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Mathematics
UTME / JAMB 2019
Fractions, Decimals, Percentages & Approximations
Solution
Evaluate \((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\) correct to 1 decimal place.
A
1.3
B
2.5
C
4.6
D
3.2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\)
= \((\frac{600}{32} \div \frac{2000}{84})^{-1}\)
= \((\frac{600}{32} \times \frac{84}{2000})^{-1}\)
= \((\frac{63}{80})^{-1}\)
= \(\frac{80}{63}\)
= 1.3 (to 1 decimal place)
Source: Myschool Past Questions Archive (Record #55085)
Mathematics
UTME / JAMB 2019
Indices, Logarithms & Surds
Solution
If 2\(^{x + y}\) = 16 and 4\(^{x - y} = \frac{1}{32}\), find the values of x and y.
A
x = \(\frac{3}{4}\), y = \(\frac{11}{4}\)
B
x = \(\frac{3}{4}\), y = \(\frac{13}{4}\)
C
x = \(\frac{2}{3}\), y = \(\frac{4}{5}\)
D
x = \(\frac{2}{3}\), y = \(\frac{13}{4}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2\(^{x + y}\) = 16 ; 4\(^{x - y}\) = \(\frac{1}{32}\).
\(\implies 2^{x + y} = 2^4\)
\(x + y = 4 ... (1)\)
\(2^{2(x - y)} = 2^{-5} \)
\(2^{2x - 2y} = 2^{-5}\)
\(\implies 2x - 2y = -5 ... (2)\)
Solving the equations (1) and (2) simultaneously, we have
x = \(\frac{3}{4}\) and y = \(\frac{13}{4}\)
Source: Myschool Past Questions Archive (Record #55231)
Mathematics
UTME / JAMB 2019
Fractions, Decimals, Percentages & Approximations
Simplify \(\frac{0.0839 \times 6.381}{5.44}\) to 2 significant figures.
A
0.2809
B
2.51
C
3.5
D
0.098
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #55277)
Mathematics
UTME / JAMB 2019
Linear, Simultaneous & Quadratic Equations
Solution
Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30
A
x = 3 or 7, y = 12 or 8
B
x = 6 or 1, y = 11 or 5
C
x = 2 or 5, y = 15 or 6
D
x = 1 or 5, y = 10 or 7
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3x + y = 21 ... (i);
xy = 30 ... (ii)
From (ii), \(y = \frac{30}{x}\). Putting the value of y in (i), we have
3x + \(\frac{30}{x}\) = 21
\(\implies\) 3x\(^2\) + 30 = 21x
3x\(^2\) - 21x + 30 = 0
3x\(^2\) - 15x - 6x + 30 = 0
3x(x - 5) - 6(x - 5) = 0
(3x - 6)(x - 5) = 0
3x - 6 = 0 \(\implies\) x = 2.
x - 5 = 0 \(\implies\) x = 5.
If x = 2, y = \(\frac{30}{2}\) = 15;
If x = 5, y = \(\frac{30}{5}\) = 6.
Source: Myschool Past Questions Archive (Record #55279)
Mathematics
UTME / JAMB 2019
Trigonometry, Elevation & Bearings
Solution
Points X and Y are 20km North and 9km East of point O, respectively. What is the bearing of Y from X? Correct to the nearest degree.
A
24°
B
56°
C
127°
D
156°
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\tan \theta = \frac{9}{20} = 0.45\)
\(\theta = \tan^{-1} (0.45) \)
= 24.23^\circ
\(\therefore\) The bearing of Y from X = 180^\circ - 24.23^\circ
= 155.77^\circ
= 156^\circ (to the nearest degree)
Source: Myschool Past Questions Archive (Record #55282)
Mathematics
UTME / JAMB 2019
Algebraic Expressions, Polynomials & Factorisation
Solution
If \(P = (\frac{Q(R - T)}{15})^{\frac{1}{3}}\), make T the subject of the formula.
A
\(T = \frac{15R - Q}{P^3}\)
B
\(T = R - \frac{15P^3}{Q}\)
C
\(T = \frac{R - 15P^3}{Q}\)
D
\(T = \frac{R + P^3}{15Q}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(P = (\frac{Q(R - T)}{15})^{\frac{1}{3}}\)
\(P^3 = \frac{Q(R - T)}{15}\)
\(Q(R - T) = 15P^3\)
\(R - T = \frac{15P^3}{Q}\)
\(T = R - \frac{15P^3}{Q}\)
Source: Myschool Past Questions Archive (Record #55288)
Mathematics
UTME / JAMB 2019
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, O is the centre of the circle ABC, < ABO = 26^\circ and < BOC = 130^\circ. Calculate < AOC.
Attached Figure / Diagram
A
26°
B
13°
C
80°
D
102°
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
< BAC = \(\frac{130}{2}\) (angle subtended at the centre)
< BAC = 65^\circ
Also, x = 26^\circ (theorem)
y = 65^\circ - 26^\circ = 39^\circ
< AOC = 180^\circ - (39^\circ + 39^\circ)
= 102^\circ
Source: Myschool Past Questions Archive (Record #55366)
Mathematics
UTME / JAMB 2019
Plane Geometry, Polygons & Circle Theorems
Solution
Each of the interior angles of a regular polygon is 140^\circ. Calculate the sum of all the interior angles of the polygon.
A
1080°
B
1260°
C
2160°
D
1800°
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Since each interior angle = 140^\circ;
Each exterior angle = 180^\circ - 140^\circ = 40^\circ
Number of sides of the polygon = \(\frac{360^\circ}{40^\circ}\)
= 9
Sum of angles in the polygon = 140^\circ x 9
= 1260^\circ
Source: Myschool Past Questions Archive (Record #55367)
Mathematics
UTME / JAMB 2019
Fractions, Decimals, Percentages & Approximations
Solution
A man bought a car newly for ₦1,250,000. He had a crash with the car and later sold it at the rate of ₦1,085,000. What is the percentage gain or loss of the man?
A
43.7% loss
B
13.2% gain
C
13.2% loss
D
43.7% gain
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Cost price of the car = N 1,250.00
Selling price = N 1,085.00
Loss = N (1250 - 1085)
= N 165.00
% loss = \(\frac{165}{1250} \times 100%\)
= 13.2% loss
Source: Myschool Past Questions Archive (Record #55368)
Mathematics
UTME / JAMB 2019
Mensuration (Areas, Perimeters & Volumes)
Solution
If the volume of a frustrum is given as \(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\), find \(\frac{\mathrm d V}{\mathrm d R}\).
A
\(\frac{\pi h}{3} (2R + r)\)
B
\(2R + r + \frac{\pi h}{3}\)
C
\(\frac{\pi h}{3} (2R^2 + r + 2r)\)
D
\(\frac{2R^2}{3} \pi h\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\)
\(V = \frac{\pi R^2 h}{3} + \frac{\pi Rr h}{3} + \frac{\pi r^2 h}{3}\)
\(\frac{\mathrm d V}{\mathrm d R} = \frac{2 \pi R h}{3} + \frac{\pi r h}{3}\)
= \(\frac{\pi}{3} (2R + r)\)
Source: Myschool Past Questions Archive (Record #55369)
Mathematics
UTME / JAMB 2019
Plane Geometry, Polygons & Circle Theorems
Solution
Express \((0.0439 \div 3.62)\) as a fraction.
A
\(\frac{21}{100}\)
B
\(\frac{21}{1000}\)
C
\(\frac{12}{1000}\)
D
\(\frac{12}{100}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\((0.0439 \div 3.62)\)
= 0.01213
\(\approxeq\) 0.012
= \(\frac{12}{1000}\)
Source: Myschool Past Questions Archive (Record #55370)
Mathematics
UTME / JAMB 2019
Indices, Logarithms & Surds
Solution
If \(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\), find the value of x.
A
x = -4
B
x = 2
C
x = -2
D
x = 4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\)
\((5^2)^{(1 - x)} \times 5^{(x + 2)} \div (5^{-3})^x = (5^4)^{-1}\)
\(5^{2 - 2x} \times 5^{x + 2} \div 5^{-3x} = 5^{-4}\)
\(5^{(2 - 2x) + (x + 2) - (-3x)} = 5^{-4}\)
Equating bases, we have
\(2 - 2x + x + 2 + 3x = -4\)
\(4 + 2x = -4 \implies 2x = -4 - 4\)
\(2x = -8\)
\(x = -4\)
Source: Myschool Past Questions Archive (Record #55371)
Mathematics
UTME / JAMB 2019
Fractions, Decimals, Percentages & Approximations
Solution
A bricklayer charges ₦1,500 per day for himself and ₦500 per day for his assistant. If a two bedroom flat was built for ₦95,000 and the bricklayer worked 10 days more than his assistant, how much did the assistant receive?
A
N20,000
B
N28,000
C
N31,200
D
N41,000
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Let the number of days worked by the assistant = t
\(\therefore\) The bricklayer worked (t + 10) days.
1500(t + 10) + 500(t) = N 95,000
1500t + 15,000 + 500t = N 95,000
2000t = N 95,000 - N 15,000
2000t = N 80,000
t = 40 days
\(\therefore\) The assistant worked for 40 days and received N (500 x 40)
= N 20,000
Source: Myschool Past Questions Archive (Record #55372)
Mathematics
UTME / JAMB 2019
Plane Geometry, Polygons & Circle Theorems
Solution
Find the equation of the locus of a point A(x, y) which is equidistant from B(0, 2) and C(2, 1)
A
4x + 2y = 3
B
4x - 3y = 1
C
4x - 2y = 1
D
4x + 2y = -1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Since A(x, y) is the point of equidistance between B and C, then
AB = AC
(AB)\(^2\) = (AC)\(^2\)
Using the distance formula,
(x - 0)\(^2\) + (y - 2)\(^2\) = (x - 2)\(^2\) + (y - 1)\(^2\)
x\(^2\) + y\(^2\) - 4y + 4 = x\(^2\) - 4x + 4 + y\(^2\) - 2y + 1
x\(^2\) - x\(^2\) + y\(^2\) - y\(^2\) + 4x - 4y + 2y = 5 - 4
4x - 2y = 1
Source: Myschool Past Questions Archive (Record #55373)
Mathematics
UTME / JAMB 2019
Fractions, Decimals, Percentages & Approximations
Solution
A factory worker earns ₦50,000 per month out of which he spends 15% on his children's education, ₦13,600 on Food, 3% on electricity and uses the rest for his personal purpose. How much does he have left?
A
N21,850
B
N18,780
C
N27,400
D
N32,500
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Education = \(\frac{15}{100} \times N 50,000\)
= N 7,500
Food = N 13,600
Electricity = \(\frac{3}{100} \times N 50,000\)
= N 1,500
Leftover : N (50,000 - (7,500 + 13,600 + 1,500))
= N 27,400
Source: Myschool Past Questions Archive (Record #55374)