Australia · Year 10 · Practice Sheet 29

1. 1.

   A force of 75 N moves an object 3 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   A population of 3,100 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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3. 3.

   Solve for x: 8x + 9 = 49.

   Formula:Solving a Linear Equation

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

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4. 4.

   A wave has frequency 186 Hz and wavelength 1.99 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A triangle has sides a = 5 cm and b = 14 cm with an included angle C = 90°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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6. 6.

   $3,400 is invested at 6% 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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7. 7.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 3 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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8. 8.

   A 37 kg object moves at 7 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A wave has frequency 214 Hz and wavelength 3.72 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A right-angled triangle has legs of 8 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    A device runs at 235 V drawing 7.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 8 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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13. 13.

    A bag has 24 equally likely marbles, of which 12 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.

    Find the force needed to accelerate a 50 kg mass at 2.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    $1,800 is invested at 8% compound interest per annum for 4 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.

    A wave has frequency 822 Hz and wavelength 4.16 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Solve using the quadratic formula: x² + 5x − 6 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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18. 18.

    A force of 23 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A wave has frequency 735 Hz and wavelength 2.51 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A population of 7,700 grows 8% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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