Taiwan · Grade 12 · Practice Sheet 31

1. 1.

   An object with initial velocity 2 m/s accelerates at 2 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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2. 2.

   A triangle has sides a = 10 cm and b = 14 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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3. 3.

   Find the force needed to accelerate a 13 kg mass at 6.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Two masses 2,400 kg and 380 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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5. 5.

   A triangle has sides a = 17 cm and b = 20 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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6. 6.

   A force of 56 N moves an object 17 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Two masses 8,900 kg and 830 kg are 9 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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8. 8.

   A wave has frequency 873 Hz and wavelength 1.23 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

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

   Formula:Sum of a Geometric Series

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

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10. 10.

    A force of 490 N acts on an area of 5.7 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A population of 7,700 grows 8% per year. Find its size after 2 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 39 kg mass at 2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A population of 7,700 grows 5% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    In a triangle, a = 16, b = 15 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    A current of 5 A flows through a 47 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A wave has frequency 540 Hz and wavelength 1.26 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A body starts at 20 m/s and accelerates at 2.8 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A cone has base radius 12 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    A force of 62 N acts on an area of 9.7 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    An object with initial velocity 8 m/s accelerates at 1.9 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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