SAT · Practice Sheet 6

1. 1.

   Mathematics

   Evaluate ∫ from 2 to 4 of 3x^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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2. 2.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

   Formula:Probability (two dice)

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

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3. 3.

   Quantitative Aptitude

   A vehicle covers 176 km in 2 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

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4. 4.

   Quantitative Aptitude

   Two varieties costing AED 12 and AED 66 per kg are mixed to give a mixture worth AED 32 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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5. 5.

   Quantitative Aptitude

   The marked price of an item is AED 700. After a 10% discount, find the selling price.

   Formula:Discount & Selling Price

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

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6. 6.

   Quantitative Aptitude

   Find the simple interest on AED 32,000 at 5% per annum for 2 year(s).

   Formula:Simple Interest

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

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7. 7.

   Mathematics

   In an arithmetic progression with first term 17 and common difference 10, find term number 24.

   Formula:AP nth Term

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

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8. 8.

   Quantitative Aptitude

   A invests AED 5,000 and B invests AED 7,000 for the same period. If the total profit is AED 33,000, find A's share.

   Formula:Partnership (profit share)

   $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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9. 9.

   Quantitative Aptitude

   Two varieties costing AED 15 and AED 99 per kg are mixed to give a mixture worth AED 68 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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10. 10.

    Mathematics

    Find the distance between the points (6, -3) and (-2, 7).

    Formula:Distance Between Two Points

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

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11. 11.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 2 and common ratio 3.

    Formula:GP Sum of n Terms

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

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12. 12.

    Quantitative Aptitude

    A vehicle covers 448 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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13. 13.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

    Formula:Probability (two dice)

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

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14. 14.

    Mathematics

    Find the distance between the points (4, 1) and (1, -8).

    Formula:Distance Between Two Points

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

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15. 15.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)

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

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16. 16.

    Mathematics

    Evaluate ∫ from 0 to 3 of 3x^1 dx.

    Formula:Definite Integral of a Power

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

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17. 17.

    Quantitative Aptitude

    A invests AED 4,000 and B invests AED 9,000 for the same period. If the total profit is AED 20,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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18. 18.

    Quantitative Aptitude

    Find the simple interest on AED 21,000 at 10% per annum for 1 year(s).

    Formula:Simple Interest

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

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19. 19.

    Quantitative Aptitude

    Find the compound interest on AED 7,000 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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20. 20.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

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