SAT · Practice Sheet 3

1. 1.

   Mathematics

   In an arithmetic progression with first term 13 and common difference 5, find term number 27.

   Formula:AP nth Term

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

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2. 2.

   Quantitative Aptitude

   Find the average of these 6 numbers: 84, 73, 24, 38, 82, 28.

   Formula:Arithmetic Mean

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

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3. 3.

   Mathematics

   In an arithmetic progression with first term 4 and common difference 3, find term number 19.

   Formula:AP nth Term

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

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4. 4.

   Quantitative Aptitude

   Pipe A fills a tank in 14 hours and pipe B in 15 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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5. 5.

   Mathematics

   Evaluate log base 3 of 27.

   Formula:Logarithm Evaluation

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

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6. 6.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 2.)

   Formula:Combinations

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

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7. 7.

   Mathematics

   Evaluate ∫ from 1 to 3 of 5x^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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8. 8.

   Quantitative Aptitude

   Pipe A fills a tank in 6 hours and pipe B in 10 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

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

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9. 9.

   Mathematics

   If f(x) = 5x³ + 6x² + 8x, find f′(3).

   Formula:Derivative of a Polynomial

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

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10. 10.

    Quantitative Aptitude

    Find the compound interest on AED 6,000 at 20% per annum compounded annually for 2 years.

    Formula:Compound Interest

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

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11. 11.

    Mathematics

    Find the slope of the line through (-4, -6) and (8, 6).

    Formula:Slope of a Line

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

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12. 12.

    Quantitative Aptitude

    A can finish a job in 12 days and B in 4 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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13. 13.

    Quantitative Aptitude

    Two varieties costing AED 11 and AED 60 per kg are mixed to give a mixture worth AED 39 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

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

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14. 14.

    Mathematics

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

    Formula:Binomial Coefficient

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

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15. 15.

    Quantitative Aptitude

    A value changes from 600 to 420. Find the percentage decrease.

    Formula:Percentage Change

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

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16. 16.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 3 and common ratio 2.

    Formula:GP Sum of n Terms

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

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17. 17.

    Quantitative Aptitude

    In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)

    Formula:Combinations

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

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18. 18.

    Quantitative Aptitude

    Find the average of these 10 numbers: 47, 26, 31, 50, 27, 26, 22, 43, 80, 83.

    Formula:Arithmetic Mean

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

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19. 19.

    Mathematics

    Evaluate log base 3 of 81.

    Formula:Logarithm Evaluation

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

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20. 20.

    Mathematics

    Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.

    Formula:Binomial Coefficient

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

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