Tanzania · Grade 11 · Practice Sheet 24

1. 1.

   A right-angled triangle has legs of 17 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Find the sum of the first 3 terms of a geometric series with first term a = 3 and common ratio r = 2.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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3. 3.

   A cone has base radius 12 cm and height 16 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.

   In a triangle, a = 7, b = 10 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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5. 5.

   A 3 kg object moves at 23 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   A wave has frequency 553 Hz and wavelength 0.43 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the force needed to accelerate a 7 kg mass at 8.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A cone has base radius 10 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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9. 9.

   Find the momentum of a 42 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A device runs at 225 V drawing 3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A force of 112 N acts on an area of 9.5 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A body starts at 15 m/s and accelerates at 5.8 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    TSh 2,800 is invested at 6% 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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14. 14.

    Find the force needed to accelerate a 33 kg mass at 7.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Two masses 7,700 kg and 610 kg are 7 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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16. 16.

    An object with initial velocity 3 m/s accelerates at 2.3 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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17. 17.

    An object has mass 224.1 g and volume 27 cm³. Find its density.

    Formula:Density

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

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18. 18.

    Find the population standard deviation of: 13, 19, 14, 20, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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19. 19.

    Solve using the quadratic formula: x² + 3x − 4 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A wave has frequency 404 Hz and wavelength 0.39 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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