New Zealand · Year 11 · Practice Sheet 44

1. 1.

   A triangle has sides a = 6 cm and b = 20 cm with an included angle C = 45°. 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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2. 2.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 1 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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3. 3.

   A triangle has sides a = 16 cm and b = 11 cm with an included angle C = 90°. 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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4. 4.

   A body starts at 18 m/s and accelerates at 4 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   Find the gravitational potential energy of a 27 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Two masses 5,800 kg and 730 kg are 10 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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7. 7.

   An object has mass 9.8 g and volume 7 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A force of 485 N acts on an area of 4.1 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Find the momentum of a 9 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    Solve using the quadratic formula: x² − 13x + 42 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    An object has mass 118.8 g and volume 44 cm³. Find its density.

    Formula:Density

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

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12. 12.

    Solve using the quadratic formula: x² + 0x − 36 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    A force of 28 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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14. 14.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 5 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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15. 15.

    A cone has base radius 12 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    Find the sum of the first 12 terms of an arithmetic series with first term a = 3 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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17. 17.

    Find the momentum of a 43 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Find the population standard deviation of: 4, 9, 12, 15, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A triangle has sides a = 20 cm and b = 10 cm with an included angle C = 90°. 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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20. 20.

    A force of 205 N acts on an area of 9.2 m². Find the pressure.

    Formula:Pressure

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

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