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Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
If \(f(x) = 3x^3 + 4x^2 + x - 8\), what is the value of f(-2)?
A
-24
B
30
C
-18
D
-50
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(f(x) = 3x^3 + 4x^2 + x - 8\)
\(f(-2) = 3(-2)^3 + 4(-2)^2 + (-2) - 8\)
= \(-24 + 16 - 2 - 8\)
= -18
Source: Myschool Past Questions Archive (Record #55037)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
Solve for x in \(\frac{4x - 6}{3} \leq \frac{3 + 2x}{2}\)
A
\(x \leq 1\frac{1}{2}\)
B
\(x \leq \frac{21}{2}\)
C
\(x \geq \frac{21}{2}\)
D
\(x \geq 1\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{4x - 6}{3} \leq \frac{3 + 2x}{2}\)
2(4x - 6) \(\leq\) 3(3 + 2x)
8x - 12 \(\leq\) 9 + 6x
8x - 6x \(\leq\) 9 + 12
2x \(\leq\) 21
\(x \leq \frac{21}{2}\)
Source: Myschool Past Questions Archive (Record #55038)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.
A
12
B
8
C
9
D
16
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(p \propto \frac{1}{\sqrt{q}}\)
\(\implies p = \frac{k}{\sqrt{q}}\)
when p = 3, q = 16.
\(3 = \frac{k}{\sqrt{16}}\)
\(k = 3 \times 4 = 12\)
\(\therefore p = \frac{12}{\sqrt{q}}\)
when p = 4,
\(4 = \frac{12}{\sqrt{q}} \implies \sqrt{q} = \frac{12}{4}\)
\(\sqrt{q} = 3 \implies q = 3^2 \)
\(q = 9\)
Source: Myschool Past Questions Archive (Record #55053)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
Tade bought 200 mangoes at 4 for ₦2.50. 30 out of the mangoes got spoilt and the remaining were sold at 2 for ₦2.40. Find the percentage profit or loss.
A
43.6% loss
B
35% profit
C
63.2% profit
D
28% loss
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
200 mangoes at 4 for N2.50
\(\implies\) Total cost price = \(\frac{200}{4} \times N 2.50\)
= N 125.00
Since 30 mangoes got spoilt \(\implies\) Left over = 200 - 30
= 170 mangoes
170 mangoes at 2 for N 2.40
\(\implies\) Total selling point = \(\frac{170}{2} \times N 2.40\)
= N 204.00
Profit : N (204.00 - 125.00) = N 79.00
% profit = \(\frac{79}{125} \times 100%\)
= 63.2% profit.
Source: Myschool Past Questions Archive (Record #55055)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
The simple interest on ₦8550 for 3 years at x% per annum is ₦4890. Calculate the value of x to the nearest whole number.
A
19%
B
20%
C
25%
D
16.3%
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
S.I = \(\frac{PRT}{100}\)
\(\implies\) N 4890 = \(\frac{8550 \times 3 \times x}{100}\)
\(x = \frac{4890 \times 100}{8550 \times 3}\)
\(x = 19.06%\)
\(x \approxeq 19%\)
Source: Myschool Past Questions Archive (Record #55062)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
Simplify 81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)
A
\(\frac{2}{5}\)
B
\(\frac{3}{5}\)
C
\(\frac{5}{2}\)
D
\(\frac{5}{3}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)
= \((\sqrt[4]{81})^{-3} \times \sqrt{25} \times (\sqrt[5]{243})^2\)
= \(\frac{5 \times 3^2}{3^{3}}\)
= \(\frac{5}{3}\)
Source: Myschool Past Questions Archive (Record #55069)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
Find the value of \(\frac{(0.5436)^3}{0.017 \times 0.219}\) to 3 significant figures.
A
46.2
B
43.1
C
534
D
431
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(\frac{(0.5436)^3}{0.017 \times 0.219}\)
= \(\frac{0.16063}{0.017 \times 0.219}\)
= 43.1 (to 3 s.f)
Source: Myschool Past Questions Archive (Record #55075)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs.
A
50 units per sec
B
35 units per sec
C
22 units per sec
D
13 units per sec
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(s = (4t + 3)(t - 2)\)
\(\frac{\mathrm d s}{\mathrm d t} = (4t + 3)(1) + (t - 2)(4)\)
= \(4t + 3 + 4t - 8\)
= 8t - 5
\(\frac{\mathrm d s}{\mathrm d t} (t = 5 secs) = 8(5) - 5\)
= 40 - 5
= 35 units per sec
Source: Myschool Past Questions Archive (Record #55079)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
The weight of a day-old chick was measured to be 0.21g. If the actual weight of the chick is 0.18g, what was the percentage error in the measurement?
A
15.5%
B
18.2%
C
14.8%
D
16.7%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Actual weight = 0.18g
Error = 0.21g - 0.18g
= 0.03g
% error = \(\frac{0.03}{0.18} \times 100%\)
= 16.7%
Source: Myschool Past Questions Archive (Record #55083)
Mathematics
UTME / JAMB 2019
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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)