Egypt · Grade 10 · Practice Sheet 39

1. 1.

   A wave has frequency 316 Hz and wavelength 1.04 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A body starts at 10 m/s and accelerates at 4.7 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   Find the gravitational potential energy of a 19 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A device runs at 159 V drawing 3.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A right-angled triangle has legs of 7 cm and 13 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   A value changes from 92 to 257. 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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7. 7.

   A cone has base radius 3 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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8. 8.

   Solve for x: 8x + 5 = 93.

   Formula:Solving a Linear Equation

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

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9. 9.

   A device runs at 77 V drawing 9.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Solve using the quadratic formula: x² + 11x + 30 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A population of 5,200 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    An object with initial velocity 15 m/s accelerates at 2.8 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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13. 13.

    E£ 2,100 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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14. 14.

    Solve for x: 4x + 2 = 50.

    Formula:Solving a Linear Equation

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

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15. 15.

    A body starts at 16 m/s and accelerates at 1.3 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    A triangle has sides a = 5 cm and b = 16 cm with an included angle C = 30°. 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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17. 17.

    E£ 1,300 is invested at 7.5% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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18. 18.

    A cone has base radius 5 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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19. 19.

    Find the gravitational potential energy of a 42 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    E£ 1,900 is invested at 6% compound interest per annum for 3 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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