Japan · Grade 10 · Practice Sheet 12

1. 1.

   ¥2,400 is invested at 10% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

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

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2. 2.

   ¥3,400 is invested at 5% 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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3. 3.

   A 6 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   A force of 27 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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5. 5.

   A wave has frequency 663 Hz and wavelength 3.03 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   A population of 8,000 grows 5% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A body starts at 19 m/s and accelerates at 1.8 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A current of 2.7 A flows through a 48 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A population of 6,800 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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11. 11.

    A value changes from 156 to 125. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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12. 12.

    A device runs at 140 V drawing 4.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    An object with initial velocity 12 m/s accelerates at 4.7 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    Find the force needed to accelerate a 56 kg mass at 2.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A 10 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    Find the force needed to accelerate a 52 kg mass at 8.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A cone has base radius 3 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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18. 18.

    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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19. 19.

    A cone has base radius 5 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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20. 20.

    A body starts at 1 m/s and accelerates at 1.7 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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