Denmark · Grade 11 · Practice Sheet 38

1. 1.

   A cone has base radius 12 cm and height 23 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 current of 5.9 A flows through a 11 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A force of 69 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   An object has mass 262.4 g and volume 32 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A device runs at 139 V drawing 2.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A force of 113 N moves an object 40 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A triangle has sides a = 20 cm and b = 17 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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8. 8.

   Find the sum of the first 7 terms of a geometric series with first term a = 7 and common ratio r = 2.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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9. 9.

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

   Formula:Quadratic Formula

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

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10. 10.

    Find the gravitational potential energy of a 40 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the sum of the first 5 terms of a geometric series with first term a = 8 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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12. 12.

    Find the momentum of a 21 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 1 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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14. 14.

    A wave has frequency 795 Hz and wavelength 2.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A right-angled triangle has legs of 6 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    Solve using the quadratic formula: x² − 4x + 0 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    An object has mass 295 g and volume 50 cm³. Find its density.

    Formula:Density

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

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18. 18.

    Find the momentum of a 36 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 113 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    kr 1,400 is invested at 6% 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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