Peru · Grado 11 · Practice Sheet 27

1. 1.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 6 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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2. 2.

   S/ 1,000 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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3. 3.

   In a triangle, a = 10, b = 16 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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4. 4.

   A force of 55 N moves an object 7 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A cone has base radius 3 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   An object with initial velocity 0 m/s accelerates at 4.9 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   A wave has frequency 774 Hz and wavelength 4.81 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Solve using the quadratic formula: x² − 5x + 6 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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9. 9.

   A cylinder has radius 3 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 5 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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11. 11.

    A force of 22 N moves an object 31 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A cone has base radius 4 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    A current of 3.5 A flows through a 10 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the population standard deviation of: 7, 3, 13, 13, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A current of 6.9 A flows through a 28 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A wave has frequency 876 Hz and wavelength 1.66 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 9 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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18. 18.

    A current of 4.7 A flows through a 58 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A population of 5,300 grows 2% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    A current of 6.3 A flows through a 4 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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