South Africa · Grade 10 · Practice Sheet 9

1. 1.

   A wave has frequency 817 Hz and wavelength 0.38 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A value changes from 49 to 152. 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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3. 3.

   In a triangle, a = 9, b = 10 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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4. 4.

   A device runs at 221 V drawing 1.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A triangle has sides a = 20 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.

   An object has mass 62.4 g and volume 26 cm³. Find its density.

   Formula:Density

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

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7. 7.

   A value changes from 76 to 123. 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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8. 8.

   A bag has 29 equally likely marbles, of which 26 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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9. 9.

   Find the momentum of a 33 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A wave has frequency 439 Hz and wavelength 3.15 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A right-angled triangle has legs of 9 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    A 31 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A current of 6.6 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A device runs at 64 V drawing 8.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    R2,800 is invested at 5% 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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16. 16.

    A 24 kg object moves at 5 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    R1,400 is invested at 3% compound interest per annum for 5 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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18. 18.

    A bag has 20 equally likely marbles, of which 3 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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19. 19.

    Find the gravitational potential energy of a 20 kg object raised 11 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Solve for x: 3x + 13 = 31.

    Formula:Solving a Linear Equation

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

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