Spain · Grado 11 · Practice Sheet 29

1. 1.

   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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2. 2.

   A wave has frequency 846 Hz and wavelength 3.65 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the population standard deviation of: 20, 6, 18, 7, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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5. 5.

   A population of 7,300 grows 3% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A force of 50 N moves an object 15 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   An object with initial velocity 5 m/s accelerates at 2 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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8. 8.

   Two masses 4,300 kg and 100 kg are 3 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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9. 9.

   A right-angled triangle has legs of 12 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    A force of 71 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    Find the population standard deviation of: 3, 3, 8, 10, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A right-angled triangle has legs of 3 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    A force of 44 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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14. 14.

    A cone has base radius 6 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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15. 15.

    €1,900 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 99 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    €3,000 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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18. 18.

    A cylinder has radius 9 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    Find the sum of the first 5 terms of a geometric series with first term a = 8 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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20. 20.

    Find the force needed to accelerate a 56 kg mass at 7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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