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Mathematics
UTME / JAMB 1979
Number and Numeration
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
Number and Numeration
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)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)
A
\(\frac{12+ 4\sqrt{5 + 7} 5 + 6\sqrt{3}}{39}\)
B
\(\frac{-(24 + 18\sqrt{6} + 8\sqrt{5} + 6\sqrt{30})}{38}\)
C
\(\frac{24 + 3\sqrt{6 + 8} 5 + 6\sqrt{30}}{19}\)
D
\(\frac{-15 + 3\sqrt{5 + 18} 5 + 6\sqrt{30}}{36}\)
E
\(\frac{-(12 + 4\sqrt{5} +9\sqrt{6} + 3\sqrt{30})}{19}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Rationalize using the reciprocal of the denominator to multiply through
(i.e. Multiply both numerator and denominator using \(4 + 3\sqrt{6}\) )
Watch your signs in the course of this.
Source: Myschool Past Questions Archive (Record #32657)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\)
A
52x + 1
B
5x + 1
C
5-5
D
52
E
53
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\) = \(\frac{5^x \times 5^{2x - 2}}{5^{3x + 3}}\)
= \(\frac{5^{x + 2x - 2}}{5^{3x + 3}}\)
= \(\frac{5^{3x - 2}}{5^{3x + 3}}\)
= 5\(^{3x - 2 - 3x - 3}\)
= 5\(^{-5}\)
Source: Myschool Past Questions Archive (Record #32658)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?
A
\(\frac{44}{3}\)\(\pi\)cm3
B
12\(\pi\)cm3
C
\(\frac{38}{3}\)\(\pi\)cm3
D
\(\frac{40}{3}\)\(\pi\)cm3
E
\(\frac{32}{33}\)\(\pi\)cm3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Volume of steel ball = \(\frac{4\pi r^2}{3}\)
= \(\frac{4}{3}\) \(\pi\) x 1
= \(\frac{4 \pi}{3}\)cm3
Vol. of cylinder = \(\pi\)r2h
= \(\pi\) x 22 x 4
Vol. of water = 16\(\pi\) - \(\frac{4 \pi}{3}\)
= \(\frac{48 - 4 \pi}{3}\)
= \(\frac{44 \pi}{3}\)cm\(^3\)
Source: Myschool Past Questions Archive (Record #32659)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\)
A
\(\frac{x^2 + y^2} {(x - y)^2}\)
B
\(\frac{2y^3} {y^2 - x^2}\)
C
\(\frac{3x^2 + y^2} {(2x - y)^2}\)
D
\(\frac{x^2 + y^2} {(x^2 - y)}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x -y}\)
= \(\frac{-y^3 - y^3}{x^2 - y^2}\)
= \(\frac{2y^3}{x^2 - y^2}\)
= \(\frac{2y^3}{y^2 - x^2}\)
Source: Myschool Past Questions Archive (Record #32660)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
Simplify 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\)
A
\(\frac{1}{6}\)
B
\(\frac{13}{20}\)
C
\(\frac{11}{30}\)
D
\(\frac{9}{4}\)
E
\(\frac{5}{3}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\) = \(\frac{29}{12}\) - \(\frac{15}{8}\) x \(\frac{6}{5}\)
= \(\frac{29}{12}\) - \(\frac{9}{4}\)
= \(\frac{29 - 27}{12}\)
= \(\frac{2}{12}\)
= \(\frac{1}{6}\)
Source: Myschool Past Questions Archive (Record #32662)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
12 men complete a job in 9 days. How many men working t the same rate would be required to complete the job in 6 days?
A
24
B
18
C
12
D
9
E
8
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
12 men in 9 days,
1 day in \(12 \times 9\) men
In 6 days we have \(\frac{12 \times 9}{6}\) men
= \(\frac{108}{6}\)
= 18 men
Source: Myschool Past Questions Archive (Record #32672)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
Simplify \(\frac{1 - x^2}{x - x^2}\), where x \(\neq\) 0
A
\(\frac{1}{x}\)
B
\(\frac{1 - x}{x}\)
C
\(\frac{1 + x}{x}\)
D
\(\frac{1}{x - 1}\)
E
\(\frac{-x - 1}{1}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{1 - x^2}{x - x^2}\), where x = \(\neq\) 0
\(\frac{1^2 - x^2}{x - x^2}\)
= \(\frac{(1 + x)(1 - x)}{x(1 - x)}\)
= \(\frac{1 + x}{x}\)
Source: Myschool Past Questions Archive (Record #32674)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
A cylinder of height h and radius r is open at one end. Its surface area is
A
2\(\pi\)rh
B
\(\pi\)r2h
C
2\(\pi\)rh + \(\pi\)r2
D
2\(\pi\)rh + 2\(\pi\)r2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
A cylinder of height h ans radius r is open at one end, its surface area is 2\(\pi\)rh + \(\pi\)r2
Source: Myschool Past Questions Archive (Record #32675)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
What is log\(_7{(49^a)}\) - log\(_{10}^{(0.01)}\)?
A
\(\frac{49^a}{100}\)
B
\(\frac{a}{2}\) + 2
C
72a + 2
D
2a + 2
E
\(\frac{2a}{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
log7(49a) - log10(0.01) = log7(72)a - log10100
log772a - log101 - log10 102
= 2a - 2
= 2a + a
Source: Myschool Past Questions Archive (Record #32678)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
The size of a quantity first doubles and then increases by a further 16%. After a short time its size decreases by 16%. What is the net increases in size of the quantity?
A
\(\frac{59300}{625}\)
B
\(\frac{50900}{625}\)
C
200%
D
+100%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let x rept. the size of the quantity
2x + \(\frac{116}{100}\) x \(\frac{-84}{100}\)
= 200%
Source: Myschool Past Questions Archive (Record #32679)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
The following table relates the number of objects f corresponding to a certain size x. What is the average size of an object?
\(\begin{array}{c|c} f & 1 & 2 & 3 & 4 & 5 \\ \hline x & 1 & 2 & 4 & 8 & 16\end{array}\)
A
\(\frac{31}{15}\)
B
\(\frac{31}{5}\)
C
\(\frac{129}{5}\)
D
\(\frac{43}{5}\)
E
\(\frac{16}{5}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
F = 1, 2, 3, 4, 5
x = 1, 2, 4, 8, 16
fx = 1, 4, 12, 32, 80, 3f = 15
(average size) = \(\frac{\sum fx}{\sum f}\)
= \(\frac{129}{15}\)
= \(\frac{43}{5}\)
Source: Myschool Past Questions Archive (Record #32680)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
If y = x\(^2\) - 2x - 3, find the least value of y and the corresponding value of x
A
x = 3, y = 3
B
x = 1, y = -3
C
x = 4, y = 1
D
x = 1, y = -4
E
x = 2, y = -3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
If the graph of eqn. y = x\(^2\) - 2x - 3 is plot and drawn, the lease value of y = -4 while the corresponding value of x = 1
x = 1, y = -4
OR
\(\frac{dy}{dx}\) = 0 = 2x - 2
2x = 2
x = 1
put x = 1 in y = 2x\(^2\) - 2x - 3
y = - 4
x= 1, y = -4
Source: Myschool Past Questions Archive (Record #32681)
Mathematics
UTME / JAMB 1979
Number and Numeration
Solution
A father is now three times as old as his son. Twelve years ago he was six times as old as his son. How old are the son and the father?
A
20 and 45
B
100 and 150
C
45 and 65
D
35 and 75
E
20 and 60
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Son = x, Father = 3x, 12 yrs ago
son = x - 12, father = 3x - 12
3x - 12 = 6(x - 12)
3x - 12 = 6x - 72
3x = 60
x = 20
Source: Myschool Past Questions Archive (Record #32682)