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Mathematics
UTME / JAMB 1979
Mensuration (Areas, Perimeters & Volumes)
Solution
An arc of circle of radius 2cm subtends an angle of 60º at the centre. Find the area of the sector
A
\(\frac{2 \pi}{3}\)cm2
B
\(\frac{\pi}{2}\)cm2
C
\(\frac{\pi}{3}\)cm2
D
\(\pi\)cm2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Area of a sector \(\frac{\theta}{360}\) x \(\pi\)r\(^2\)
= \(\frac{60^o}{360^o}\) x \(\pi\)2\(^2\)
= \(\frac{2 \pi}{3}\)cm2
Source: WAEC / JAMB / NECO Classroom Archive (Record #32676)
Mathematics
UTME / JAMB 1979
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure, PQ is parallel to SQ; QS bisects < PSQ, < PQS is 65º, and < RPS is 20º. What is the size of < PRS?
Attached Figure / Diagram
A
45o
B
35o
C
40o
D
30o
E
42o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
PSR = 65º x 2 = 130^\circ
PRS = 180º - (130º + 20º) º = 30
Source: WAEC / JAMB / NECO Classroom Archive (Record #32737)
Mathematics
UTME / JAMB 1979
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The mean of the numbers 1.2, 1.0, 0.9, 1.4, 0.8, 0.8, 1.2 and 1.1 is
A
1.5
B
0.8
C
1.0
D
1.02
E
1.05
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\frac{1.2 + 1.0 + 0.9 + 1.4 + 0.8 + 0.8 + 1.2}{8}\) = \(\frac{8.4}{8}\)
= 1.05
Source: Myschool Past Questions Archive (Record #32644)
Mathematics
UTME / JAMB 1979
Indices, Logarithms & Surds
Solution
\((1.28 \times 10^{4}) \div (6.4 \times 10^{2})\) equals
A
2 x 10-5
B
2 x 10-1
C
2 x 101
D
2 x 10-4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\((1.28 \times 10^{4}) \div (6.4 \times 10^{2})\)
= \(\frac{1.28 \times 10^{4}}{6.4 \times 10^{2}}\)
\(\equiv \frac{12.8 \times 10^{3}}{6.4 \times 10^{2}}\)
= \(2 \times 10^{1}\)
Source: Myschool Past Questions Archive (Record #32645)
Mathematics
UTME / JAMB 1979
Mensuration (Areas, Perimeters & Volumes)
Solution
If the value of \(\pi\) is taken to be \(\frac{22}{7}\), the area of a semi-circle of diameter 42m is
A
5544m2
B
1386m2
C
132m2
D
264m2
E
693m2
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\pi\) = \(\frac{22}{7}\), Diameter D = 42m
Area of a circle = \(\frac{\pi D^2}{4}\) when a diameter is given
area of a semicircle \(\frac{\pi D^2}{4}\) x \(\frac{1}{2}\)
= \(\frac{22}{7}\) x \(\frac{5541.7694}{4}\) x \(\frac{1}{2}\)
= \(\frac{11}{7} \times 441\)
= 693m\(^{2}\)
Source: Myschool Past Questions Archive (Record #32646)
Mathematics
UTME / JAMB 1979
Algebraic Expressions, Polynomials & Factorisation
Solution
(3.2)2 - (1.8)2 equals
A
7.0
B
2.56
C
13.48
D
2.0
E
0.07
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(3.2)2 - (1.8)2 = (3.2 + 1.8)(3.2 - 1.8)
= 5 x 1.4
= 7
Source: Myschool Past Questions Archive (Record #32647)
Mathematics
UTME / JAMB 1979
Indices, Logarithms & Surds
Solution
In \(\bigtriangleup\)PQR, PQ = 10cm, QR = 8cm and RP = 6cm, the perpendicular RS is drawn from R to PQ. Find the length of RS
A
4cm
B
32cm
C
\(\frac{30}{7}\)
D
\(\frac{40}{7}\)
E
4.8cm
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Cos Q = \(\frac{r^2 + p^2 - q^2}{2rp}\)
= \(\frac{10^2 + 8^2 - 6^2}{2(10)(8)}\)
= \(\frac{164 - 36}{160}\)
= \(\frac{128}{160}\)
= 0.8
Q = Cos-1 o.8
= 37o x rep. from rto = 1
x = 8 sin 37o
x = 4.8cm
Source: Myschool Past Questions Archive (Record #32648)
Mathematics
UTME / JAMB 1979
Fractions, Decimals, Percentages & Approximations
Solution
After getting a rise of 15%, a man's new monthly salary is N345. How much per month did he earn before the increase?
A
N330
B
N396.75
C
N300
D
N293.25
E
N360
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let x represent his monthly salary before increase 15% of
x = 345
% profit = (100 + 15)%
= 115%
\(\frac{115}{100}\)x = 345
115x = 34500
x = N300.00
Source: Myschool Past Questions Archive (Record #32649)
Mathematics
UTME / JAMB 1979
Number Bases & Modular Arithmetic
Solution
In base ten, the number 101101 (base 2) equals
A
15
B
4
C
45
D
32
E
90
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(101101)2 \(\begin{array}{c|c} 2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^o\\ \hline 1 & 0 & 1 & 1 & 0 & 1\end{array}\)
= 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 2o
= 32 + 0 + 8 + 4 + 0 + 1
= (45)\(_{10}\)
Source: Myschool Past Questions Archive (Record #32650)
Mathematics
UTME / JAMB 1979
Fractions, Decimals, Percentages & Approximations
Solution
The annul profits of a transport business were divided between the partners A and B in the ratio 3 : 5. If B received N3000 more than A, the total profit was
A
N5000
B
N1800
C
N12000
D
N24000
E
N8000
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
A : B = 3 : 5
Total ratio = 3 + 5 = 8
Let rept, the total profit, A receives \(\frac{3x}{8}\)
\(\frac{5x}{8}\) - \(\frac{3}{x}\) = 3000
\(\frac{5x}{8}\) - \(\frac{3x}{8}\) = 3000
= \(\frac{2x}{8}\)
= 3000
2x = 2400
x = 1200
N12,000
Source: Myschool Past Questions Archive (Record #32651)
Mathematics
UTME / JAMB 1979
Variations
Solution
x is directly proportional to y and inversely proportional to z. If x = 9 when y = 24 and z = 8, what is the value of x when y = 5 and z = 6?
A
\(\frac{5}{6}\)
B
11
C
3\(\frac{3}{5}\)
D
2\(\frac{1}{2}\)
E
1\(\frac{1}{5}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x \(\alpha\) y = x \(\alpha\) \(\frac{1}{z}\)
x \(\alpha\) \(\frac{1}{z}\)
x = k \(\frac{y}{z}\)
k = \(\frac{xz}{y}\) = \(\frac{9 \times 8}{24}\)
= 3
x = \(\frac{xz}{y}\)
= \(\frac{3 \times 5}{6}\)
= \(\frac{15}{6}\)
= \(\frac{5}{2}\)
= 2\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #32652)
Mathematics
UTME / JAMB 1979
Plane Geometry, Polygons & Circle Theorems
Solution
The solution of the equation x2 - 2x = 8 is
A
x = 0 or 2
B
x = -2 or 4
C
x = 2
D
x = -4
E
x = 2 or 4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x2 - 2x = 8 = 8
x2 - 2x - 8 = 0
(x2 - 4x) + (2x - 8) = 0
When x + 2 = 0
x = -2, when x - 4 = 0
x = 4
-2 or 4
Source: Myschool Past Questions Archive (Record #32653)
Mathematics
UTME / JAMB 1979
Plane Geometry, Polygons & Circle Theorems
Solution
A trader goes to Ghana for y days with y cedis. For the first x days, he spends X cedis per day. The amount he has to spend per day for the rest of his stay is
A
\(\frac{y(y - x)}{y - x}\) cedis
B
\(\frac{Yy - Xx)}{y - x}\) cedis
C
\(\frac{Y - Xy)}{y - x}\) cedis
D
\(\frac{Y - X}{y - x}\) cedis
E
\(\frac{Y - Xx}{y - x}\) cedis
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
The amount he has to spend per day for the rest of his stay is \(\frac{Y - Xx}{y - x}\) cedis
Source: Myschool Past Questions Archive (Record #32654)
Mathematics
UTME / JAMB 1979
Linear, Simultaneous & Quadratic Equations
Solution
Multiply (3x + 5y + 4z) by (2x - 3y + z)
A
6x2 + xy - 15y2 + 4z2 + 11xz - 7yz
B
6x2 + 3xy - 15y2 + 4z2
C
6x2 + 3xy - y2 + 4z2
D
6x2 + 3xy - 15y + z2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(3x + 5y + 4z)(2x - 3y + z)
6x2 + 9xy + 3x2 + 10xy - 15y2 + 5yz + 8xz - 12yz + 4z2
= 6x2 + xy - 15y2 + 4z2 + 11xz - 7yz
Source: Myschool Past Questions Archive (Record #32655)
Mathematics
UTME / JAMB 1979
Mensuration (Areas, Perimeters & Volumes)
Solution
A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board?
A
20sq.cm
B
100sq.cm
C
25sq.cm
D
16sq.cm
E
36sq.cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Perimeter of a square = 4(S) where S is each side of the square
Perimeter = 20(given)
4S = 20
S = \(\frac{20}{4}\) = 5
Area S\(^2\) = 5\(^2\) = 25
Source: Myschool Past Questions Archive (Record #32656)