ACT · Practice Sheet 23

1. 1.

   Physics

   An object starts at 5 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 →
2. 2.

   Quantitative Aptitude

   Find the compound interest on $10,000 at 20% per annum compounded annually for 2 years.

   Formula:Compound Interest

   $A = P\left(1+\dfrac{R}{100}\right)^{T}$

   View formula →
3. 3.

   Quantitative Aptitude

   The marked price of an item is $1,200. After a 20% discount, find the selling price.

   Formula:Discount & Selling Price

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

   View formula →
4. 4.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)

   Formula:Permutations

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

   View formula →
5. 5.

   Quantitative Aptitude

   What is 30% of 900?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

   View formula →
6. 6.

   Quantitative Aptitude

   Find the compound interest on $19,000 at 10% per annum compounded annually for 3 years.

   Formula:Compound Interest

   $A = P\left(1+\dfrac{R}{100}\right)^{T}$

   View formula →
7. 7.

   Mathematics

   Find the sum of the first 6 terms of a GP with first term 5 and common ratio 2.

   Formula:GP Sum of n Terms

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

   View formula →
8. 8.

   Mathematics

   Find term number 5 of a geometric progression with first term 6 and common ratio 3.

   Formula:GP nth Term

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

   View formula →
9. 9.

   Quantitative Aptitude

   Find the average of these 6 numbers: 65, 78, 68, 70, 20, 65.

   Formula:Arithmetic Mean

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

   View formula →
10. 10.

    Quantitative Aptitude

    Two varieties costing $36 and $95 per kg are mixed to give a mixture worth $70 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

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

    View formula →
11. 11.

    Physics

    A projectile is launched at 47 m/s at 45° 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.

    Physics

    Find the electrical power when 104 V drives a current of 4 A.

    Formula:Electrical Power

    $P = VI$

    View formula →
13. 13.

    Mathematics

    Find the slope of the line through (-1, 3) and (4, -5).

    Formula:Slope of a Line

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

    View formula →
14. 14.

    Quantitative Aptitude

    A vehicle covers 360 km in 9 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

    View formula →
15. 15.

    Mathematics

    If f(x) = 2x³ + 2x² + 2x, find f′(5).

    Formula:Derivative of a Polynomial

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

    View formula →
16. 16.

    Physics

    A projectile is launched at 31 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 →
17. 17.

    Physics

    Find the momentum of a 21 kg body moving at 2 m/s.

    Formula:Linear Momentum

    $p = mv$

    View formula →
18. 18.

    Physics

    A projectile is launched at 30 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 →
19. 19.

    Physics

    A constant force of 150 N moves an object 19 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

    View formula →
20. 20.

    Quantitative Aptitude

    A value changes from 200 to 100. Find the percentage decrease.

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

    View formula →

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