New Zealand · Year 10 · Practice Sheet 15

1. 1.

   A right-angled triangle has legs of 3 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Solve for x: 4x + 4 = 28.

   Formula:Solving a Linear Equation

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

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3. 3.

   A force of 58 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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4. 4.

   A device runs at 151 V drawing 5.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A wave has frequency 815 Hz and wavelength 4.19 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 10 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   A device runs at 26 V drawing 4.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the force needed to accelerate a 29 kg mass at 1.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A force of 14 N moves an object 29 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A population of 7,000 grows 8% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    $1,400 is invested at 6% 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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12. 12.

    A cylinder has radius 6 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    A triangle has sides a = 17 cm and b = 14 cm with an included angle C = 120°. 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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14. 14.

    An object has mass 15.6 g and volume 12 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A force of 64 N moves an object 8 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A value changes from 148 to 87. 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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17. 17.

    A cylinder has radius 12 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    $3,800 is invested at 3% 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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19. 19.

    A 38 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    Solve for x: 4x + 2 = 14.

    Formula:Solving a Linear Equation

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

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