EmSAT Achieve · Practice Sheet 17

1. 1.

   Physics

   A projectile is launched at 25 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

   Formula:Projectile Range

   $R = \dfrac{u^{2}\sin 2\theta}{g}$

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2. 2.

   Physics

   A constant force of 35 N moves an object 50 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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3. 3.

   Biology

   Calculate the BMI of a person weighing 90 kg with height 1.67 m.

   Formula:Body Mass Index

   $BMI = \dfrac{m}{h^{2}}$

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4. 4.

   Mathematics

   Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.

   Formula:Binomial Coefficient

   $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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5. 5.

   Physics

   A force of 654 N acts on an area of 7 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Physics

   Find the density of an object with mass 11 g and volume 29 cm³.

   Formula:Density

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

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7. 7.

   Physics

   Calculate the potential energy of a 8 kg object at a height of 14 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Mathematics

   Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.

   Formula:Binomial Coefficient

   $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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9. 9.

   Physics

   Find the force required to accelerate a 8 kg mass at 2 m/s².

   Formula:Newton's Second Law (F = ma)

   $F = ma$

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10. 10.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻2 mol/L.

    Formula:pH of a Solution

    $pH = -\log_{10}[H^{+}]$

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11. 11.

    Chemistry

    16 mL of a 5 M solution is diluted to 241 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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12. 12.

    Physics

    A constant force of 173 N moves an object 17 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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13. 13.

    Mathematics

    In an arithmetic progression with first term 6 and common difference 6, find term number 16.

    Formula:AP nth Term

    $a_n = a + (n-1)d$

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14. 14.

    Mathematics

    Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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15. 15.

    Physics

    If 3,626 J of work is done in 8 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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16. 16.

    Biology

    Under a microscope, an object of actual size 0.8 mm appears 10.4 mm. Find the magnification.

    Formula:Microscope Magnification

    $M = \dfrac{\text{image size}}{\text{actual size}}$

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17. 17.

    Physics

    Find the density of an object with mass 291 g and volume 17 cm³.

    Formula:Density

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

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18. 18.

    Physics

    Find the voltage across a 29 Ω resistor carrying a current of 10 A.

    Formula:Ohm's Law

    $V = IR$

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19. 19.

    Mathematics

    Find the slope of the line through (2, -6) and (3, 2).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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20. 20.

    Physics

    Find the voltage across a 18 Ω resistor carrying a current of 2 A.

    Formula:Ohm's Law

    $V = IR$

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