EmSAT Achieve · Practice Sheet 10

1. 1.

   Physics

   A projectile is launched at 41 m/s at 60° 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

   Calculate the potential energy of a 30 kg object at a height of 11 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Mathematics

   Evaluate ∫ from 1 to 5 of 4x^3 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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4. 4.

   Chemistry

   Find the pH of a solution with [H⁺] = 2×10⁻5 mol/L.

   Formula:pH of a Solution

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

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5. 5.

   Chemistry

   52 mL of a 5 M solution is diluted to 193 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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6. 6.

   Physics

   Calculate the potential energy of a 49 kg object at a height of 48 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Mathematics

   Find term number 3 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

   $a_n = a\,r^{\,n-1}$

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8. 8.

   Physics

   Find the voltage across a 21 Ω resistor carrying a current of 6 A.

   Formula:Ohm's Law

   $V = IR$

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9. 9.

   Physics

   If 2,933 J of work is done in 27 s, find the power.

   Formula:Power

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

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10. 10.

    Physics

    Find the momentum of a 12 kg body moving at 22 m/s.

    Formula:Linear Momentum

    $p = mv$

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11. 11.

    Biology

    Calculate the BMI of a person weighing 100 kg with height 1.64 m.

    Formula:Body Mass Index

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

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12. 12.

    Physics

    A force of 598 N acts on an area of 46 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Chemistry

    How many moles are present in 500 g of calcium carbonate (CaCO₃) (molar mass = 100 g/mol)?

    Formula:Number of Moles

    $n = \dfrac{m}{M}$

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14. 14.

    Biology

    In a monohybrid cross (Aa × Aa) producing 16 F₂ offspring, how many are expected to show the dominant and the recessive phenotype (3:1 ratio)?

    Formula:Monohybrid Cross (3:1)

    $\text{Dominant}:\text{Recessive} = 3:1$

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15. 15.

    Physics

    If 513 J of work is done in 6 s, find the power.

    Formula:Power

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

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16. 16.

    Physics

    A projectile is launched at 40 m/s at 60° 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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17. 17.

    Physics

    A force of 613 N acts on an area of 42 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Chemistry

    How many moles are present in 146.25 g of sodium chloride (NaCl) (molar mass = 58.5 g/mol)?

    Formula:Number of Moles

    $n = \dfrac{m}{M}$

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19. 19.

    Physics

    Find the force required to accelerate a 27 kg mass at 10 m/s².

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

    $F = ma$

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20. 20.

    Biology

    Under a microscope, an object of actual size 3.5 mm appears 129.5 mm. Find the magnification.

    Formula:Microscope Magnification

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

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