Iraq · Grade 10 · Practice Sheet 35

1. 1.

   A right-angled triangle has legs of 15 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A cone has base radius 8 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   A right-angled triangle has legs of 19 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   A force of 25 N moves an object 3 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   Find the force needed to accelerate a 2 kg mass at 7.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A force of 99 N acts on an area of 2.6 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A wave has frequency 345 Hz and wavelength 4.64 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Solve for x: 3x + 16 = 31.

   Formula:Solving a Linear Equation

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

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9. 9.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    IQD 3,500 is invested at 4% 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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11. 11.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 3 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    A wave has frequency 410 Hz and wavelength 1.21 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A population of 8,400 grows 5% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    A device runs at 58 V drawing 2.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A population of 6,800 grows 5% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    A force of 45 N moves an object 39 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the momentum of a 8 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A cone has base radius 7 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.

    An object with initial velocity 0 m/s accelerates at 2.5 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    A triangle has sides a = 6 cm and b = 5 cm with an included angle C = 45°. 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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