Japan · Grade 10 · Practice Sheet 1

1. 1.

   A body starts at 19 m/s and accelerates at 3 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A 28 kg object moves at 7 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Find the momentum of a 47 kg object moving at 4 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A cone has base radius 11 cm and height 19 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.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 12 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   An object with initial velocity 4 m/s accelerates at 4.7 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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7. 7.

   Find the gravitational potential energy of a 17 kg object raised 32 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   ¥1,300 is invested at 6% compound interest per annum for 4 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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9. 9.

   An object has mass 280.5 g and volume 33 cm³. Find its density.

   Formula:Density

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

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10. 10.

    An object with initial velocity 11 m/s accelerates at 4.4 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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11. 11.

    Find the force needed to accelerate a 56 kg mass at 8.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A cylinder has radius 8 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    A current of 5.4 A flows through a 42 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A 37 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 6 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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16. 16.

    A bag has 25 equally likely marbles, of which 17 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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17. 17.

    A triangle has sides a = 11 cm and b = 6 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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18. 18.

    A wave has frequency 306 Hz and wavelength 2.19 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A device runs at 43 V drawing 3.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 7 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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