Bahrain · Grade 12 · Practice Sheet 13

1. 1.

   A cone has base radius 11 cm and height 9 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 device runs at 136 V drawing 3.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A population of 1,900 grows 2% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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4. 4.

   BD 3,000 is invested at 8% 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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5. 5.

   Find the population standard deviation of: 3, 3, 6, 9, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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6. 6.

   In a triangle, a = 12, b = 5 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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7. 7.

   A 26 kg object moves at 14 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   A wave has frequency 59 Hz and wavelength 2.06 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A triangle has sides a = 15 cm and b = 7 cm with an included angle C = 90°. 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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10. 10.

    A force of 199 N acts on an area of 0.5 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A triangle has sides a = 13 cm and b = 10 cm with an included angle C = 90°. 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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12. 12.

    A body starts at 10 m/s and accelerates at 4.5 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A population of 5,500 grows 2% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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14. 14.

    In a triangle, a = 14, b = 13 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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15. 15.

    Find the gravitational potential energy of a 33 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Find the force needed to accelerate a 11 kg mass at 2.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A force of 33 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Find the momentum of a 3 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    Find the population standard deviation of: 6, 6, 11, 12, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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20. 20.

    A device runs at 92 V drawing 8.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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