Ghana · Grade 10 · Practice Sheet 2

1. 1.

   A population of 3,700 grows 2% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   GH₵ 1,200 is invested at 5% 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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3. 3.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 11 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   A cylinder has radius 2 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   A value changes from 170 to 163. 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 triangle has sides a = 19 cm and b = 15 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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7. 7.

   GH₵ 500 is invested at 5% compound interest per annum for 2 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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8. 8.

   A force of 93 N moves an object 27 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   An object with initial velocity 7 m/s accelerates at 1.1 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

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

    Formula:Exponential Growth

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

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11. 11.

    Find the momentum of a 25 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    An object with initial velocity 4 m/s accelerates at 4.1 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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13. 13.

    A 20 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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14. 14.

    Find the gravitational potential energy of a 16 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A 8 kg object moves at 18 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    A body starts at 9 m/s and accelerates at 4 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    In a triangle, a = 8, b = 8 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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18. 18.

    Find the momentum of a 30 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    An object has mass 30.6 g and volume 6 cm³. Find its density.

    Formula:Density

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

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20. 20.

    Find the momentum of a 11 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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