Jamb practice questions

JAMB Mathematics Practice Questions on Indices

1. Simplify: 3⁴ × 3² ÷ 3³

   • A) 3³
   • B) 3²
   • C) 3⁵
   • D) 3¹

2. Evaluate: (2³)² × 2^-5

   • A) 2⁰
   • B) 2¹
   • C) 2^-2
   • D) 2⁴

3. Simplify: (5³ × 5^-2) ÷ 5^-1

   • A) 5⁰
   • B) 5²
   • C) 5⁴
   • D) 5⁶

4. If x^a × x^b = x¹², find a + b when x = 2.

   • A) 6
   • B) 10
   • C) 12
   • D) 24

5. Simplify: (4/9)^-1/2

   • A) 3/2
   • B) 2/3
   • C) 9/4
   • D) 4/9

6. Express 27x^-3y² in simplified form with positive indices.

   • A) 27y²/x³
   • B) 27y^-2/x^-3
   • C) 27y²x^-3
   • D) x³/27y²

7. Simplify: 3²ⁿ⁺¹ ÷ 3^n-1

   • A) 3ⁿ⁺²
   • B) 3^n-2
   • C) 3ⁿ⁺¹
   • D) 3³ⁿ

8. If 2^x = 8, find x.

   • A) 1
   • B) 2
   • C) 3
   • D) 4

9. Simplify: (4³ × 4^-2)^1/2

   • A) 2
   • B) 4
   • C) 16
   • D) 8

10. Express 1/2^-3 in standard form.

    • A) 8
    • B) 1/8
    • C) -8
    • D) 1/4

Number Base JAMB Practice Questions

1. Convert 101101₂ to base 10.

1. 45
2. 49
3. 53
4. 57

2. What is 764₁₀ in base 5?

1. 11024₅
2. 10114₅
3. 10424₅
4. 11244₅

3. Simplify 234₅ + 132₅ and express the answer in base 5.

1. 1011₅
2. 1001₅
3. 2021₅
4. 2011₅

4. If 231₄ = x₂, find x.

1. 1001011₂
2. 110011₂
3. 1000111₂
4. 111011₂

5. What is the value of 110101₂ × 11₂ in base 2?

1. 10111011₂
2. 10110011₂
3. 11011101₂
4. 11110111₂

6. Convert 3F₁₆ to base 10.

1. 57
2. 63
3. 47
4. 59

7. The decimal number 240 is equivalent to what in base 8?

1. 370₈
2. 360₈
3. 350₈
4. 340₈

8. Simplify 1234₆ - 432₆ and express the result in base 6.

1. 534₆
2. 535₆
3. 452₆
4. 534₆

9. If 110011₂ = x₈, find x.

1. 63₈
2. 61₈
3. 51₈
4. 33₈

10. Convert 245₈ to base 10.

1. 165
2. 173
3. 158
4. 161

11. What is the base 16 equivalent of 198₁₀?

1. C6₁₆
2. 6C₁₆
3. C8₁₆
4. 8C₁₆

12. Simplify 1011₂ + 1101₂ and express the result in base 2.

1. 11000₂
2. 10000₂
3. 10100₂
4. 11100₂

13. Express 357₁₀ as a number in base 12.

1. 259₁₂
2. 25A₁₂
3. 2A5₁₂
4. 2B5₁₂

14. Convert 110101₂ to hexadecimal (base 16).

1. 35₁₆
2. 37₁₆
3. 2D₁₆
4. 34₁₆

15. If x₈ = 111₂, find x.

1. 5₈
2. 7₈
3. 3₈
4. 1₈

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JAMB Chemistry Past Questions

Topics: Chemical and Physical Changes, Atoms, Molecules, Elements, Ions, Compounds, Dalton's Atomic Theory, Rutherford and Bohr's Postulates, Isotopes, Relative Atomic Mass, Relative Molecular Mass.

1. Which of the following is a physical change?

A. Burning of paper
B. Melting of ice
C. Rusting of iron
D. Digestion of food

2. An example of a chemical change is:

A. Boiling water
B. Freezing water
C. Burning wood
D. Melting wax

3. Which of the following statements is true about atoms?

A. Atoms are indivisible and indestructible
B. Atoms of the same element differ in mass
C. Atoms are the smallest particles of matter
D. Atoms can be created during chemical reactions

4. The nucleus of an atom contains:

A. Protons and neutrons
B. Protons and electrons
C. Electrons and neutrons
D. Protons only

5. Which scientist proposed the idea that atoms are indivisible?

A. J.J. Thomson
B. John Dalton
C. Ernest Rutherford
D. Niels Bohr

6. According to Rutherford’s model of the atom, the nucleus is:

A. Positively charged
B. Negatively charged
C. Neutral
D. Surrounded by stationary electrons

7. Niels Bohr’s model of the atom explains:

A. The arrangement of protons in the nucleus
B. The arrangement of electrons in orbits
C. The neutrality of atoms
D. The existence of isotopes

8. Isotopes are atoms of the same element that:

A. Have different atomic numbers
B. Have different mass numbers
C. Have different numbers of protons
D. Have the same mass numbers

9. The relative atomic mass of an element is determined by:

A. Adding the masses of protons and electrons
B. The mass of one atom of the element
C. Comparing the element's mass to carbon-12
D. The number of neutrons in the nucleus

10. The relative molecular mass of a compound is:

A. Equal to the atomic mass of the compound
B. The sum of the atomic masses of the elements in the molecule
C. Always greater than 100
D. The mass of a single atom

11. Calculate the relative molecular mass of H<sub>2</sub>O. (H = 1, O = 16)

A. 18
B. 20
C. 16
D. 12

12. Calculate the number of molecules in 9 g of water (H = 1, O = 16, Avogadro’s number = 6.02 x 10<sup>23</sup>)

A. 3.01 x 10<sup>23</sup>
B. 6.02 x 10<sup>23</sup>
C. 9.03 x 10<sup>23</sup>
D. 1.20 x 10<sup>23</sup>

13. Which of these statements is correct about ions?

A. An ion is always positively charged
B. Ions are formed when atoms lose or gain electrons
C. An ion has equal numbers of protons and electrons
D. Ions are electrically neutral

14. The molar mass of CO<sub>2</sub> is:

A. 22 g/mol
B. 44 g/mol
C. 28 g/mol
D. 16 g/mol

15. What is the empirical formula of a compound containing 40% carbon, 6.7% hydrogen, and 53.3% oxygen? (C = 12, H = 1, O = 16)

A. CHO
B. CH<sub>2</sub>O
C. C<sub>2</sub>H<sub>2</sub>O
D. C<sub>3</sub>H<sub>6</sub>O

16. What is the charge on a sulfate ion (SO<sub>4</sub>)?

A. -1
B. -2
C. +1
D. +2

17. Which of the following substances is a compound?

A. Nitrogen
B. Oxygen
C. Water
D. Diamond

18. Calculate the number of moles in 88 g of CO<sub>2</sub>. (C = 12, O = 16)

A. 2 moles
B. 4 moles
C. 1 mole
D. 0.5 moles

19. Which of the following postulates is part of Dalton's atomic theory?

A. Atoms can be destroyed in chemical reactions
B. Atoms combine in simple whole-number ratios to form compounds
C. Atoms of different elements have the same properties
D. Atoms of the same element have different masses

20. An example of an isotope is:

A. Carbon-12 and Carbon-14
B. Oxygen and Nitrogen
C. Sodium-23 and Magnesium-24
D. Hydrogen and Helium

JAMB Physics Past Questions

1. Which of the following is a fundamental quantity?

• (A) Time
• (B) Velocity
• (C) Force
• (D) Energy

2. The unit of acceleration is:

• (A) m/s
• (B) m<sup>2</sup>/s
• (C) m/s<sup>2</sup>
• (D) s/m

3. A car travels 120 km in 3 hours. What is its average speed?

• (A) 20 km/h
• (B) 40 km/h
• (C) 60 km/h
• (D) 80 km/h

4. Displacement is an example of a:

• (A) Scalar quantity
• (B) Vector quantity
• (C) Derived quantity
• (D) Fundamental quantity

5. The SI unit of force is:

• (A) Newton
• (B) Joule
• (C) Watt
• (D) Pascal

6. Which of the following represents a derived quantity?

• (A) Mass
• (B) Time
• (C) Pressure
• (D) Length

7. A body moves with a velocity of 15 m/s for 10 seconds. What is the total distance covered?

• (A) 100 m
• (B) 150 m
• (C) 200 m
• (D) 250 m

8. Which of these laws is used to find the resultant of two forces acting at an angle?

• (A) Hooke’s Law
• (B) Parallelogram Law of Vectors
• (C) Newton’s Law
• (D) Pascal’s Principle

9. A vector quantity has:

• (A) Only magnitude
• (B) Only direction
• (C) Both magnitude and direction
• (D) None of the above

10. Resolve a force of 50 N acting at an angle of 30° into its horizontal component.

• (A) 25 N
• (B) 43.3 N
• (C) 50 N
• (D) 60 N