SAT · Practice Sheet 3

1. 1.

   Mathematics

   Find the sum of the first 20 terms of an AP with first term 17 and common difference 2.

   Formula:AP Sum of n Terms

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

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2. 2.

   Quantitative Aptitude

   Pipe A fills a tank in 14 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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3. 3.

   Mathematics

   Evaluate ∫ from 1 to 4 of 4x^3 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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4. 4.

   Quantitative Aptitude

   Find the compound interest on $5,000 at 10% per annum compounded annually for 3 years.

   Formula:Compound Interest

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

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5. 5.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)

   Formula:Permutations

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

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6. 6.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 5 and common ratio 2.

   Formula:GP Sum of n Terms

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

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7. 7.

   Mathematics

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

   Formula:Derivative of a Polynomial

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

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8. 8.

   Quantitative Aptitude

   Find the HCF and LCM of 11 and 27.

   Formula:LCM & HCF

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

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9. 9.

   Mathematics

   For the quadratic 4x² − 4x − 2 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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10. 10.

    Mathematics

    Evaluate ∫ from 1 to 3 of 1x^2 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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11. 11.

    Quantitative Aptitude

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

    Formula:Combinations

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

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12. 12.

    Quantitative Aptitude

    The sum of the ages of two people is 45 years, and one is 9 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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13. 13.

    Quantitative Aptitude

    Find the average of these 5 numbers: 73, 88, 79, 81, 72.

    Formula:Arithmetic Mean

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

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14. 14.

    Quantitative Aptitude

    The sum of the ages of two people is 57 years, and one is 3 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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15. 15.

    Quantitative Aptitude

    Find the compound interest on $12,000 at 10% per annum compounded annually for 3 years.

    Formula:Compound Interest

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

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16. 16.

    Mathematics

    Evaluate ∫ from 2 to 4 of 4x^2 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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17. 17.

    Quantitative Aptitude

    Find the average of these 10 numbers: 90, 61, 61, 40, 52, 26, 78, 57, 83, 72.

    Formula:Arithmetic Mean

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

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18. 18.

    Mathematics

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

    Formula:Slope of a Line

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

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19. 19.

    Quantitative Aptitude

    A vehicle covers 335 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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20. 20.

    Mathematics

    Find the distance between the points (-6, 5) and (-2, 4).

    Formula:Distance Between Two Points

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

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