Japan · Grade 10 · Practice Sheet 24

1. 1.

   Find the momentum of a 25 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A device runs at 31 V drawing 8.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A force of 356 N acts on an area of 3.9 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   ¥3,100 is invested at 5% 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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5. 5.

   A value changes from 193 to 34. 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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6. 6.

   Find the force needed to accelerate a 22 kg mass at 6.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A current of 3.3 A flows through a 20 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A bag has 13 equally likely marbles, of which 10 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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9. 9.

   ¥4,800 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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10. 10.

    A cone has base radius 9 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    In a triangle, a = 14, b = 7 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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12. 12.

    A 12 kg object moves at 22 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    Solve for x: 9x + 11 = 83.

    Formula:Solving a Linear Equation

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

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14. 14.

    A wave has frequency 600 Hz and wavelength 3.31 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A value changes from 37 to 219. 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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16. 16.

    ¥2,700 is invested at 8% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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17. 17.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 11 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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18. 18.

    A value changes from 33 to 228. 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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19. 19.

    Solve for x: 4x + 9 = 37.

    Formula:Solving a Linear Equation

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

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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 = 4.

    Formula:Sum of an Arithmetic Series

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

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