EmSAT Achieve · Practice Sheet 24

1. 1.

   Physics

   Find the density of an object with mass 264 g and volume 8 cm³.

   Formula:Density

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

   View formula →
2. 2.

   Mathematics

   If f(x) = 1x³ + 5x² + 8x, find f′(3).

   Formula:Derivative of a Polynomial

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

   View formula →
3. 3.

   Physics

   Calculate the potential energy of a 16 kg object at a height of 31 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
4. 4.

   Physics

   Find the density of an object with mass 460 g and volume 7 cm³.

   Formula:Density

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

   View formula →
5. 5.

   Mathematics

   Find the slope of the line through (0, 3) and (1, 0).

   Formula:Slope of a Line

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

   View formula →
6. 6.

   Physics

   A projectile is launched at 45 m/s at 60° to the horizontal. Find its range (g = 9.8 m/s²).

   Formula:Projectile Range

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

   View formula →
7. 7.

   Mathematics

   Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

   Formula:Binomial Coefficient

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

   View formula →
8. 8.

   Mathematics

   If f(x) = 4x³ + 3x² + 1x, find f′(5).

   Formula:Derivative of a Polynomial

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

   View formula →
9. 9.

   Physics

   Calculate the potential energy of a 27 kg object at a height of 27 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
10. 10.

    Biology

    In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.1. Find the dominant allele frequency p and the percentage of heterozygous carriers.

    Formula:Hardy–Weinberg Equilibrium

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

    View formula →
11. 11.

    Physics

    Find the density of an object with mass 366 g and volume 9 cm³.

    Formula:Density

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

    View formula →
12. 12.

    Physics

    If 2,105 J of work is done in 19 s, find the power.

    Formula:Power

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

    View formula →
13. 13.

    Chemistry

    How many moles are present in 36 g of water (H₂O) (molar mass = 18 g/mol)?

    Formula:Number of Moles

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

    View formula →
14. 14.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 4 and common ratio 3.

    Formula:GP Sum of n Terms

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

    View formula →
15. 15.

    Chemistry

    Find the pressure of 3 mol of an ideal gas at 230 K in a 17 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

    View formula →
16. 16.

    Physics

    A body moving at 14 m/s accelerates at 3 m/s² for 9 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

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

    View formula →
17. 17.

    Chemistry

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

    Formula:pH of a Solution

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

    View formula →
18. 18.

    Biology

    In a monohybrid cross (Aa × Aa) producing 36 F₂ offspring, how many are expected to show the dominant and the recessive phenotype (3:1 ratio)?

    Formula:Monohybrid Cross (3:1)

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

    View formula →
19. 19.

    Physics

    A force of 290 N acts on an area of 45 m². Find the pressure.

    Formula:Pressure

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

    View formula →
20. 20.

    Physics

    Find the force required to accelerate a 19 kg mass at 15 m/s².

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

    $F = ma$

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.