Spain · Grado 9 · Practice Sheet 21

1. 1.

   A right-angled triangle has legs of 3 cm and 13 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A circle has a radius of 25 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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3. 3.

   A bag has 24 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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4. 4.

   A train moves at 33 km/h for 5.8 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   A circle has a radius of 23 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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6. 6.

   A wave has frequency 545 Hz and wavelength 1.66 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A cylinder has radius 6 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Find the gravitational potential energy of a 37 kg object raised 34 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A force of 20 N moves an object 38 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    €32 is shared in the ratio 1 : 1. Find each share.

    Formula:Dividing in a Ratio

    $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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11. 11.

    A 3 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A device runs at 189 V drawing 1.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A force of 56 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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14. 14.

    A force of 213 N acts on an area of 3.3 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    €1,900 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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16. 16.

    A cone has base radius 11 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    A circle has a radius of 7 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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18. 18.

    Find the circumference of a circle whose radius is 12 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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19. 19.

    Find the force needed to accelerate a 53 kg mass at 7.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Solve for x: 4x + 17 = 49.

    Formula:Solving a Linear Equation

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

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