GCSE Maths · Practice Sheet 6

1. 1.

   Quantitative Aptitude

   What is 60% of 400?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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2. 2.

   Quantitative Aptitude

   The marked price of an item is £1,900. After a 40% discount, find the selling price.

   Formula:Discount & Selling Price

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

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3. 3.

   Mathematics

   Find the slope of the line through (-1, 3) and (0, -6).

   Formula:Slope of a Line

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

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4. 4.

   Mathematics

   Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.

   Formula:Binomial Coefficient

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

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5. 5.

   Mathematics

   Find term number 6 of a geometric progression with first term 4 and common ratio 3.

   Formula:GP nth Term

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

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6. 6.

   Quantitative Aptitude

   The sum of the ages of two people is 88 years, and one is 14 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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7. 7.

   Quantitative Aptitude

   Find the HCF and LCM of 16 and 22.

   Formula:LCM & HCF

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

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8. 8.

   Quantitative Aptitude

   Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

   Formula:Probability (two dice)

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

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9. 9.

   Quantitative Aptitude

   Find the HCF and LCM of 6 and 21.

   Formula:LCM & HCF

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

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10. 10.

    Mathematics

    Find the binomial coefficient C(8, 4) — the coefficient of x^4 in (1 + x)^8.

    Formula:Binomial Coefficient

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

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11. 11.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)

    Formula:Permutations

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

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12. 12.

    Quantitative Aptitude

    Two varieties costing £13 and £98 per kg are mixed to give a mixture worth £38 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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13. 13.

    Mathematics

    Evaluate ∫ from 2 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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14. 14.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

    Formula:Probability (two dice)

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

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15. 15.

    Quantitative Aptitude

    Find the HCF and LCM of 10 and 38.

    Formula:LCM & HCF

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

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16. 16.

    Mathematics

    In an arithmetic progression with first term 3 and common difference 8, find term number 23.

    Formula:AP nth Term

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

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17. 17.

    Mathematics

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

    Formula:Distance Between Two Points

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

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18. 18.

    Mathematics

    Evaluate ∫ from 2 to 3 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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19. 19.

    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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20. 20.

    Mathematics

    For the quadratic 5x² − 9x − 1 = 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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