Colombia · Grado 10 · Practice Sheet 18

1. 1.

   A triangle has sides a = 9 cm and b = 13 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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2. 2.

   Solve for x: 4x + 3 = 43.

   Formula:Solving a Linear Equation

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

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3. 3.

   A value changes from 153 to 55. 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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4. 4.

   A device runs at 184 V drawing 6.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   An object has mass 54 g and volume 36 cm³. Find its density.

   Formula:Density

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

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6. 6.

   Find the force needed to accelerate a 18 kg mass at 3.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A cylinder has radius 5 cm and height 19 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 49 kg object raised 36 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A device runs at 194 V drawing 1.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the sum of the first 14 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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11. 11.

    A current of 2.2 A flows through a 50 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A value changes from 100 to 57. 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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13. 13.

    A force of 6 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    An object with initial velocity 1 m/s accelerates at 1.8 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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15. 15.

    $1,400 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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16. 16.

    A current of 7.6 A flows through a 52 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A right-angled triangle has legs of 19 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    An object has mass 257.6 g and volume 46 cm³. Find its density.

    Formula:Density

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

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19. 19.

    A value changes from 180 to 203. 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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20. 20.

    An object has mass 71.4 g and volume 21 cm³. Find its density.

    Formula:Density

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

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