Cambodia · Grade 10 · Practice Sheet 37

1. 1.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 12 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   Find the momentum of a 51 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A current of 7.9 A flows through a 59 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   An object has mass 86.4 g and volume 27 cm³. Find its density.

   Formula:Density

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

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5. 5.

   Find the momentum of a 31 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A cylinder has radius 9 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   A force of 23 N moves an object 14 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the force needed to accelerate a 26 kg mass at 1.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A right-angled triangle has legs of 13 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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10. 10.

    ៛ 1,900 is invested at 6% 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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11. 11.

    An object with initial velocity 8 m/s accelerates at 4.1 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    A wave has frequency 655 Hz and wavelength 0.39 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 2 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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14. 14.

    ៛ 1,600 is invested at 3% 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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15. 15.

    A triangle has sides a = 13 cm and b = 5 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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16. 16.

    In a triangle, a = 9, b = 10 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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17. 17.

    A body starts at 16 m/s and accelerates at 1.4 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A population of 7,200 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    An object has mass 75.6 g and volume 18 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A bag has 13 equally likely marbles, of which 7 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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