Mongolia · Grade 11 · Practice Sheet 30

1. 1.

   A right-angled triangle has legs of 17 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   ₮800 is invested at 5% compound interest per annum for 4 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.

   In a triangle, a = 6, b = 12 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   A triangle has sides a = 10 cm and b = 15 cm with an included angle C = 90°. 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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5. 5.

   Two masses 8,600 kg and 800 kg are 16 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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6. 6.

   A right-angled triangle has legs of 14 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   Find the momentum of a 3 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Two masses 6,900 kg and 530 kg are 6 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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9. 9.

   A force of 409 N acts on an area of 8.7 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A body starts at 1 m/s and accelerates at 5.5 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    Solve using the quadratic formula: x² − 5x + 4 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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12. 12.

    Find the population standard deviation of: 15, 13, 8, 17, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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13. 13.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 3 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    Find the sum of the first 5 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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15. 15.

    A force of 340 N acts on an area of 3.8 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the gravitational potential energy of a 48 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Find the momentum of a 27 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A wave has frequency 429 Hz and wavelength 2.49 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A triangle has sides a = 14 cm and b = 9 cm with an included angle C = 45°. 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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20. 20.

    A 16 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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