SAT · Practice Sheet 9

1. 1.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 2.)

   Formula:Permutations

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

   View formula →
2. 2.

   Mathematics

   If f(x) = 1x³ + 6x² + 2x, find f′(3).

   Formula:Derivative of a Polynomial

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

   View formula →
3. 3.

   Quantitative Aptitude

   Find the simple interest on $9,000 at 10% per annum for 4 year(s).

   Formula:Simple Interest

   $SI = \dfrac{P\times R\times T}{100}$

   View formula →
4. 4.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 3 and common ratio 3.

   Formula:GP Sum of n Terms

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

   View formula →
5. 5.

   Quantitative Aptitude

   Pipe A fills a tank in 5 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

   View formula →
6. 6.

   Mathematics

   In an arithmetic progression with first term 6 and common difference 9, find term number 15.

   Formula:AP nth Term

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

   View formula →
7. 7.

   Mathematics

   Find the sum of the first 6 terms of an AP with first term 13 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

   What is 30% of 420?

   Formula:Percentage of a Number

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

   View formula →
9. 9.

   Quantitative Aptitude

   A value changes from 800 to 720. Find the percentage decrease.

   Formula:Percentage Change

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

   View formula →
10. 10.

    Mathematics

    Find the distance between the points (7, 7) and (-6, 4).

    Formula:Distance Between Two Points

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

    View formula →
11. 11.

    Quantitative Aptitude

    Find the average of these 6 numbers: 36, 41, 90, 75, 86, 46.

    Formula:Arithmetic Mean

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

    View formula →
12. 12.

    Mathematics

    For the quadratic 5x² + 5x + 4 = 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 →
13. 13.

    Mathematics

    Evaluate ∫ from 1 to 5 of 3x^3 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 →
14. 14.

    Quantitative Aptitude

    The marked price of an item is $800. After a 30% discount, find the selling price.

    Formula:Discount & Selling Price

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

    View formula →
15. 15.

    Quantitative Aptitude

    What is 60% of 340?

    Formula:Percentage of a Number

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

    View formula →
16. 16.

    Mathematics

    Find the sum of the first 13 terms of an AP with first term 13 and common difference 6.

    Formula:AP Sum of n Terms

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

    View formula →
17. 17.

    Mathematics

    Find the distance between the points (-2, -7) and (6, -8).

    Formula:Distance Between Two Points

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

    View formula →
18. 18.

    Quantitative Aptitude

    A vehicle covers 664 km in 8 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

    View formula →
19. 19.

    Mathematics

    Evaluate log base 10 of 1,000,000.

    Formula:Logarithm Evaluation

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

    View formula →
20. 20.

    Quantitative Aptitude

    Find the simple interest on $14,000 at 6% per annum for 2 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

    View formula →

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