EmSAT Achieve · Practice Sheet 32

1. 1.

   Physics

   Find the kinetic energy of a 1 kg object moving at 19 m/s.

   Formula:Kinetic Energy

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

   View formula →
2. 2.

   Chemistry

   Find the pressure of 5 mol of an ideal gas at 350 K in a 12 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

   View formula →
3. 3.

   Physics

   Find the voltage across a 48 Ω resistor carrying a current of 9 A.

   Formula:Ohm's Law

   $V = IR$

   View formula →
4. 4.

   Mathematics

   Evaluate log base 5 of 125.

   Formula:Logarithm Evaluation

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

   View formula →
5. 5.

   Physics

   Find the electrical power when 223 V drives a current of 1 A.

   Formula:Electrical Power

   $P = VI$

   View formula →
6. 6.

   Physics

   A projectile is launched at 20 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 →
7. 7.

   Mathematics

   Find the slope of the line through (3, 7) and (4, -2).

   Formula:Slope of a Line

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

   View formula →
8. 8.

   Physics

   An object starts at 20 m/s and accelerates at 6 m/s² for 9 s. Find its final velocity.

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

   $v = u + at$

   View formula →
9. 9.

   Mathematics

   Find term number 3 of a geometric progression with first term 1 and common ratio 3.

   Formula:GP nth Term

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

   View formula →
10. 10.

    Physics

    Find the electrical power when 95 V drives a current of 8 A.

    Formula:Electrical Power

    $P = VI$

    View formula →
11. 11.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 4 and common ratio 2.

    Formula:GP Sum of n Terms

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

    View formula →
12. 12.

    Physics

    Find the force required to accelerate a 14 kg mass at 17 m/s².

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

    $F = ma$

    View formula →
13. 13.

    Physics

    Find the momentum of a 43 kg body moving at 35 m/s.

    Formula:Linear Momentum

    $p = mv$

    View formula →
14. 14.

    Physics

    Calculate the potential energy of a 13 kg object at a height of 46 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
15. 15.

    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation

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

    View formula →
16. 16.

    Mathematics

    For the quadratic 3x² + 5x − 1 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

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

    View formula →
17. 17.

    Chemistry

    Find the pressure of 1 mol of an ideal gas at 342 K in a 5 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

    View formula →
18. 18.

    Chemistry

    How many moles are present in 88 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

    Formula:Number of Moles

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

    View formula →
19. 19.

    Mathematics

    Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

    Formula:Binomial Coefficient

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

    View formula →
20. 20.

    Mathematics

    For the quadratic 1x² − 6x − 9 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

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

    View formula →

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