EmSAT Achieve · Practice Sheet 25

1. 1.

   Mathematics

   In an arithmetic progression with first term 2 and common difference 8, find term number 28.

   Formula:AP nth Term

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

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2. 2.

   Biology

   Under a microscope, an object of actual size 1.6 mm appears 56 mm. Find the magnification.

   Formula:Microscope Magnification

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

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3. 3.

   Physics

   A force of 301 N acts on an area of 48 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Physics

   A projectile is launched at 27 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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5. 5.

   Mathematics

   For the quadratic 4x² + 9x − 8 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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6. 6.

   Physics

   If 3,538 J of work is done in 49 s, find the power.

   Formula:Power

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

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7. 7.

   Mathematics

   If f(x) = 2x³ + 5x² + 3x, find f′(5).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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8. 8.

   Biology

   In a monohybrid cross (Aa × Aa) producing 148 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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9. 9.

   Mathematics

   If f(x) = 4x³ + 5x² + 1x, find f′(2).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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10. 10.

    Physics

    A force of 528 N acts on an area of 23 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Chemistry

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

    Formula:pH of a Solution

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

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12. 12.

    Mathematics

    Find the sum of the first 14 terms of an AP with first term 15 and common difference 3.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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13. 13.

    Physics

    Find the electrical power when 136 V drives a current of 18 A.

    Formula:Electrical Power

    $P = VI$

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14. 14.

    Chemistry

    Find the molarity of a solution containing 3 mol of solute in 4 L of solution.

    Formula:Molarity

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

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15. 15.

    Biology

    In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.4. Find the dominant allele frequency p and the percentage of heterozygous carriers.

    Formula:Hardy–Weinberg Equilibrium

    $p + q = 1,\;\; 2pq = \text{carriers}$

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16. 16.

    Mathematics

    Find the sum of the first 5 terms of an AP with first term 12 and common difference 7.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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17. 17.

    Physics

    Find the momentum of a 25 kg body moving at 2 m/s.

    Formula:Linear Momentum

    $p = mv$

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18. 18.

    Physics

    Find the voltage across a 36 Ω resistor carrying a current of 11 A.

    Formula:Ohm's Law

    $V = IR$

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19. 19.

    Mathematics

    If f(x) = 3x³ + 5x² + 7x, find f′(1).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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20. 20.

    Chemistry

    Find the pH of a solution with [H⁺] = 1×10⁻4 mol/L.

    Formula:pH of a Solution

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

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