ACT · Practice Sheet 2

1. 1.

   Mathematics

   Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

   Formula:Binomial Coefficient

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

   View formula →
2. 2.

   Physics

   A force of 592 N acts on an area of 39 m². Find the pressure.

   Formula:Pressure

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

   View formula →
3. 3.

   Physics

   Find the momentum of a 22 kg body moving at 5 m/s.

   Formula:Linear Momentum

   $p = mv$

   View formula →
4. 4.

   Physics

   A body moving at 1 m/s accelerates at 5 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 →
5. 5.

   Physics

   An object starts at 13 m/s and accelerates at 5 m/s² for 10 s. Find its final velocity.

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

   $v = u + at$

   View formula →
6. 6.

   Physics

   Find the electrical power when 52 V drives a current of 14 A.

   Formula:Electrical Power

   $P = VI$

   View formula →
7. 7.

   Physics

   If 3,864 J of work is done in 11 s, find the power.

   Formula:Power

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

   View formula →
8. 8.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

   View formula →
9. 9.

   Mathematics

   Evaluate ∫ from 0 to 5 of 5x^1 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 →
10. 10.

    Physics

    Find the force required to accelerate a 11 kg mass at 3 m/s².

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

    $F = ma$

    View formula →
11. 11.

    Quantitative Aptitude

    Find the simple interest on $11,000 at 10% per annum for 1 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

    View formula →
12. 12.

    Physics

    Find the kinetic energy of a 12 kg object moving at 6 m/s.

    Formula:Kinetic Energy

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

    View formula →
13. 13.

    Physics

    Calculate the potential energy of a 14 kg object at a height of 8 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
14. 14.

    Quantitative Aptitude

    The sum of the ages of two people is 36 years, and one is 4 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

    View formula →
15. 15.

    Quantitative Aptitude

    The marked price of an item is $400. After a 10% discount, find the selling price.

    Formula:Discount & Selling Price

    $SP = MP\left(1-\dfrac{d}{100}\right)$

    View formula →
16. 16.

    Physics

    If 259 J of work is done in 32 s, find the power.

    Formula:Power

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

    View formula →
17. 17.

    Mathematics

    Find the distance between the points (-1, 3) and (-7, -4).

    Formula:Distance Between Two Points

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

    View formula →
18. 18.

    Quantitative Aptitude

    A can finish a job in 15 days and B in 13 days. Working together, how long will they take?

    Formula:Time & Work (combined)

    $T = \dfrac{xy}{x+y}$

    View formula →
19. 19.

    Quantitative Aptitude

    An item is bought for $300 and sold for $390. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

    View formula →
20. 20.

    Quantitative Aptitude

    A invests $8,000 and B invests $7,000 for the same period. If the total profit is $14,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

    View formula →

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