Kuwait · Grade 10 · Practice Sheet 35

1. 1.

   A value changes from 189 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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2. 2.

   Solve using the quadratic formula: x² − 1x − 2 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   Solve for x: 6x + 15 = 33.

   Formula:Solving a Linear Equation

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

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4. 4.

   A force of 413 N acts on an area of 8.9 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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5. 5.

   A bag has 11 equally likely marbles, of which 6 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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6. 6.

   KD 1,500 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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7. 7.

   A force of 126 N acts on an area of 0.5 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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8. 8.

   A wave has frequency 626 Hz and wavelength 2.07 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   KD 3,400 is invested at 5% 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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10. 10.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    A wave has frequency 95 Hz and wavelength 1.38 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A device runs at 116 V drawing 9.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A population of 1,900 grows 8% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    A device runs at 148 V drawing 3.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the momentum of a 30 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the force needed to accelerate a 19 kg mass at 3.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A wave has frequency 368 Hz and wavelength 3.31 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A current of 7.8 A flows through a 55 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A triangle has sides a = 7 cm and b = 19 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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20. 20.

    An object with initial velocity 6 m/s accelerates at 4.5 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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