Kenya · Grade 10 · Practice Sheet 20

1. 1.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 7 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 triangle has sides a = 16 cm and b = 11 cm with an included angle C = 30°. 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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3. 3.

   Solve for x: 2x + 12 = 34.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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4. 4.

   Find the gravitational potential energy of a 37 kg object raised 27 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Solve for x: 9x + 2 = 65.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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6. 6.

   An object has mass 216 g and volume 30 cm³. Find its density.

   Formula:Density

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

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7. 7.

   A current of 2.8 A flows through a 26 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A bag has 24 equally likely marbles, of which 18 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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9. 9.

   A device runs at 88 V drawing 3.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A value changes from 64 to 136. 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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11. 11.

    Find the force needed to accelerate a 8 kg mass at 5.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    KSh 1,600 is invested at 7.5% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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13. 13.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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14. 14.

    In a triangle, a = 12, b = 14 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    A triangle has sides a = 14 cm and b = 17 cm with an included angle C = 60°. 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.

    In a triangle, a = 11, b = 8 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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17. 17.

    Solve using the quadratic formula: x² + 7x + 6 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    In a triangle, a = 14, b = 11 and the included angle C = 80°. 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.

    A device runs at 65 V drawing 6.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the momentum of a 58 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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