Oman · Grade 10 · Practice Sheet 25

1. 1.

   Find the force needed to accelerate a 25 kg mass at 5.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   An object has mass 130.2 g and volume 21 cm³. Find its density.

   Formula:Density

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

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3. 3.

   A right-angled triangle has legs of 8 cm and 13 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 3 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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5. 5.

   In a triangle, a = 16, b = 8 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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6. 6.

   A wave has frequency 368 Hz and wavelength 4.09 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 8 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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8. 8.

   A cone has base radius 3 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   A right-angled triangle has legs of 14 cm and 15 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    A value changes from 105 to 65. 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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11. 11.

    A force of 32 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 5 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

    A force of 45 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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14. 14.

    Solve for x: 4x + 11 = 59.

    Formula:Solving a Linear Equation

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

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15. 15.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 6 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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16. 16.

    Find the gravitational potential energy of a 46 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    An object has mass 264 g and volume 30 cm³. Find its density.

    Formula:Density

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

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18. 18.

    In a triangle, a = 12, b = 11 and the included angle C = 110°. 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.

    A value changes from 21 to 259. 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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20. 20.

    An object has mass 421.4 g and volume 49 cm³. Find its density.

    Formula:Density

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

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