Tunisia · Grade 10 · Practice Sheet 45

1. 1.

   A cylinder has radius 11 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   DT 3,100 is invested at 8% 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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3. 3.

   Find the force needed to accelerate a 12 kg mass at 4.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Solve for x: 9x + 9 = 63.

   Formula:Solving a Linear Equation

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

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5. 5.

   DT 2,200 is invested at 7.5% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

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

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6. 6.

   A wave has frequency 184 Hz and wavelength 3.22 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   A wave has frequency 91 Hz and wavelength 1.27 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   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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10. 10.

    Find the momentum of a 38 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Solve for x: 3x + 11 = 23.

    Formula:Solving a Linear Equation

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

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12. 12.

    DT 4,300 is invested at 6% 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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13. 13.

    Find the force needed to accelerate a 60 kg mass at 6.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A body starts at 11 m/s and accelerates at 4.8 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    An object has mass 165.6 g and volume 46 cm³. Find its density.

    Formula:Density

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

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16. 16.

    A cylinder has radius 3 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    A population of 4,400 grows 10% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A force of 57 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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19. 19.

    A value changes from 145 to 132. 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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20. 20.

    In a triangle, a = 11, b = 5 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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