ACT · Practice Sheet 15

1. 1.

   Physics

   Find the force required to accelerate a 34 kg mass at 13 m/s².

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

   $F = ma$

   View formula →
2. 2.

   Quantitative Aptitude

   A can finish a job in 6 days and B in 4 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

   View formula →
3. 3.

   Physics

   An object starts at 6 m/s and accelerates at 1 m/s² for 11 s. Find its final velocity.

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

   $v = u + at$

   View formula →
4. 4.

   Mathematics

   Find the slope of the line through (-3, -5) and (5, -8).

   Formula:Slope of a Line

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

   View formula →
5. 5.

   Physics

   If 4,993 J of work is done in 44 s, find the power.

   Formula:Power

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

   View formula →
6. 6.

   Physics

   Find the voltage across a 5 Ω resistor carrying a current of 1 A.

   Formula:Ohm's Law

   $V = IR$

   View formula →
7. 7.

   Physics

   A constant force of 53 N moves an object 31 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

   View formula →
8. 8.

   Quantitative Aptitude

   Find the average of these 10 numbers: 69, 20, 30, 85, 89, 75, 68, 74, 69, 41.

   Formula:Arithmetic Mean

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

   View formula →
9. 9.

   Mathematics

   If f(x) = 2x³ + 3x² + 9x, find f′(3).

   Formula:Derivative of a Polynomial

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

   View formula →
10. 10.

    Physics

    Find the momentum of a 20 kg body moving at 5 m/s.

    Formula:Linear Momentum

    $p = mv$

    View formula →
11. 11.

    Physics

    A projectile is launched at 28 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 →
12. 12.

    Mathematics

    Find the sum of the first 6 terms of an AP with first term 17 and common difference 3.

    Formula:AP Sum of n Terms

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

    View formula →
13. 13.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 2.)

    Formula:Combinations

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

    View formula →
14. 14.

    Quantitative Aptitude

    Pipe A fills a tank in 9 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

    View formula →
15. 15.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)

    Formula:Combinations

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

    View formula →
16. 16.

    Quantitative Aptitude

    A vehicle covers 588 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

    View formula →
17. 17.

    Mathematics

    For the quadratic 4x² + 5x − 7 = 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 →
18. 18.

    Quantitative Aptitude

    Two varieties costing $29 and $94 per kg are mixed to give a mixture worth $82 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

    $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

    View formula →
19. 19.

    Quantitative Aptitude

    Divide $2,519 between two people in the ratio 4:7. How much does each receive?

    Formula:Sharing in a Ratio

    $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

    View formula →
20. 20.

    Physics

    Find the voltage across a 31 Ω resistor carrying a current of 8 A.

    Formula:Ohm's Law

    $V = IR$

    View formula →

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