Chile · Grado 11 · Practice Sheet 44

1. 1.

   A force of 130 N acts on an area of 1.3 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A population of 4,000 grows 2% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 2 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   A force of 88 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   Find the momentum of a 1 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A force of 449 N acts on an area of 3.3 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A cylinder has radius 2 cm and height 21 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 population standard deviation of: 20, 18, 18, 7, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 10 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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10. 10.

    An object with initial velocity 14 m/s accelerates at 2.3 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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11. 11.

    A cylinder has radius 14 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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12. 12.

    A triangle has sides a = 19 cm and b = 9 cm with an included angle C = 120°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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13. 13.

    A force of 499 N acts on an area of 0.8 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A 33 kg object moves at 5 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    Find the force needed to accelerate a 2 kg mass at 6.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A force of 479 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A population of 6,800 grows 10% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    An object with initial velocity 15 m/s accelerates at 4.4 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 2 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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20. 20.

    A right-angled triangle has legs of 3 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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