Kenya · Grade 10 · Practice Sheet 48

1. 1.

   A 11 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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2. 2.

   An object has mass 111 g and volume 15 cm³. Find its density.

   Formula:Density

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

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3. 3.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 4 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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4. 4.

   KSh 3,800 is invested at 6% 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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5. 5.

   A body starts at 13 m/s and accelerates at 2 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   A population of 4,400 grows 5% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   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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8. 8.

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

   Formula:Quadratic Formula

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

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9. 9.

   In a triangle, a = 10, b = 7 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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10. 10.

    A triangle has sides a = 5 cm and b = 5 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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11. 11.

    Find the force needed to accelerate a 27 kg mass at 2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Solve for x: 9x + 16 = 79.

    Formula:Solving a Linear Equation

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

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13. 13.

    A device runs at 123 V drawing 5.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A body starts at 0 m/s and accelerates at 2.9 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    An object with initial velocity 11 m/s accelerates at 1.3 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    A body starts at 5 m/s and accelerates at 4.9 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A force of 83 N moves an object 40 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A device runs at 103 V drawing 1.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the momentum of a 23 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A right-angled triangle has legs of 7 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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