Tanzania · Grade 12 · Practice Sheet 9

1. 1.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 5 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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2. 2.

   A device runs at 90 V drawing 6.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the momentum of a 44 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A force of 199 N acts on an area of 1.9 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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6. 6.

   A device runs at 95 V drawing 8.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A population of 4,000 grows 5% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A force of 437 N acts on an area of 6.3 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   An object with initial velocity 11 m/s accelerates at 1.3 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

    Find the force needed to accelerate a 10 kg mass at 7.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 33 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    Two masses 7,300 kg and 900 kg are 18 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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13. 13.

    In a triangle, a = 15, b = 15 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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14. 14.

    A body starts at 6 m/s and accelerates at 5.2 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A triangle has sides a = 8 cm and b = 5 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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16. 16.

    A 8 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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17. 17.

    Solve using the quadratic formula: x² + 4x + 3 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 9 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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19. 19.

    Solve using the quadratic formula: x² + 2x − 24 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    TSh 700 is invested at 6% compound interest per annum for 5 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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