SAT · Practice Sheet 29

1. 1.

   Quantitative Aptitude

   Two varieties costing AED 15 and AED 63 per kg are mixed to give a mixture worth AED 57 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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2. 2.

   Mathematics

   For the quadratic 3x² + 5x − 4 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

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

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3. 3.

   Mathematics

   Find the distance between the points (7, 3) and (7, 2).

   Formula:Distance Between Two Points

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

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4. 4.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)

   Formula:Permutations

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

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5. 5.

   Mathematics

   Find the slope of the line through (-6, -5) and (3, 4).

   Formula:Slope of a Line

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

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6. 6.

   Mathematics

   If f(x) = 4x³ + 1x² + 6x, find f′(1).

   Formula:Derivative of a Polynomial

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

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7. 7.

   Quantitative Aptitude

   Find the HCF and LCM of 18 and 25.

   Formula:LCM & HCF

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

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8. 8.

   Quantitative Aptitude

   A value changes from 500 to 750. Find the percentage increase.

   Formula:Percentage Change

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

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9. 9.

   Mathematics

   Evaluate ∫ from 2 to 5 of 2x^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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10. 10.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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11. 11.

    Mathematics

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

    Formula:Slope of a Line

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

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12. 12.

    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation

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

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13. 13.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 4 and common ratio 3.

    Formula:GP Sum of n Terms

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

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14. 14.

    Quantitative Aptitude

    A value changes from 700 to 595. Find the percentage decrease.

    Formula:Percentage Change

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

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15. 15.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

    Formula:Probability (two dice)

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

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16. 16.

    Quantitative Aptitude

    An item is bought for AED 800 and sold for AED 880. Find the profit percentage.

    Formula:Profit Percentage

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

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17. 17.

    Quantitative Aptitude

    Find the compound interest on AED 17,000 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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18. 18.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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19. 19.

    Quantitative Aptitude

    An item is bought for AED 400 and sold for AED 440. Find the profit percentage.

    Formula:Profit Percentage

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

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20. 20.

    Quantitative Aptitude

    The sum of the ages of two people is 39 years, and one is 15 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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