Tanzania · Grade 12 · Practice Sheet 37

1. 1.

   TSh 2,200 is invested at 4% compound interest per annum for 4 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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2. 2.

   A triangle has sides a = 12 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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3. 3.

   A device runs at 124 V drawing 1.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A 34 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   TSh 2,000 is invested at 5% 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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7. 7.

   An object with initial velocity 2 m/s accelerates at 2.1 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   Solve using the quadratic formula: x² + 2x − 15 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   A population of 3,300 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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10. 10.

    A 15 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    A wave has frequency 505 Hz and wavelength 1.5 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    TSh 3,100 is invested at 3% 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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13. 13.

    An object with initial velocity 3 m/s accelerates at 3.4 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 5 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    A body starts at 9 m/s and accelerates at 3.5 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the force needed to accelerate a 7 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A wave has frequency 629 Hz and wavelength 4.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A cone has base radius 3 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    Find the force needed to accelerate a 36 kg mass at 2.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the momentum of a 33 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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