Spain · Grado 9 · Practice Sheet 38

1. 1.

   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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2. 2.

   A value changes from 97 to 249. 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.

   €2,000 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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4. 4.

   A wave has frequency 181 Hz and wavelength 0.45 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A cone has base radius 2 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   A current of 6.2 A flows through a 24 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Find the force needed to accelerate a 41 kg mass at 5.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A force of 112 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A current of 5 A flows through a 17 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A right-angled triangle has legs of 12 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    Find the gravitational potential energy of a 16 kg object raised 37 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A current of 2.5 A flows through a 47 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A right-angled triangle has legs of 16 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    A bag has 14 equally likely marbles, of which 7 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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15. 15.

    Solve for x: 6x + 2 = 38.

    Formula:Solving a Linear Equation

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

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16. 16.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    Find the circumference of a circle whose radius is 15 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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18. 18.

    A current of 4.7 A flows through a 42 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A 14 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A right-angled triangle has legs of 20 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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