SAT · Practice Sheet 40

1. 1.

   Mathematics

   Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

   Formula:Binomial Coefficient

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

   View formula →
2. 2.

   Quantitative Aptitude

   The sum of the ages of two people is 73 years, and one is 15 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

   View formula →
3. 3.

   Quantitative Aptitude

   The marked price of an item is $500. After a 10% discount, find the selling price.

   Formula:Discount & Selling Price

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

   View formula →
4. 4.

   Mathematics

   Find the distance between the points (-5, 8) and (-1, 8).

   Formula:Distance Between Two Points

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

   View formula →
5. 5.

   Quantitative Aptitude

   Pipe A fills a tank in 12 hours and pipe B in 8 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

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

   Formula:Derivative of a Polynomial

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

   View formula →
7. 7.

   Quantitative Aptitude

   Find the compound interest on $5,000 at 20% 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 can finish a job in 4 days and B in 20 days. Working together, how long will they take?

   Formula:Time & Work (combined)

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

   View formula →
9. 9.

   Quantitative Aptitude

   An item is bought for $200 and sold for $230. Find the profit percentage.

   Formula:Profit Percentage

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

   View formula →
10. 10.

    Mathematics

    Evaluate ∫ from 0 to 5 of 2x^1 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 →
11. 11.

    Mathematics

    Find the distance between the points (-5, -7) and (8, -6).

    Formula:Distance Between Two Points

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

    View formula →
12. 12.

    Mathematics

    In an arithmetic progression with first term 14 and common difference 1, find term number 29.

    Formula:AP nth Term

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

    View formula →
13. 13.

    Quantitative Aptitude

    The sum of the ages of two people is 77 years, and one is 13 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

    View formula →
14. 14.

    Quantitative Aptitude

    Find the average of these 10 numbers: 52, 26, 28, 58, 89, 62, 66, 61, 65, 21.

    Formula:Arithmetic Mean

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

    View formula →
15. 15.

    Quantitative Aptitude

    Divide $2,565 between two people in the ratio 6:3. How much does each receive?

    Formula:Sharing in a Ratio

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

    View formula →
16. 16.

    Mathematics

    In an arithmetic progression with first term 12 and common difference 7, find term number 10.

    Formula:AP nth Term

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

    View formula →
17. 17.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)

    Formula:Permutations

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

    View formula →
18. 18.

    Mathematics

    Find the slope of the line through (7, 6) and (-3, 3).

    Formula:Slope of a Line

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

    View formula →
19. 19.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)

    Formula:Combinations

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

    View formula →
20. 20.

    Quantitative Aptitude

    Find the average of these 6 numbers: 29, 84, 38, 85, 40, 53.

    Formula:Arithmetic Mean

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

    View formula →

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