Israel · Grade 11 · Practice Sheet 16

1. 1.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 8 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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2. 2.

   In a triangle, a = 5, b = 12 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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3. 3.

   A force of 59 N moves an object 37 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   An object with initial velocity 2 m/s accelerates at 2.2 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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5. 5.

   Find the force needed to accelerate a 5 kg mass at 0.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A population of 2,300 grows 10% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   A force of 55 N acts on an area of 9.5 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   An object with initial velocity 4 m/s accelerates at 4.7 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   A current of 6 A flows through a 55 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Two masses 6,500 kg and 460 kg are 8 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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11. 11.

    An object with initial velocity 9 m/s accelerates at 2.9 m/s² for 6 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 force needed to accelerate a 11 kg mass at 1.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A 36 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    An object has mass 62.7 g and volume 33 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A force of 94 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A cone has base radius 2 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    A force of 41 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Two masses 4,600 kg and 850 kg are 15 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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19. 19.

    A triangle has sides a = 14 cm and b = 5 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 cylinder has radius 7 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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