Switzerland · Grade 9 · Practice Sheet 23

1. 1.

   A right-angled triangle has legs of 4 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A cone has base radius 6 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   Find the momentum of a 34 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A circle has a radius of 20 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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5. 5.

   A train moves at 65 km/h for 4.9 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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6. 6.

   A cone has base radius 10 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A bag has 16 equally likely marbles, of which 8 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 train moves at 32 km/h for 2.2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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9. 9.

   An object has mass 159.6 g and volume 28 cm³. Find its density.

   Formula:Density

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

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10. 10.

    Find the force needed to accelerate a 10 kg mass at 7.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A wave has frequency 365 Hz and wavelength 1.23 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the momentum of a 16 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A bag has 10 equally likely marbles, of which 2 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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14. 14.

    Solve for x: 3x + 17 = 23.

    Formula:Solving a Linear Equation

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

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15. 15.

    Find the force needed to accelerate a 33 kg mass at 8.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the gravitational potential energy of a 28 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A circle has a radius of 10 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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18. 18.

    CHF 2,900 is invested at 4% compound interest per annum for 3 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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19. 19.

    A cone has base radius 6 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    CHF 3,600 is invested at 8% simple interest per year for 6 years. Find the interest earned.

    Formula:Simple Interest

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

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