Belgium · Year 10 · Practice Sheet 44

1. 1.

   €2,300 is invested at 3% 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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2. 2.

   Find the force needed to accelerate a 7 kg mass at 8.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A cylinder has radius 8 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   In a triangle, a = 14, b = 7 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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6. 6.

   A force of 245 N acts on an area of 9.8 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A triangle has sides a = 12 cm and b = 6 cm with an included angle C = 90°. 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.

   In a triangle, a = 8, b = 13 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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9. 9.

   A device runs at 139 V drawing 7.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    €2,800 is invested at 8% 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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11. 11.

    A bag has 14 equally likely marbles, of which 7 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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12. 12.

    A population of 1,900 grows 8% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the momentum of a 55 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A force of 344 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Find the force needed to accelerate a 43 kg mass at 3.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A force of 10 N moves an object 29 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 has mass 170 g and volume 50 cm³. Find its density.

    Formula:Density

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

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18. 18.

    A current of 4.8 A flows through a 15 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the force needed to accelerate a 15 kg mass at 3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the gravitational potential energy of a 16 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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