Taiwan · Grade 11 · Practice Sheet 46

1. 1.

   Find the force needed to accelerate a 12 kg mass at 1.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   NT$ 2,800 is invested at 8% 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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3. 3.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 1 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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4. 4.

   An object with initial velocity 0 m/s accelerates at 4 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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5. 5.

   Find the momentum of a 28 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the force needed to accelerate a 24 kg mass at 6.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A device runs at 25 V drawing 8.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A force of 59 N moves an object 32 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A cylinder has radius 8 cm and height 8 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 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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11. 11.

    Find the force needed to accelerate a 47 kg mass at 5.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A right-angled triangle has legs of 19 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    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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14. 14.

    A cylinder has radius 8 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    A device runs at 178 V drawing 0.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A force of 258 N acts on an area of 7 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    An object has mass 144 g and volume 45 cm³. Find its density.

    Formula:Density

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

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18. 18.

    A right-angled triangle has legs of 3 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A force of 397 N acts on an area of 4.2 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Find the population standard deviation of: 7, 14, 11, 5, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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