Peru · Grado 10 · Practice Sheet 15

1. 1.

   A triangle has sides a = 15 cm and b = 18 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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2. 2.

   Solve for x: 9x + 11 = 83.

   Formula:Solving a Linear Equation

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

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3. 3.

   A force of 104 N moves an object 29 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A bag has 27 equally likely marbles, of which 7 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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5. 5.

   A cone has base radius 9 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   A right-angled triangle has legs of 3 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   A force of 67 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the force needed to accelerate a 13 kg mass at 0.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Solve using the quadratic formula: x² − 4x − 5 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A force of 295 N acts on an area of 9.8 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A force of 25 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A wave has frequency 113 Hz and wavelength 2.73 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A 10 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    Find the force needed to accelerate a 6 kg mass at 4.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A current of 5.3 A flows through a 20 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A force of 459 N acts on an area of 8.5 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    An object has mass 450 g and volume 50 cm³. Find its density.

    Formula:Density

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

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18. 18.

    A population of 2,300 grows 10% 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.

    A cylinder has radius 6 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A right-angled triangle has legs of 14 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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