Belgium · Year 11 · Practice Sheet 8

1. 1.

   Find the force needed to accelerate a 54 kg mass at 6.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   An object has mass 244.8 g and volume 48 cm³. Find its density.

   Formula:Density

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

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3. 3.

   A force of 232 N acts on an area of 2.5 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   In a triangle, a = 6, b = 6 and the included angle C = 40°. 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 sum of the first 15 terms of an arithmetic series with first term a = 7 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   Find the sum of the first 6 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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7. 7.

   A cone has base radius 6 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A triangle has sides a = 8 cm and b = 5 cm with an included angle C = 60°. 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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9. 9.

   A device runs at 31 V drawing 5.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A triangle has sides a = 8 cm and b = 16 cm with an included angle C = 45°. 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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11. 11.

    A force of 64 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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12. 12.

    Two masses 8,100 kg and 760 kg are 7 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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13. 13.

    A current of 2.3 A flows through a 57 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the momentum of a 30 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    €2,800 is invested at 4% 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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16. 16.

    A force of 29 N moves an object 27 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    An object with initial velocity 9 m/s accelerates at 2 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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18. 18.

    A force of 28 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A population of 4,800 grows 5% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    A current of 7.6 A flows through a 10 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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