Tanzania · Grade 10 · Practice Sheet 46

1. 1.

   A force of 291 N acts on an area of 7.8 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A triangle has sides a = 20 cm and b = 17 cm with an included angle C = 90°. 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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4. 4.

   Solve for x: 7x + 10 = 66.

   Formula:Solving a Linear Equation

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

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5. 5.

   TSh 1,900 is invested at 3% simple interest per year for 4 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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6. 6.

   A force of 68 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A bag has 13 equally likely marbles, of which 9 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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8. 8.

   A wave has frequency 319 Hz and wavelength 3.5 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the force needed to accelerate a 30 kg mass at 3.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    An object with initial velocity 15 m/s accelerates at 1.3 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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11. 11.

    Solve for x: 9x + 20 = 119.

    Formula:Solving a Linear Equation

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

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12. 12.

    A wave has frequency 50 Hz and wavelength 0.77 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A force of 116 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A right-angled triangle has legs of 5 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 11 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    TSh 500 is invested at 5% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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17. 17.

    A cylinder has radius 13 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    A body starts at 14 m/s and accelerates at 3.6 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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20. 20.

    A wave has frequency 193 Hz and wavelength 0.24 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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