Australia · Year 11 · Practice Sheet 37

1. 1.

   An object has mass 233.1 g and volume 37 cm³. Find its density.

   Formula:Density

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

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2. 2.

   An object with initial velocity 4 m/s accelerates at 1.9 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   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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4. 4.

   A right-angled triangle has legs of 13 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   A wave has frequency 748 Hz and wavelength 4.04 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A body starts at 14 m/s and accelerates at 2.4 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   A device runs at 177 V drawing 8.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A cone has base radius 12 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   In a triangle, a = 14, b = 6 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    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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11. 11.

    An object has mass 148.5 g and volume 27 cm³. Find its density.

    Formula:Density

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

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12. 12.

    Find the momentum of a 43 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    An object has mass 284.4 g and volume 36 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A current of 5 A flows through a 11 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    An object has mass 52.8 g and volume 22 cm³. Find its density.

    Formula:Density

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

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16. 16.

    Solve using the quadratic formula: x² − 11x + 30 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    $4,000 is invested at 8% compound interest per annum for 5 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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18. 18.

    An object with initial velocity 4 m/s accelerates at 2.7 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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19. 19.

    A force of 62 N acts on an area of 5.3 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A force of 21 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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