Argentina · Grado 11 · Practice Sheet 40

1. 1.

   Find the force needed to accelerate a 3 kg mass at 2.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A force of 86 N moves an object 5 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   $4,000 is invested at 4% 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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4. 4.

   A current of 6.6 A flows through a 59 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 4 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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6. 6.

   A force of 84 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A cylinder has radius 11 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 6 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   A body starts at 4 m/s and accelerates at 2 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    An object with initial velocity 5 m/s accelerates at 3.9 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 5 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    In a triangle, a = 11, b = 5 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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13. 13.

    A body starts at 16 m/s and accelerates at 4.5 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    Solve using the quadratic formula: x² − 9x + 18 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    $2,100 is invested at 6% 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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16. 16.

    Find the population standard deviation of: 10, 6, 12, 13, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 5 and common difference d = 2.

    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 3.1 A flows through a 50 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A device runs at 97 V drawing 8.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A force of 347 N acts on an area of 6.8 m². Find the pressure.

    Formula:Pressure

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

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