South Korea · Grade 10 · Practice Sheet 5

1. 1.

   A current of 1.6 A flows through a 18 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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2. 2.

   Find the gravitational potential energy of a 24 kg object raised 35 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   ₩1,800 is invested at 6% compound interest per annum for 2 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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4. 4.

   A cylinder has radius 2 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   An object with initial velocity 3 m/s accelerates at 2.2 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A device runs at 10 V drawing 1.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Solve using the quadratic formula: x² − 8x + 12 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   A force of 100 N moves an object 23 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the gravitational potential energy of a 39 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Find the force needed to accelerate a 15 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 103 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A 37 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A right-angled triangle has legs of 7 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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14. 14.

    A bag has 27 equally likely marbles, of which 8 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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15. 15.

    Solve using the quadratic formula: x² − 7x + 6 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    A population of 8,900 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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17. 17.

    A bag has 15 equally likely marbles, of which 14 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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18. 18.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 2 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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19. 19.

    An object with initial velocity 7 m/s accelerates at 1.2 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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20. 20.

    Solve for x: 2x + 12 = 20.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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