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Mathematics
UTME / JAMB 1978
Indices, Logarithms & Surds
Solution
The vectors a and b are given in terms of two perpendicular units vectors i and j on a plane by a = 2i - 3j, b = -i + 2j. Find the magnitude of the vector a + 3b
A
2
B
4
C
\(\sqrt{10}\)
D
35
E
2.2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
a = 2i - 3j - 3i + 6j
= -i + 3j
= \(\sqrt{5 \times 2}\)
= \(\sqrt{10}\)
Source: Myschool Past Questions Archive (Record #32726)
Mathematics
UTME / JAMB 1978
Fractions, Decimals, Percentages & Approximations
Solution
Add the same number to the numerator and denominator of \(\frac{3}{18}\). If the resulting fraction is \(\frac{1}{2}\), then the number added is
A
13
B
14
C
15
D
12
E
11
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let x be the no. \(\frac{3 + x}{
Source: Myschool Past Questions Archive (Record #32727)
Mathematics
UTME / JAMB 1978
Algebraic Expressions, Polynomials & Factorisation
Solution
The smallest number such that when it is divided by 8 has a remainder of 6 and when it is divided by 9, has a remainder of 7 is
A
387
B
493
C
502
D
441
E
634
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Possible multiples of 8 and 9 = 72, 144, 216, 288, 360, 432, 576, 648.
\(\frac{387}{8}\) has remainder = 3; \(\frac{387}{9}\) has remainder 0.
\(\frac{493}{8}\) has remainder 5; \(\frac{493}{9}\) has remainder 7.
\(\frac{502}{8}\) has remainder 6; \(\frac{502}{9}\) has remainder 7.
\(\frac{441}{8}\) has remainder 1; \(\frac{441}{9}\) has remainder 0.
\(\frac{634}{8}\) has remainder 2; \(\frac{634}{9}\) has remainder 4.
Hence 502 is the answer.
Source: Myschool Past Questions Archive (Record #32728)
Mathematics
UTME / JAMB 1978
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure, DE//BC: DB//FE: DE = 2cm, FC = 3cm, AE = 4cm. Determine the length of EC.
Attached Figure / Diagram
A
4cm
B
6cm
C
3cm
D
2cm
E
1cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Angles ADE and EFC are similar,
Therefore,
= \(\frac{x}{3} = \frac{4}{2}\)
= \(\frac{x}{3} = 2\)
x = 3 x 2 = 6
Source: Myschool Past Questions Archive (Record #32729)
Mathematics
UTME / JAMB 1978
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure, AB is parallel to CD then x + y + z is
Attached Figure / Diagram
A
185o
B
200o
C
270o
D
360o
E
195o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x + y + z = 360^\circ (angles at a point)
Source: Myschool Past Questions Archive (Record #32730)