Portugal · Ano 11 · Practice Sheet 14

1. 1.

   Find the momentum of a 49 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A force of 48 N moves an object 11 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the sum of the first 7 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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5. 5.

   In a triangle, a = 14, b = 5 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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6. 6.

   A current of 1.9 A flows through a 7 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Find the force needed to accelerate a 10 kg mass at 1.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A force of 57 N moves an object 23 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A wave has frequency 818 Hz and wavelength 4.59 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    An object with initial velocity 13 m/s accelerates at 1.6 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    €1,500 is invested at 5% compound interest per annum for 3 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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12. 12.

    Find the sum of the first 8 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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13. 13.

    Find the population standard deviation of: 8, 4, 20, 17, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 10 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    A body starts at 7 m/s and accelerates at 1.3 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A 2 kg object moves at 18 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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18. 18.

    €3,400 is invested at 3% 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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19. 19.

    A current of 5 A flows through a 44 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    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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