AMANIAMPONG

SHS
[CONTEST 1]
20TH JUNE, 2025
ROUND 1 – FUNDAMENTALS
PREAMBLE
Find the values of the constants a, b, and c in the given quadratic inequality
for the given solution set.

1 3
1. ax2 + bx + c > 0 for the solution set {𝑥: − < 𝑥 < }
2 2

ANS: a = −4, b = 4 and c = 3

1 2
2. ax2 + bx + c < 0 for the solution set {𝑥: 𝑥 < 𝑜𝑟 𝑥 > }
3 3

ANS: a = −9, b = 9 and c = −2

3. ax2 + bx + c ≥ 0 for the solution set {𝑥: −1 ≤ 𝑥 ≤ 3}
ANS: a = −1, b = 2 and c = 3
4. ax2 + bx + c ≤ 0 for the solution set {𝑥: 𝑥 ≤ 2 𝑜𝑟 𝑥 ≥ 5}
ANS: a = −1, b = 7 and c = −10

PREAMBLE
Find the image of the given line after reflection in the given point.
5. 3x + 4y + 2 = 0 in the point 𝐴(2, −1)
ANS: 3x + 4y – 6 = 0
6. x + 2y – 1 = 0 in the point 𝐵(4,3)
ANS: x + 2y – 19 = 0
7. 5x – 3y + 7 = 0 in the point 𝐶(−1, −2)
ANS: 5x – 3y – 9 = 0
8. 6x – 2y + 5 = 0 in the point 𝐷(5,7)
ANS: 6x – 2y – 37 = 0

Kontonkyi!
 PREAMBLE
Bacteria can be named based on its arrangement and shape give the
supposed name of the following bacteria based on their arrangement and
shape.
1. In chains and spherical
ANS: Streptococci or streptococcus.

2. In fours and rodlike

ANS: Tetrabacilli or tetrabacillus

3. In clumps and chains

ANS: Staphylococci or staphylococcus

4. In pairs and chains

ANS: Diplococci or Diplococcus

PREAMBLE
Identify whether the following structures are homologous or analogous
structures
5. Leaves of a cactus and a rose plant
ANS: Homologous structures

6. Teeth of a Dog and a Whale Baleen

ANS: Homologous structures

7. Fins of Sharks and Dolphins

ANS: Analogous structures

8. Legless body of Snakes and Millipedes

ANS: Analogous structures

1. A single circular loop of wire has a radius of 0.2 m and carries a current
of 5.0 A. Find the magnetic field at the center of the loop.
ANS: 6.3 x 10−7 T

Kontonkyi!
 2. A circular coil of 20 turns has a radius of 0.05 m and carries a current of
2.0 A. Calculate the magnitude of the magnetic flux density at the center
of the coil.
ANS: 5.0 x 10−4 T

3. A 50 turn circular coil has a radius of 0.30 m and carries a current of

0.50A. Determine the magnetic field at the center of the coil.
ANS: 5.2 x10−5 T

4. A flat coil is used in a magnetic sensor consist of 100 turns, each of

radius 0.10 m and carries a current of 1.5A. Find the magnetic field at the
center of the coil.
ANS: 9.4 x 10−4 T

5. Calculate the mean square speed of hydrogen gas at 600K. [take molar
mass M = 2x 10−3 kg/ mol]
ANS:7.5 x 106 m2/s2

6. Calculate the mean square speed of an oxygen molecule at a temperature

of 300K. [Take M= 32 x 10−3 kg/mol].
ANS:2.3 x 105m2/s2

7. The mean square speed of a monatomic ideal gas is measured to be 4.5 x

105 m2/s2. Determine the temperature of the gas if it is helium. [Take M =
4.0 x 10−3 kg/mol]
ANS:72K

8. Two gases, nitrogen (N2) and neon (Ne) are kept at the same temperature
of 400K. Which gas has the higher mean square speed and by what
factor? [MN2 = 28 x 10−3 , MNe = 20 x 10−3 kg/mol]
ANS: (Neon has a higher mean square speed) by a factor of 1.4
1. What is the oxidation number of sulfur in H₂SO₃?
ANS: +4
2. What is the oxidation number of nitrogen in HNO₃?
ANS: +5

Kontonkyi!
 3. Determine the oxidation number of chlorine in NaClO₃.
ANS: +5
4. What is the oxidation number of carbon in CO?
ANS: +2

5. Calculate the number of moles in 9.0 g of water. (H = 1, O = 16)

ANS: 0.50 mol
6. What is the mass of 0.10 mol of calcium oxide (CaO)? (Ca = 40, O = 16)
ANS: 5.6 g
7. How many atoms are present in 0.25 mol of oxygen gas (O₂)?
ANS: 3.01 × 10²³
8. Find the molar mass of (NH₄)₂SO₄. (N = 14, H = 1, S = 32, O = 16)
ANS: 132 g/mol

ROUND 2 – SPEED RACE

1. The area of a circular ink blot is increasing at the rate of 2 cm2/sec. Find
the rate of change of the circumference at the instance when the radius is
1.5cm.
4
ANS: cm/sec
3

2. Find the value of a if one root of the equation ax2 + 3x – 6 = 0 is twice

the other.
1
ANS: a = −
3
2𝑥+3
3. Differentiate and simplify your answer.
4𝑥 2 −9
2
ANS: − 2
(2𝑥−3)

Kontonkyi!
 4. In organisms in class arachnida which structure aid them to catch and
handle prey and also help males transfer sperm.
ANS: Pedipalp

5. What are stenotopic organisms

ANS: They are organisms that can survive only under a small range of
environmental factors. (they have low tolerance)

6. What is the function of Liming in improving soil fertility.

ANS: It helps reduce soil acidity

7. The bob of a conical pendulum moves at 0.20 m s −1 in a horizontal circle

of radius 0.40 m. Find the angle between the string of the pendulum and
the vertical.
ANS: 1.0 × 10−2 rad = 0.57°

8. Find the optical power in air of a biconvex lens with two spherical
surfaces, one of radius 0.20 m and the other of radius 0.40 m. The
refractive index of the material of the lens is 1.8.
ANS: +6.0 diopters

9. A uniform solid sphere rolls from rest down a plane inclined at 30° to the
horizontal without slipping. Find the speed of the center of mass of the
sphere when it has travelled 7 m down the plane
ANS: 7 m𝑠 −1

10.A gas occupies 3.0 dm³ at 27 °C. What is its volume at 127 °C, assuming
constant pressure?
ANS: 4.0 dm³
11.What is the IUPAC name of CH₃CH₂COOH?
ANS: Propanoic acid
12.What is the pH of a 0.001 mol/dm³ HCl solution?
ANS: 3

Kontonkyi!
 ROUND 3 – TRUE/FALSE

1. Two triangles with equal areas are always congruent. ANS: FALSE
2. Side-side-side is a valid test for both triangle similarity and congruence.
ANS: TRUE
3. If two triangles have two pairs of equal angles, the triangles must be
congruent. ANS: FALSE
4. In similar triangles, the ratio of corresponding altitudes is the same as the
ratio of corresponding sides. ANS: TRUE
5. A 2 × 3 matrix can be multiplied by a 3 × 4 matrix. ANS. TRUE
6. The inverse of a matrix exists for all square matrices. ANS: FALSE
7. If 𝐴 is a 2×2 matrix with determinant 1, then 𝐴−1 inverse is equal to the
adjoint of 𝐴. ANS: TRUE
8. The product of a matrix and its inverse is always the identity matrix.
ANS: TRUE
1. Forest is a living renewable material. ANS: TRUE

2. Waves are non-living renewable material. ANS: TRUE

3. The sun is a non-living, non-renewable material. ANS: FALSE

4. Wind is a living renewable material. ANS: FALSE

5. Splash zone is a portion of the littoral zone submerged under water.

ANS: FALSE

6. Bathyal zone is deeper than abyssal zone. ANS: FALSE

7. Inter-tidal zone is deeper than the splash zone. ANS: FALSE

8. The subtidal zone extends directly from the low-tides mark. ANS: TRUE

Kontonkyi!
 1. The gravitational force between two objects depends only on their masses
and the distance between them. ANS: FALSE

2. Gravitational force can be either attractive or repulsive, depending on the

masses involved. ANS: FALSE

3. The gravitational field inside a uniform spherical shell of mass is zero at

every point. ANS: TRUE

4. The acceleration due to gravity on earth is small at all altitudes. ANS:

FALSE

5. Centripetal acceleration always acts tangential to the circular paths. ANS:

FALSE

6. The formular for centripetal acceleration is 𝑉 2 /𝑟 . ANS: TRUE

7. An object moving in circle at constant speed has zero acceleration. ANS:

FALSE

8. If the radius of a circular motion is double, keeping speed constant, the

centripetal acceleration is halved. ANS: TRUE

1. Weak acids completely dissociate in water. ANS: FALSE

2. A pH of 1 represents a strongly acidic solution. ANS: TRUE

3. A salt formed from a strong acid and strong base is neutral. ANS: TRUE
4. Ammonia acts as a base in water. ANS: TRUE
5. Ionic bonds are formed by the transfer of electrons. ANS: TRUE
6. Covalent compounds conduct electricity in molten form. ANS: FALSE
7. Methane (CH₄) has a tetrahedral molecular geometry. ANS: TRUE
8. In polar covalent bonds, electrons are shared equally. ANS: FALSE

Kontonkyi!
 ROUND 4 – RIDDLES

1. I speak in terms but not in solutions

2. I lack equality but I have structure
3. You can factor me but you cannot always solve me.
4. Letters and numbers live in me.
WHO AM I? ANS: ALGEBRAIC EXPRESSION

1. I am found in organisms like yeast and certain bacteria

2. My metabolic pathway depends on the presence or absence of air
3. I’m not strict like some of my cousins; I adapt to survive anywhere
4. I can thrive where oxygen is but won’t panic when it goes
5. In my flexible ways I switch between aerobic and anaerobic days
WHO AM I? ANS: FACULTATIVE ANAEROBE

1. I am not a measure of how loud something is, yet I often influence what you
hear.
2. I am found in both light and sound, though I behave differently in each
3. My unit is named after a German physicist.
4. In alternating current, I determine how many circles occur in a second.
5. Musicians tune to me; and I’m the heartbeat of a wave
WHO AM I? ANS: FREQUENCY

1. I am a colourless, odourless gas.

2. I do not support combustion.
3. I am used to preserve dry food and inflate crisp packets.
4. I make up 78% of the Earth’s atmosphere.
5. I am chemically unreactive.
WHO AM I? ANS: NITROGEN (N₂)

Kontonkyi!