Greece · Grade 12 · Practice Sheet 23

1. 1.

   A population of 4,700 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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2. 2.

   Find the force needed to accelerate a 23 kg mass at 3.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A force of 70 N moves an object 7 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A triangle has sides a = 20 cm and b = 16 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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5. 5.

   A population of 7,000 grows 5% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A force of 264 N acts on an area of 7 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A wave has frequency 240 Hz and wavelength 1 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A force of 60 N acts on an area of 10 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   An object with initial velocity 4 m/s accelerates at 1.6 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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10. 10.

    Find the gravitational potential energy of a 33 kg object raised 16 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the force needed to accelerate a 47 kg mass at 2.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A 3 kg object moves at 16 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A population of 5,200 grows 5% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    Find the sum of the first 13 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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15. 15.

    Find the sum of the first 8 terms of a geometric series with first term a = 4 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.

    Find the force needed to accelerate a 2 kg mass at 2.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A force of 9 N moves an object 12 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A wave has frequency 466 Hz and wavelength 4.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the force needed to accelerate a 47 kg mass at 2.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 76 N moves an object 22 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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