Vietnam · Grade 10 · Practice Sheet 30

1. 1.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   A body starts at 0 m/s and accelerates at 5.3 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   Find the force needed to accelerate a 58 kg mass at 6.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Solve for x: 2x + 20 = 42.

   Formula:Solving a Linear Equation

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

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5. 5.

   A force of 200 N acts on an area of 3.7 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 8 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   In a triangle, a = 9, b = 11 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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8. 8.

   Find the force needed to accelerate a 34 kg mass at 1.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A wave has frequency 656 Hz and wavelength 4.64 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A bag has 20 equally likely marbles, of which 9 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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11. 11.

    Find the force needed to accelerate a 51 kg mass at 5.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A force of 107 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    VND 2,600 is invested at 8% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

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

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14. 14.

    A cylinder has radius 6 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    A value changes from 34 to 31. 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.

    A force of 103 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A population of 1,500 grows 3% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    Find the gravitational potential energy of a 26 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A population of 2,300 grows 3% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    Find the momentum of a 38 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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