Saudi Arabia · Grade 12 · Practice Sheet 11

1. 1.

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

   Formula:Sum of a Geometric Series

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

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2. 2.

   Two masses 5,200 kg and 890 kg are 11 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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3. 3.

   A force of 99 N moves an object 22 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the sum of the first 7 terms of a geometric series with first term a = 7 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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5. 5.

   SAR 500 is invested at 5% compound interest per annum for 3 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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6. 6.

   Find the momentum of a 37 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   Two masses 6,900 kg and 410 kg are 19 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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8. 8.

   Find the force needed to accelerate a 34 kg mass at 5.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Two masses 5,200 kg and 760 kg are 20 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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10. 10.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 9 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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11. 11.

    A cone has base radius 10 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    Find the momentum of a 11 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A wave has frequency 866 Hz and wavelength 1.87 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A triangle has sides a = 14 cm and b = 15 cm with an included angle C = 120°. 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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15. 15.

    In a triangle, a = 17, b = 14 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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16. 16.

    A body starts at 1 m/s and accelerates at 2.6 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A device runs at 200 V drawing 3.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the sum of the first 7 terms of a geometric series with first term a = 5 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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19. 19.

    In a triangle, a = 12, b = 18 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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20. 20.

    Find the population standard deviation of: 10, 18, 4, 20, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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