Egypt · Grade 10 · Practice Sheet 6

1. 1.

   Solve for x: 2x + 18 = 24.

   Formula:Solving a Linear Equation

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

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2. 2.

   A population of 7,300 grows 2% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A value changes from 41 to 83. 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 right-angled triangle has legs of 11 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 11 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   A device runs at 30 V drawing 4.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A 37 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   An object has mass 24 g and volume 15 cm³. Find its density.

   Formula:Density

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

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9. 9.

   Find the momentum of a 50 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    Find the force needed to accelerate a 19 kg mass at 2.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 48 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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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 value changes from 178 to 93. 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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14. 14.

    A 9 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    E£ 1,100 is invested at 8% compound interest per annum for 2 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.

    E£ 1,500 is invested at 4% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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17. 17.

    A triangle has sides a = 9 cm and b = 6 cm with an included angle C = 60°. 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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18. 18.

    Find the force needed to accelerate a 19 kg mass at 6.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A wave has frequency 468 Hz and wavelength 3.27 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A population of 8,500 grows 2% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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