Vietnam · Grade 12 · Practice Sheet 19

1. 1.

   In a triangle, a = 6, b = 6 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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2. 2.

   A body starts at 15 m/s and accelerates at 1.5 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   Two masses 6,400 kg and 240 kg are 13 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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4. 4.

   Find the force needed to accelerate a 30 kg mass at 1.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A force of 118 N moves an object 18 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 8 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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7. 7.

   VND 700 is invested at 6% 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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8. 8.

   Find the force needed to accelerate a 28 kg mass at 7.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A device runs at 57 V drawing 5.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the force needed to accelerate a 51 kg mass at 3.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    An object with initial velocity 7 m/s accelerates at 4.4 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    VND 2,700 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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13. 13.

    A current of 6.2 A flows through a 16 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A 3 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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15. 15.

    Find the force needed to accelerate a 39 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A device runs at 33 V drawing 3.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the momentum of a 7 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A triangle has sides a = 16 cm and b = 19 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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19. 19.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 11 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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20. 20.

    Find the sum of the first 4 terms of a geometric series with first term a = 7 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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