Norway · Grade 12 · Practice Sheet 7

1. 1.

   An object with initial velocity 7 m/s accelerates at 1.1 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   kr 2,800 is invested at 4% compound interest per annum for 4 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 momentum of a 54 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A body starts at 0 m/s and accelerates at 5.7 m/s² for 7 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 23 kg object raised 38 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Solve using the quadratic formula: x² − 5x + 6 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   Find the force needed to accelerate a 55 kg mass at 1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A wave has frequency 229 Hz and wavelength 0.6 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Two masses 9,000 kg and 180 kg are 17 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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10. 10.

    A wave has frequency 819 Hz and wavelength 4.75 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A population of 4,200 grows 5% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    Find the force needed to accelerate a 53 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    In a triangle, a = 9, b = 11 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    Two masses 1,000 kg and 130 kg are 20 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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15. 15.

    A triangle has sides a = 12 cm and b = 20 cm with an included angle C = 60°. 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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16. 16.

    A body starts at 11 m/s and accelerates at 1.3 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A force of 428 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A body starts at 0 m/s and accelerates at 5.1 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A wave has frequency 179 Hz and wavelength 4.16 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    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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