EmSAT Achieve · Practice Sheet 40

1. 1.

   Mathematics

   Evaluate ∫ from 2 to 3 of 1x^2 dx.

   Formula:Definite Integral of a Power

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

   View formula →
2. 2.

   Chemistry

   Find the pressure of 4 mol of an ideal gas at 312 K in a 2 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

   View formula →
3. 3.

   Biology

   Calculate the BMI of a person weighing 94 kg with height 1.58 m.

   Formula:Body Mass Index

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

   View formula →
4. 4.

   Mathematics

   Find the distance between the points (-6, 3) and (6, 1).

   Formula:Distance Between Two Points

   $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

   View formula →
5. 5.

   Mathematics

   Evaluate log base 2 of 32.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

   View formula →
6. 6.

   Physics

   Find the momentum of a 24 kg body moving at 18 m/s.

   Formula:Linear Momentum

   $p = mv$

   View formula →
7. 7.

   Chemistry

   Find the pressure of 1 mol of an ideal gas at 306 K in a 18 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

   View formula →
8. 8.

   Physics

   A projectile is launched at 39 m/s at 30° to the horizontal. Find its range (g = 9.8 m/s²).

   Formula:Projectile Range

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

   View formula →
9. 9.

   Chemistry

   Find the pressure of 2 mol of an ideal gas at 313 K in a 3 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

   View formula →
10. 10.

    Chemistry

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

    Formula:Number of Moles

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

    View formula →
11. 11.

    Physics

    An object starts at 4 m/s and accelerates at 4 m/s² for 4 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

    View formula →
12. 12.

    Physics

    If 1,431 J of work is done in 28 s, find the power.

    Formula:Power

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

    View formula →
13. 13.

    Mathematics

    Find the distance between the points (-5, -4) and (-3, -5).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

    View formula →
14. 14.

    Mathematics

    Evaluate ∫ from 2 to 5 of 2x^3 dx.

    Formula:Definite Integral of a Power

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

    View formula →
15. 15.

    Physics

    Find the kinetic energy of a 16 kg object moving at 13 m/s.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2}mv^{2}$

    View formula →
16. 16.

    Physics

    Find the voltage across a 4 Ω resistor carrying a current of 12 A.

    Formula:Ohm's Law

    $V = IR$

    View formula →
17. 17.

    Mathematics

    Find the distance between the points (-6, -8) and (-3, 1).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

    View formula →
18. 18.

    Chemistry

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

    Formula:pH of a Solution

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

    View formula →
19. 19.

    Mathematics

    In an arithmetic progression with first term 9 and common difference 9, find term number 17.

    Formula:AP nth Term

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

    View formula →
20. 20.

    Biology

    In a population at Hardy–Weinberg equilibrium, the recessive allele frequency q = 0.3. Find the dominant allele frequency p and the percentage of heterozygous carriers.

    Formula:Hardy–Weinberg Equilibrium

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

    View formula →

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