ACT · Practice Sheet 47

1. 1.

   Mathematics

   Find the sum of the first 8 terms of an AP with first term 15 and common difference 2.

   Formula:AP Sum of n Terms

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

   View formula →
2. 2.

   Physics

   Find the force required to accelerate a 17 kg mass at 5 m/s².

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

   $F = ma$

   View formula →
3. 3.

   Physics

   If 2,360 J of work is done in 32 s, find the power.

   Formula:Power

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

   View formula →
4. 4.

   Quantitative Aptitude

   Find the average of these 10 numbers: 30, 41, 43, 60, 39, 78, 28, 48, 81, 72.

   Formula:Arithmetic Mean

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

   View formula →
5. 5.

   Quantitative Aptitude

   The marked price of an item is $2,000. After a 5% discount, find the selling price.

   Formula:Discount & Selling Price

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

   View formula →
6. 6.

   Physics

   Find the density of an object with mass 376 g and volume 33 cm³.

   Formula:Density

   $\rho = \dfrac{m}{V}$

   View formula →
7. 7.

   Quantitative Aptitude

   Find the compound interest on $20,000 at 10% per annum compounded annually for 3 years.

   Formula:Compound Interest

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

   View formula →
8. 8.

   Quantitative Aptitude

   A vehicle covers 300 km in 5 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

   View formula →
9. 9.

   Quantitative Aptitude

   A value changes from 900 to 1,125. Find the percentage increase.

   Formula:Percentage Change

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

   View formula →
10. 10.

    Quantitative Aptitude

    What is 15% of 1,200?

    Formula:Percentage of a Number

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

    View formula →
11. 11.

    Physics

    A force of 325 N acts on an area of 28 m². Find the pressure.

    Formula:Pressure

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

    View formula →
12. 12.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)

    Formula:Combinations

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

    View formula →
13. 13.

    Quantitative Aptitude

    A can finish a job in 7 days and B in 19 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

    View formula →
14. 14.

    Quantitative Aptitude

    An item is bought for $200 and sold for $260. Find the profit percentage.

    Formula:Profit Percentage

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

    View formula →
15. 15.

    Quantitative Aptitude

    A can finish a job in 16 days and B in 11 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

    View formula →
16. 16.

    Physics

    A projectile is launched at 12 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 →
17. 17.

    Physics

    Find the density of an object with mass 340 g and volume 7 cm³.

    Formula:Density

    $\rho = \dfrac{m}{V}$

    View formula →
18. 18.

    Mathematics

    In an arithmetic progression with first term 15 and common difference 4, find term number 13.

    Formula:AP nth Term

    $a_n = a + (n-1)d$

    View formula →
19. 19.

    Quantitative Aptitude

    Find the average of these 10 numbers: 23, 59, 31, 35, 66, 56, 63, 31, 41, 50.

    Formula:Arithmetic Mean

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

    View formula →
20. 20.

    Mathematics

    In an arithmetic progression with first term 1 and common difference 3, find term number 29.

    Formula:AP nth Term

    $a_n = a + (n-1)d$

    View formula →

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