Kuwait · Grade 10 · Practice Sheet 25

1. 1.

   A bag has 14 equally likely marbles, of which 10 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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2. 2.

   A 29 kg object moves at 5 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A triangle has sides a = 16 cm and b = 12 cm with an included angle C = 30°. 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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4. 4.

   A cylinder has radius 6 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   KD 4,600 is invested at 5% simple interest per year for 4 years. Find the interest earned.

   Formula:Simple Interest

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

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7. 7.

   Find the momentum of a 5 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Solve for x: 3x + 1 = 28.

   Formula:Solving a Linear Equation

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

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9. 9.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A wave has frequency 794 Hz and wavelength 3.36 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Solve using the quadratic formula: x² + 1x − 30 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    Find the gravitational potential energy of a 14 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    KD 3,600 is invested at 5% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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14. 14.

    A device runs at 187 V drawing 4.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    An object has mass 151.8 g and volume 22 cm³. Find its density.

    Formula:Density

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

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16. 16.

    KD 3,200 is invested at 3% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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17. 17.

    Find the force needed to accelerate a 37 kg mass at 0.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A force of 103 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    An object with initial velocity 4 m/s accelerates at 2.4 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    A 33 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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