Ghana · Grade 10 · Practice Sheet 26

1. 1.

   A cone has base radius 11 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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2. 2.

   A 19 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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3. 3.

   A force of 267 N acts on an area of 4.7 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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4. 4.

   Find the force needed to accelerate a 38 kg mass at 2.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the gravitational potential energy of a 8 kg object raised 5 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   A value changes from 130 to 60. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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7. 7.

   Solve using the quadratic formula: x² − 5x + 6 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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8. 8.

   A bag has 19 equally likely marbles, of which 13 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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9. 9.

   An object has mass 147 g and volume 30 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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10. 10.

    An object with initial velocity 11 m/s accelerates at 5 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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11. 11.

    Solve for x: 2x + 6 = 16.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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12. 12.

    A force of 82 N acts on an area of 1 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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13. 13.

    Solve using the quadratic formula: x² − 4x − 12 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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14. 14.

    A device runs at 204 V drawing 1.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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16. 16.

    Solve using the quadratic formula: x² + 6x + 8 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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17. 17.

    A triangle has sides a = 6 cm and b = 12 cm with an included angle C = 45°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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18. 18.

    GH₵ 2,000 is invested at 3% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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19. 19.

    A cylinder has radius 12 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A wave has frequency 124 Hz and wavelength 2.13 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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