Japan · Grade 10 · Practice Sheet 33

1. 1.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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2. 2.

   A cone has base radius 9 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   A wave has frequency 203 Hz and wavelength 2.04 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the momentum of a 20 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   An object with initial velocity 2 m/s accelerates at 3.7 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A current of 6.3 A flows through a 13 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   ¥1,700 is invested at 7.5% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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8. 8.

   A 23 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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9. 9.

   A population of 1,000 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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10. 10.

    Find the sum of the first 10 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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11. 11.

    A triangle has sides a = 19 cm and b = 11 cm with an included angle C = 60°. 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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12. 12.

    Solve for x: 5x + 11 = 51.

    Formula:Solving a Linear Equation

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

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13. 13.

    A triangle has sides a = 20 cm and b = 15 cm with an included angle C = 45°. 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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14. 14.

    Find the momentum of a 18 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A force of 10 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A wave has frequency 417 Hz and wavelength 1.63 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A device runs at 78 V drawing 9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    In a triangle, a = 14, b = 11 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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19. 19.

    ¥1,700 is invested at 8% 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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20. 20.

    A wave has frequency 402 Hz and wavelength 4.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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