New Zealand · Year 12 · Practice Sheet 26

1. 1.

   A wave has frequency 69 Hz and wavelength 3.79 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A body starts at 11 m/s and accelerates at 3.1 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A triangle has sides a = 17 cm and b = 10 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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4. 4.

   Two masses 5,700 kg and 160 kg are 11 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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5. 5.

   Find the sum of the first 6 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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6. 6.

   An object with initial velocity 5 m/s accelerates at 4 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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7. 7.

   Find the gravitational potential energy of a 31 kg object raised 30 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   A device runs at 94 V drawing 3.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   $800 is invested at 3% 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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10. 10.

    A 18 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    An object with initial velocity 9 m/s accelerates at 4.2 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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13. 13.

    Find the gravitational potential energy of a 46 kg object raised 32 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A population of 3,300 grows 3% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    Find the sum of the first 6 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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16. 16.

    A force of 415 N acts on an area of 2.3 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    $2,200 is invested at 3% 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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18. 18.

    Find the force needed to accelerate a 46 kg mass at 2.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    In a triangle, a = 11, b = 16 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    Find the force needed to accelerate a 46 kg mass at 4.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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