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Mathematics
UTME / JAMB 2019
Statistics
Diagram
Solution
The histogram above represents the number of candidates who did Further Mathematics examination in a school. How many candidates scored more than 40?
Attached Figure / Diagram
A
100
B
79
C
150
D
90
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Number of students that scored above 40 = 55 + 45 + 30 + 15 + 5
= 150 students.
Source: WAEC / JAMB / NECO Classroom Archive (Record #55453)
Mathematics
WAEC / WASSCE 2019
Measures of Location (Mean, Median, Mode)
Solution
8, 18, 10,14, 18, 11, 13, 14, 13, 17, 15, 8, 16, and 13
The following are scores obtained by some students in a test. How many students scored above the mean score?
A
10
B
9
C
8
D
7
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Mean = \(\frac{8 + 18 + 10 + 14 + 18 + 11 + 13 + 14 + 13 + 17 + 15 + 8 + 16 + 13}{14}\)
Mean = \(\frac{188}{14}\)
Mean = 13.4
Number above the mean is 7
Source: WAEC / JAMB / NECO Classroom Archive (Record #57395)
Mathematics
WAEC / WASSCE 2019
Probability
Solution
A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colours?
A
\(\frac{2}{3}\)
B
\(\frac{3}{5}\)
C
\(\frac{7}{20}\)
D
\(\frac{12}{25}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(\(\frac{2}{5} \times \frac {3}{5}) + (\frac{3}{5} \times \frac{2}{5})\)
\(\frac{6}{25} + \frac{6}{25} = \frac{12}{25}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #57331)
Mathematics
UTME / JAMB 2019
Algebra
Solution
Make q the subject of the formula in the equation \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)
A
\(q = \frac{b^2(mn - a^2)}{a^2 p}\)
B
\(q = \frac{m^2 n - a^2}{p^2}\)
C
\(q = \frac{mn - 2b^2}{a^2}\)
D
\(q = \frac{b^2 (n^2 - ma^2)}{n}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)
\(\frac{mn}{a^2} - 1 = \frac{pq}{b^2}\)
\(\frac{mn - a^2}{a^2} = \frac{pq}{b^2}\)
\(pq = \frac{b^2 (mn - a^2)}{a^2}\)
\(q = \frac{b^2(mn - a^2)}{a^2 p}\)
Source: Myschool Past Questions Archive (Record #54942)
Mathematics
UTME / JAMB 2019
Geometry and Trigonometry
Solution
The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78^\circ. Find the height of the tree correct to the nearest whole number.
A
148m
B
382m
C
282m
D
248m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\tan 78 = \frac{h}{60}\)
\(h = 60 \tan 78\)
\(h = 60 \times 4.705 = 282.27m\)
\(\approxeq\) 282m to the nearest whole number.
Source: Myschool Past Questions Archive (Record #54944)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
A binary operation \(\otimes\) is defined by \(m \otimes n = mn + m - n\) on the set of real numbers, for all m, n \(\in\) R. Find the value of 3 \(\otimes\) (2 \(\otimes\) 4).
A
6
B
25
C
15
D
18
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(m \otimes n = mn + m - n\)
3 \(\otimes\) (2 \(\otimes\) 4)
2 \(\otimes\) 4 = 2(4) + 2 - 4 = 6
3 \(otimes\) 6 = 3(6) + 3 - 6 = 15
Source: Myschool Past Questions Archive (Record #54945)
Mathematics
UTME / JAMB 2019
Geometry and Trigonometry
Solution
Age in years
7
8
9
10
11
No of pupils
4
13
30
44
9
The table above shows the number of pupils in a class with respect to their ages. If a pie chart is constructed to represent the age, the angle corresponding to 8 years old is
A
48.6°
B
56.3°
C
46.8°
D
13°
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total number of pupils : 4 + 13 + 30 + 44 + 9 = 100
The number of 8 - year olds = 13
The angle represented by the 8-year olds on the pie chart = \(\frac{13}{100} \times 360^\circ\)
= 46.8^\circ
Source: Myschool Past Questions Archive (Record #54946)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
In a class of 50 students, 40 students offered Physics and 30 offered Biology. How many offered both Physics and Biology?
A
42
B
20
C
70
D
54
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
n(Total) = 50
n(Physics) = 40
n(Biology) = 30
Let n(Physics and Biology) = x
n(Physics only) = 40 -x
n(Biology only) = 30 - x
40 - x + 30 - x + x = 50
70 - x = 50
x = 20
Source: Myschool Past Questions Archive (Record #54947)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
Rationalize \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)
A
\(-5 - 2\sqrt{6}\)
B
\(-5 + 3\sqrt{2}\)
C
\(5 - 2\sqrt{3}\)
D
\(5 + 2\sqrt{6}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)
= \((\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}})(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}})\)
= \(\frac{2 + \sqrt{6} + \sqrt{6} + 3}{2 - \sqrt{6} + \sqrt{6} - 3}\)
= \(\frac{5 + 2\sqrt{6}}{-1}\)
= \(- 5 - 2\sqrt{6}\)
Source: Myschool Past Questions Archive (Record #54951)
Mathematics
UTME / JAMB 2019
Geometry and Trigonometry
Diagram
Solution
Find the length of the chord |AB| in the diagram shown above.
Attached Figure / Diagram
A
4.2 cm
B
4.3 cm
C
3.2 cm
D
3.4 cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Length of chord = \(2r \sin (\frac{\theta}{2})\)
= \(2(3) \sin (\frac{68}{2})\)
= \(6 \sin 34\)
= \(6 \times 0.559\)
= 3.354 cm \(\approxeq\) 3.4 cm
Source: Myschool Past Questions Archive (Record #54955)
Mathematics
UTME / JAMB 2019
Geometry and Trigonometry
Solution
Given \(\sin 58^\circ = \cos p^\circ\), find p.
A
48°
B
58°
C
32°
D
52°
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\sin \theta = \cos (90 - \theta)\)
\(\sin \theta = \cos (90 - 58)\)
= \(\cos 32\)
Source: Myschool Past Questions Archive (Record #54956)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
\(\frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}}\)
A
\(\frac{31}{50}\)
B
\(\frac{20}{31}\)
C
\(\frac{31}{20}\)
D
\(\frac{50}{31}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}}\)
\(\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4}\)
= \(\frac{5}{6}\)
\(\frac{1}{4} + \frac{3}{5} - \frac{1}{3} = \frac{15 + 36 - 20}{60}\)
= \(\frac{31}{60}\)
\(\therefore \frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}} = \frac{5}{6} \div \frac{31}{60}\)
= \(\frac{5}{6} \times \frac{60}{31}\)
= \(\frac{50}{31}\)
Source: Myschool Past Questions Archive (Record #54958)
Mathematics
UTME / JAMB 2019
Number and Numeration
If \(6x^3 + 2x^2 - 5x + 1\) divides \(x^2 - x - 1\), find the remainder.
A
9x + 9
B
2x + 6
C
6x + 8
D
5x - 3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #54960)
Mathematics
UTME / JAMB 2019
Statistics and Probability
Solution
If a fair coin is tossed 3 times, what is the probability of getting at least two heads?
A
\(\frac{2}{3}\)
B
\(\frac{4}{5}\)
C
\(\frac{2}{5}\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The outcomes are {HHH, HHT, HTT, HTH, THH, THT, TTH, TTT}
P(at least two heads) = \(\frac{4}{8}\)
= \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #54961)
Mathematics
UTME / JAMB 2019
Number and Numeration
Solution
In how many ways can the word MATHEMATICIAN be arranged?
A
6794800 ways
B
2664910 ways
C
6227020800 ways
D
129729600 ways
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
MATHEMATICIAN = 13 letters with 2M, 3A, 2T, 2I.
Hence, the word MATHEMATICIAN can be arranged in \(\frac{13!}{2! 3! 2! 2!}\)
= 129729600 ways
Source: Myschool Past Questions Archive (Record #54962)