Portugal · Ano 11 · Practice Sheet 25

1. 1.

   €800 is invested at 5% 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.

   A population of 4,300 grows 10% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A device runs at 28 V drawing 4.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   €2,000 is invested at 4% 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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5. 5.

   A triangle has sides a = 19 cm and b = 10 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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6. 6.

   In a triangle, a = 7, b = 5 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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7. 7.

   A population of 2,000 grows 2% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A population of 7,500 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    Find the population standard deviation of: 7, 18, 15, 5, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    A current of 4.2 A flows through a 35 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    €2,400 is invested at 5% 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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13. 13.

    A cone has base radius 10 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    In a triangle, a = 12, b = 11 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    A body starts at 4 m/s and accelerates at 1.2 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the population standard deviation of: 14, 11, 19, 17, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    An object has mass 138.7 g and volume 19 cm³. Find its density.

    Formula:Density

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

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18. 18.

    Find the gravitational potential energy of a 2 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Two masses 7,600 kg and 240 kg are 6 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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20. 20.

    A body starts at 4 m/s and accelerates at 5.8 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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