Russia · Grade 12 · Practice Sheet 40

1. 1.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   A body starts at 1 m/s and accelerates at 5.2 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A 22 kg object moves at 10 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   In a triangle, a = 17, b = 13 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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5. 5.

   Find the gravitational potential energy of a 12 kg object raised 39 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   A body starts at 19 m/s and accelerates at 4.5 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A device runs at 92 V drawing 8.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A cone has base radius 2 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    ₽500 is invested at 8% 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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11. 11.

    A force of 43 N acts on an area of 5.3 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A cone has base radius 7 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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13. 13.

    Find the force needed to accelerate a 55 kg mass at 8.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A wave has frequency 802 Hz and wavelength 2.1 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A device runs at 195 V drawing 9.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the population standard deviation of: 15, 9, 17, 14, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    Find the gravitational potential energy of a 41 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A device runs at 115 V drawing 9.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A force of 7 N moves an object 38 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    An object with initial velocity 3 m/s accelerates at 3.3 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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