Iraq · Grade 10 · Practice Sheet 33

1. 1.

   In a triangle, a = 12, b = 14 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   A cone has base radius 10 cm and height 23 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 wave has frequency 51 Hz and wavelength 4.1 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the force needed to accelerate a 53 kg mass at 1.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A device runs at 84 V drawing 5.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A force of 62 N moves an object 40 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   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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8. 8.

   IQD 3,800 is invested at 5% 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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9. 9.

   Solve using the quadratic formula: x² + 0x − 1 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A body starts at 8 m/s and accelerates at 4.3 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A current of 1.4 A flows through a 13 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A population of 7,100 grows 3% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A 39 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    An object has mass 177.6 g and volume 37 cm³. Find its density.

    Formula:Density

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

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15. 15.

    In a triangle, a = 15, b = 7 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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16. 16.

    Solve for x: 5x + 11 = 36.

    Formula:Solving a Linear Equation

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

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17. 17.

    An object with initial velocity 5 m/s accelerates at 1.5 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    A triangle has sides a = 9 cm and b = 6 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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19. 19.

    In a triangle, a = 7, b = 8 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    A 39 kg object moves at 23 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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