New Zealand · Year 9 · Practice Sheet 25

1. 1.

   $1,800 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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2. 2.

   A right-angled triangle has legs of 18 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   A car travels 318 km in 3 hours. Find its average speed.

   Formula:Speed

   $v = \dfrac{d}{t}$

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4. 4.

   Find the momentum of a 36 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the gravitational potential energy of a 35 kg object raised 38 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Solve for x: 5x + 12 = 52.

   Formula:Solving a Linear Equation

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

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7. 7.

   Find the force needed to accelerate a 17 kg mass at 2.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A train moves at 23 km/h for 2.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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9. 9.

   $2,800 is invested at 7.5% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

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

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10. 10.

    Find the force needed to accelerate a 42 kg mass at 0.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A value changes from 67 to 199. 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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12. 12.

    A 32 kg object moves at 22 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    Solve for x: 6x + 14 = 74.

    Formula:Solving a Linear Equation

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

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14. 14.

    $1,300 is invested at 3% 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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15. 15.

    $2,200 is invested at 6% 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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16. 16.

    Solve for x: 3x + 16 = 43.

    Formula:Solving a Linear Equation

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

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17. 17.

    Find the force needed to accelerate a 30 kg mass at 6.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A cylinder has radius 12 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A wave has frequency 386 Hz and wavelength 3.49 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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