Nigeria · Grade 10 · Practice Sheet 2

1. 1.

   A value changes from 60 to 216. 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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2. 2.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 5 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   A wave has frequency 631 Hz and wavelength 0.71 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Solve for x: 3x + 3 = 9.

   Formula:Solving a Linear Equation

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

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5. 5.

   Find the gravitational potential energy of a 27 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   An object with initial velocity 6 m/s accelerates at 2.7 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   An object has mass 403.2 g and volume 48 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A body starts at 12 m/s and accelerates at 4.9 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   An object with initial velocity 15 m/s accelerates at 2.7 m/s² for 6 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 29 kg mass at 4.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A device runs at 18 V drawing 3.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A force of 77 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A 9 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    A population of 5,300 grows 2% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    Find the sum of the first 12 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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16. 16.

    Find the momentum of a 1 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A cylinder has radius 7 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    A right-angled triangle has legs of 9 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A cone has base radius 12 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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20. 20.

    An object with initial velocity 3 m/s accelerates at 4 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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