Egypt · Grade 9 · Practice Sheet 46

1. 1.

   A cylinder has radius 4 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   A value changes from 166 to 182. 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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3. 3.

   E£ 3,700 is invested at 10% 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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4. 4.

   A right-angled triangle has legs of 18 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   A current of 1.4 A flows through a 12 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A circle has a radius of 4 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   Find the force needed to accelerate a 29 kg mass at 8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A force of 425 N acts on an area of 9.7 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Find the gravitational potential energy of a 14 kg object raised 20 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Find the force needed to accelerate a 54 kg mass at 3.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A cone has base radius 5 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    A force of 84 N moves an object 32 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Solve for x: 9x + 19 = 55.

    Formula:Solving a Linear Equation

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

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14. 14.

    Find the momentum of a 42 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A cone has base radius 2 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    Solve for x: 6x + 13 = 67.

    Formula:Solving a Linear Equation

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

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17. 17.

    Find the circumference of a circle whose radius is 26 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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18. 18.

    A wave has frequency 74 Hz and wavelength 2.11 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Solve for x: 4x + 5 = 17.

    Formula:Solving a Linear Equation

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

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20. 20.

    A circle has a radius of 5 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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