Singapore · Grade 12 · Practice Sheet 10

1. 1.

   Find the population standard deviation of: 8, 2, 9, 13, 11 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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2. 2.

   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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3. 3.

   Find the force needed to accelerate a 57 kg mass at 8.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A cone has base radius 8 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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5. 5.

   In a triangle, a = 10, b = 10 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   A force of 44 N moves an object 11 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A triangle has sides a = 5 cm and b = 8 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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8. 8.

   A body starts at 3 m/s and accelerates at 3.2 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   Find the sum of the first 7 terms of a geometric series with first term a = 5 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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10. 10.

    A body starts at 11 m/s and accelerates at 4.2 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A device runs at 159 V drawing 2.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A 8 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A current of 0.9 A flows through a 48 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A 23 kg object moves at 25 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    A device runs at 10 V drawing 6.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A triangle has sides a = 17 cm and b = 20 cm with an included angle C = 30°. 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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17. 17.

    A current of 7.6 A flows through a 30 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A force of 308 N acts on an area of 6.7 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Find the momentum of a 14 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A population of 2,400 grows 3% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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