Qatar · Grade 10 · Practice Sheet 3

1. 1.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 2 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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2. 2.

   Find the momentum of a 47 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   QAR 500 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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4. 4.

   Find the force needed to accelerate a 18 kg mass at 2.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   QAR 4,900 is invested at 3% 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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6. 6.

   Solve for x: 8x + 11 = 43.

   Formula:Solving a Linear Equation

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

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7. 7.

   A value changes from 142 to 35. 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 right-angled triangle has legs of 4 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   A wave has frequency 792 Hz and wavelength 4.73 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 11 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    A population of 6,500 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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12. 12.

    An object has mass 184.9 g and volume 43 cm³. Find its density.

    Formula:Density

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

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13. 13.

    Find the force needed to accelerate a 10 kg mass at 6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A force of 13 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A device runs at 14 V drawing 9.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A triangle has sides a = 5 cm and b = 14 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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17. 17.

    An object with initial velocity 2 m/s accelerates at 1.2 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    A population of 6,300 grows 2% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    An object has mass 60.2 g and volume 7 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A body starts at 4 m/s and accelerates at 5 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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