ACT · Practice Sheet 18

1. 1.

   Mathematics

   If f(x) = 4x³ + 2x² + 3x, find f′(5).

   Formula:Derivative of a Polynomial

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

   View formula →
2. 2.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 9?

   Formula:Probability (two dice)

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

   View formula →
3. 3.

   Mathematics

   Find the slope of the line through (5, 7) and (-2, 6).

   Formula:Slope of a Line

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

   View formula →
4. 4.

   Physics

   Find the voltage across a 36 Ω resistor carrying a current of 10 A.

   Formula:Ohm's Law

   $V = IR$

   View formula →
5. 5.

   Mathematics

   Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.

   Formula:Binomial Coefficient

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

   View formula →
6. 6.

   Physics

   Find the kinetic energy of a 14 kg object moving at 8 m/s.

   Formula:Kinetic Energy

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

   View formula →
7. 7.

   Mathematics

   Evaluate log base 2 of 8.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

   View formula →
8. 8.

   Quantitative Aptitude

   The marked price of an item is $1,100. After a 40% discount, find the selling price.

   Formula:Discount & Selling Price

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

   View formula →
9. 9.

   Physics

   A projectile is launched at 20 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.

    Mathematics

    If f(x) = 5x³ + 5x² + 2x, find f′(3).

    Formula:Derivative of a Polynomial

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

    View formula →
11. 11.

    Mathematics

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

    Formula:GP nth Term

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

    View formula →
12. 12.

    Mathematics

    In an arithmetic progression with first term 4 and common difference 9, find term number 22.

    Formula:AP nth Term

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

    View formula →
13. 13.

    Physics

    A body moving at 12 m/s accelerates at 4 m/s² for 10 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^{2}$

    View formula →
14. 14.

    Mathematics

    Find term number 5 of a geometric progression with first term 1 and common ratio 2.

    Formula:GP nth Term

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

    View formula →
15. 15.

    Quantitative Aptitude

    Find the HCF and LCM of 31 and 16.

    Formula:LCM & HCF

    $\text{LCM}\times\text{HCF} = a\times b$

    View formula →
16. 16.

    Physics

    A body moving at 12 m/s accelerates at 5 m/s² for 3 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^{2}$

    View formula →
17. 17.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)

    Formula:Permutations

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

    View formula →
18. 18.

    Quantitative Aptitude

    Pipe A fills a tank in 15 hours and pipe B in 12 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns

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

    View formula →
19. 19.

    Quantitative Aptitude

    Two varieties costing $27 and $100 per kg are mixed to give a mixture worth $67 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

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

    View formula →
20. 20.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)

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

    View formula →

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