Iraq · Grade 10 · Practice Sheet 29

1. 1.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 4 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A force of 57 N moves an object 14 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 4 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   A wave has frequency 259 Hz and wavelength 3.3 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A force of 111 N acts on an area of 7.9 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   A right-angled triangle has legs of 13 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   A wave has frequency 103 Hz and wavelength 3.07 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A force of 270 N acts on an area of 6.7 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Solve for x: 3x + 2 = 8.

   Formula:Solving a Linear Equation

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

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10. 10.

    Find the force needed to accelerate a 44 kg mass at 6.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    An object with initial velocity 10 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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12. 12.

    A right-angled triangle has legs of 18 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    A body starts at 5 m/s and accelerates at 3.1 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    A wave has frequency 463 Hz and wavelength 2.23 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A population of 5,300 grows 3% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    In a triangle, a = 17, b = 11 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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17. 17.

    A device runs at 106 V drawing 4.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Solve for x: 4x + 12 = 40.

    Formula:Solving a Linear Equation

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

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19. 19.

    Solve using the quadratic formula: x² + 2x − 3 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A device runs at 140 V drawing 4.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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