Zambia · Grade 10 · Practice Sheet 40

1. 1.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 3 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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2. 2.

   A current of 0.8 A flows through a 58 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A bag has 13 equally likely marbles, of which 11 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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4. 4.

   A right-angled triangle has legs of 17 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   A value changes from 127 to 81. 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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6. 6.

   A force of 20 N moves an object 9 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   An object has mass 40 g and volume 16 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A device runs at 103 V drawing 9.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Find the sum of the first 20 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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10. 10.

    A device runs at 175 V drawing 5.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A triangle has sides a = 9 cm and b = 17 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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12. 12.

    Find the momentum of a 29 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Solve using the quadratic formula: x² − 10x + 24 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A device runs at 160 V drawing 3.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A cylinder has radius 12 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 6 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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17. 17.

    Find the gravitational potential energy of a 43 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    In a triangle, a = 12, b = 10 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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19. 19.

    An object has mass 70.8 g and volume 12 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A right-angled triangle has legs of 19 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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