ACT · Practice Sheet 24

1. 1.

   Physics

   A projectile is launched at 32 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 →
2. 2.

   Physics

   Find the force required to accelerate a 49 kg mass at 19 m/s².

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

   $F = ma$

   View formula →
3. 3.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

   Formula:Probability (two dice)

   $P = \dfrac{\text{favourable}}{\text{total}}$

   View formula →
4. 4.

   Mathematics

   Evaluate ∫ from 0 to 4 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 →
5. 5.

   Mathematics

   Find the distance between the points (0, -4) and (-3, -1).

   Formula:Distance Between Two Points

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

   View formula →
6. 6.

   Physics

   A force of 823 N acts on an area of 40 m². Find the pressure.

   Formula:Pressure

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

   View formula →
7. 7.

   Mathematics

   Find the sum of the first 14 terms of an AP with first term 2 and common difference 5.

   Formula:AP Sum of n Terms

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

   View formula →
8. 8.

   Quantitative Aptitude

   Find the average of these 8 numbers: 40, 65, 78, 73, 80, 62, 76, 34.

   Formula:Arithmetic Mean

   $\bar{x} = \dfrac{\sum x}{n}$

   View formula →
9. 9.

   Physics

   A projectile is launched at 25 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 →
10. 10.

    Physics

    Find the kinetic energy of a 11 kg object moving at 9 m/s.

    Formula:Kinetic Energy

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

    View formula →
11. 11.

    Quantitative Aptitude

    A vehicle covers 220 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

    View formula →
12. 12.

    Quantitative Aptitude

    The marked price of an item is $1,500. After a 20% discount, find the selling price.

    Formula:Discount & Selling Price

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

    View formula →
13. 13.

    Mathematics

    Find the slope of the line through (2, 2) and (-8, 3).

    Formula:Slope of a Line

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

    View formula →
14. 14.

    Physics

    An object starts at 5 m/s and accelerates at 4 m/s² for 11 s. Find its final velocity.

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

    $v = u + at$

    View formula →
15. 15.

    Mathematics

    Find the sum of the first 12 terms of an AP with first term 18 and common difference 2.

    Formula:AP Sum of n Terms

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

    View formula →
16. 16.

    Physics

    A constant force of 105 N moves an object 19 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

    View formula →
17. 17.

    Physics

    Find the electrical power when 178 V drives a current of 13 A.

    Formula:Electrical Power

    $P = VI$

    View formula →
18. 18.

    Physics

    A force of 831 N acts on an area of 41 m². Find the pressure.

    Formula:Pressure

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

    View formula →
19. 19.

    Physics

    Calculate the potential energy of a 39 kg object at a height of 37 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
20. 20.

    Quantitative Aptitude

    The marked price of an item is $900. After a 15% discount, find the selling price.

    Formula:Discount & Selling Price

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

    View formula →

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