Japan · Grade 11 · Practice Sheet 19

1. 1.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   A force of 423 N acts on an area of 2.4 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Find the momentum of a 2 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   An object with initial velocity 9 m/s accelerates at 2 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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5. 5.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   Find the momentum of a 28 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A wave has frequency 451 Hz and wavelength 3.6 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   An object has mass 27 g and volume 18 cm³. Find its density.

   Formula:Density

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

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9. 9.

   Find the force needed to accelerate a 16 kg mass at 1.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    ¥2,700 is invested at 5% compound interest per annum for 3 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 243 N acts on an area of 5.7 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    In a triangle, a = 14, b = 6 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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13. 13.

    Find the population standard deviation of: 12, 17, 11, 12, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A device runs at 191 V drawing 7.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A cone has base radius 3 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    A body starts at 14 m/s and accelerates at 5 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A current of 5.6 A flows through a 4 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A right-angled triangle has legs of 3 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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19. 19.

    A triangle has sides a = 12 cm and b = 5 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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20. 20.

    Find the population standard deviation of: 15, 11, 19, 19, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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