Ethiopia · Grade 10 · Practice Sheet 21

1. 1.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 9 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 value changes from 97 to 88. 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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3. 3.

   An object has mass 300 g and volume 50 cm³. Find its density.

   Formula:Density

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

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4. 4.

   Find the momentum of a 40 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A population of 7,200 grows 2% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A value changes from 49 to 35. 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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7. 7.

   Find the force needed to accelerate a 17 kg mass at 5.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Br 800 is invested at 4% 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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9. 9.

   A cylinder has radius 11 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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10. 10.

    An object has mass 46.2 g and volume 14 cm³. Find its density.

    Formula:Density

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

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11. 11.

    A body starts at 14 m/s and accelerates at 1.7 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A 33 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    An object has mass 202.5 g and volume 25 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A right-angled triangle has legs of 19 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A device runs at 217 V drawing 6.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the force needed to accelerate a 7 kg mass at 1.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    An object with initial velocity 1 m/s accelerates at 2.2 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    A cylinder has radius 2 cm and height 26 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    Find the momentum of a 15 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Solve for x: 2x + 8 = 30.

    Formula:Solving a Linear Equation

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

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