Tanzania · Grade 11 · Practice Sheet 32

1. 1.

   Find the gravitational potential energy of a 3 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   TSh 3,000 is invested at 4% 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.

   A cone has base radius 7 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   Solve using the quadratic formula: x² + 7x + 10 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   Find the momentum of a 35 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A body starts at 15 m/s and accelerates at 4.5 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A cylinder has radius 2 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   In a triangle, a = 13, b = 9 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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10. 10.

    An object with initial velocity 9 m/s accelerates at 4 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    A force of 306 N acts on an area of 7.1 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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12. 12.

    A body starts at 19 m/s and accelerates at 3.2 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A wave has frequency 29 Hz and wavelength 3.86 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A population of 4,800 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    An object with initial velocity 15 m/s accelerates at 2.1 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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16. 16.

    Find the force needed to accelerate a 8 kg mass at 1.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A force of 93 N moves an object 12 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A right-angled triangle has legs of 8 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A force of 23 N acts on an area of 2.8 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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20. 20.

    A wave has frequency 706 Hz and wavelength 3.32 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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