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Mathematics
UTME / JAMB 2020
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector of cassava in a pie chart?
A
180\(^o\)
B
36\(^o\)
C
60\(^o\)
D
108\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total number of acres = 2 + 5 + 3 + 11 + 9 = 30
The angle of acres = 2 + 5 + 3 + 11 + 9 = 30
The angle of the sector for cassava in a pie chart = \(\frac{3}{30} \times 360^o = 36^o\)
Source: Myschool Past Questions Archive (Record #56858)
Mathematics
UTME / JAMB 2020
Sequences & Series (AP & GP)
Solution
Three consecutive terms of a geometric progression are give as n - 2, n and n + 3. Find the common ratio
A
\(\frac{3}{2}\)
B
\(\frac{2}{3}\)
C
\(\frac{1}{2}\)
D
\(\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{h}{n - 2} = \frac{n + 3}{n}\)
n\(^2\) = (n + 3) (n - 2)
n\(^2\) = n\(^2\) + n - 6
n\(^2\) + n - 6 - n\(^2\) = 0
n - 6 = 0
n = 6
Common ratio: \(\frac{n}{n - 2} = \frac{6}{6 - 2} = \frac{6}{4}\) = \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #56859)
Mathematics
UTME / JAMB 2020
Sets, Logic & Venn Diagrams
Solution
In a class of 40 students, 32 offer mathematics, 24 offer physics and 4 offer neither mathematics nor physics. How many offer both mathematics and physics?
A
4
B
8
C
16
D
20
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
40 = 32 - x + x + 24 + 4
40 = 60 - x
x = 60 - 40
x = 20
Source: Myschool Past Questions Archive (Record #56860)
Mathematics
UTME / JAMB 2020
Plane Geometry, Polygons & Circle Theorems
Solution
The sum of the interior angle of pentagon is 6x + 6y. Find y in terms of x.
A
y = 6 - x
B
y = 90 - x
C
y = 120 - x
D
y = 150 - x
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Sum of interior angles = (2n - 4) 90\(^o\)
For perntagon, n = 5
Sum of interior angles = 6 x 90\(^o\) = 540\(^o\)
6x + 6y = 540\(^o\)
6(x + y) = 540\(^o\)
x + y = \(\frac{540^o}{6}\) = 90\(^o\)
y = 90\(^o\)
y = 90 - x
Source: Myschool Past Questions Archive (Record #56861)
Mathematics
UTME / JAMB 2020
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group.
A
7
B
9
C
15
D
42
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x \(\frac{\sum x}{N}\)
15 = \(\frac{\sum x }{N}\)
\(\sum x\) = 15N........(i)
y = \(\frac{\sum y}{Ny} = \frac{\sum x + 45}{N + 1}\)
\(\frac{18}{1} = \frac{15N + 45}{N + 1}\)
18(N + 1) = 15N + 45
18N + 18 = 15N + 45
18N - 15N = 45 - 18
3N = 27
N = \(\frac{27}{3}\)
= 9
Source: Myschool Past Questions Archive (Record #56862)
Mathematics
UTME / JAMB 2020
Trigonometry, Elevation & Bearings
Solution
A surveyor walks 500m up a hill which slopes at an angle of 30\(^o\). Calculate the vertical height through which he rises
A
252m
B
500m
C
250m
D
255m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{h}{500}\) = sin 30\(^o\)
= 500 sin 30\(^o\)
= 500 x \(\frac{1}{2}\)
= 250m
Source: Myschool Past Questions Archive (Record #56863)
Mathematics
UTME / JAMB 2020
Indices, Logarithms & Surds
Solution
Find the non-zero positive value of x which satisfies the equation
\(\begin{bmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x \end{bmatrix}\) = 0
A
2
B
\(\sqrt{3}\)
C
\(\sqrt{2}\)
D
1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\begin{bmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x \end{bmatrix}\) = 0
To find the value of x, we will have to calculate for the determined of the given matrix and equate it to 0
x[x\(^2\) - 1] - 1[x - 0] + 0[0 - 1] = 0
x\(^3\) - x] - x + 0 = 0
x\(^3\) - x - x = 0
x\(^3\) - 2x = 0
x\(^3\) = 2x
x\(^2\) = 2
take the square root of both sides
x = \(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #56864)
Biology
UTME / JAMB 2020
Variety of Organisms & Classification of Living Things
Diagram
Solution
Use the diagram to answer the question.
The structure labelled i is
Attached Figure / Diagram
A
photosensitive
B
radiosensitive
C
chemoreceptive
D
tactile
medium Difficulty
Verified Correct Answer: Option D
Biological Concept & Syllabus Guide
The part labeled I is commonly called tactile hairs, sinus hairs, whiskers, or vibrissae. ( are the long, specialized hairs found on the face and nose of rodents like rats, etc, and other animals like pussy cats)
Source: Official Exam / Past Question Archive
Biology
UTME / JAMB 2020
Nervous, Hormonal Coordination & Sense Organs
Solution
The hormone which regulates the amount of glucose in the blood is called?
A
Adrenalin
B
Auxin
C
Insulin
D
Thyroxine
medium Difficulty
Verified Correct Answer: Option C
Biological Concept & Syllabus Guide
Insulin helps control blood glucose levels by signaling the liver and muscle and fat cells to take in glucose from the blood.
Source: Myschool Past Questions Archive (Record #56755)
Biology
UTME / JAMB 2020
Excretion & Homeostasis
Solution
Deamination occurs in the?
A
Kidney
B
Pancreas
C
Spleen
D
Liver
medium Difficulty
Verified Correct Answer: Option D
Biological Concept & Syllabus Guide
Deamination is used to break down amino acids for energy, and occurs primarily in the liver.
Source: Myschool Past Questions Archive (Record #56756)
Biology
UTME / JAMB 2020
Basic Ecological Concepts, Ecosystems & Biomes
Solution
In an agricultural ecosystem, the biotic component consist of
A
crops, pests and beneficial insects
B
crops, temperature and humidity
C
pests, beneficial insects and water
D
crops, water and soil
medium Difficulty
Verified Correct Answer: Option A
Biological Concept & Syllabus Guide
The living components of an ecosystem are called the biotic components, option A has all living components.
Source: Myschool Past Questions Archive (Record #56760)
Biology
UTME / JAMB 2020
Nutrition in Plants & Animals (Photosynthesis & Food Substances)
Solution
Epiphytes growing on the branches of trees provide an example of the relationship known as?
A
parasitism
B
commensalism
C
saprophytism
D
holophytism
medium Difficulty
Verified Correct Answer: Option B
Biological Concept & Syllabus Guide
Commensalism is a type of symbiosis, specifically, a biological relationship in which one specie benefits from an interaction, while the host species is neither positively or negatively affected to any tangible degree.
Source: Myschool Past Questions Archive (Record #56762)
Biology
UTME / JAMB 2020
Variety of Organisms & Classification of Living Things
Solution
The hypha of rhizopus is said to be non-septate because it
A
does not contain chloropyll
B
has no cross wall
C
is vacuoled
D
stores oil globus
medium Difficulty
Verified Correct Answer: Option B
Biological Concept & Syllabus Guide
Hyphae that have walls between the cells are called septate hyphae; hyphae that lack walls and cell membranes between the cells are called nonseptate or coenocytic hyphae)
Source: Myschool Past Questions Archive (Record #56766)
Biology
UTME / JAMB 2020
Cell Structure, Organization & Cell Division
Solution
The function of ribosome in cells is
A
protein synthesis
B
starch synthesis
C
transport of material
D
lipid storage
medium Difficulty
Verified Correct Answer: Option A
Biological Concept & Syllabus Guide
A ribosome is a cell organelle. It functions as a micro-machine for making proteins.
Source: Myschool Past Questions Archive (Record #56767)
Biology
UTME / JAMB 2020
Reproduction in Plants & Animals
Solution
In which of the following does external fertilization take place?
A
toad
B
lizard
C
bird
D
cockroach
medium Difficulty
Verified Correct Answer: Option A
Biological Concept & Syllabus Guide
External fertilization is a mode of reproduction in which a male organism's sperm fertilizes a female organism's egg outside of the female's body. Many fish, amphibians, and other sexual aquatic animals use external fertilization (the exceptions are aquatic mammals, sharks, and some other special types of fish).
Source: Myschool Past Questions Archive (Record #56770)