}}{y^{\beta}}\)
x\(\frac{3}{8}\) x y\(\frac{-6}{7}\) x y\(\frac{1}{7}\) = x\(\alpha\)
= x\(\frac{3}{8}\) + \(\frac{5}{8}\) + y\(\frac{6}{7}\) + \(\frac{1}{7}\)
= x\(\alpha\)y\(\beta\)
x1y\(\frac{-5}{7}\) = x\(\alpha\)y\(\beta\)
\(\alpha\) = 1, \(\beta\) = \(\frac{5}{7}\)
Source: Myschool Past Questions Archive (Record #32489)