GCSE Maths · Practice Sheet 27

1. 1.

   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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2. 2.

   Quantitative Aptitude

   The sum of the ages of two people is 82 years, and one is 10 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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3. 3.

   Quantitative Aptitude

   What is 40% of 360?

   Formula:Percentage of a Number

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

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4. 4.

   Quantitative Aptitude

   In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)

   Formula:Combinations

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

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5. 5.

   Mathematics

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

   Formula:AP nth Term

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

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6. 6.

   Quantitative Aptitude

   An item is bought for £800 and sold for £1,000. Find the profit percentage.

   Formula:Profit Percentage

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

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7. 7.

   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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8. 8.

   Mathematics

   Find term number 3 of a geometric progression with first term 4 and common ratio 2.

   Formula:GP nth Term

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

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9. 9.

   Quantitative Aptitude

   What is 30% of 640?

   Formula:Percentage of a Number

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

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10. 10.

    Quantitative Aptitude

    Find the simple interest on £17,000 at 5% per annum for 5 year(s).

    Formula:Simple Interest

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

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11. 11.

    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation

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

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12. 12.

    Mathematics

    Evaluate ∫ from 0 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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13. 13.

    Mathematics

    Find the sum of the first 8 terms of an AP with first term 2 and common difference 7.

    Formula:AP Sum of n Terms

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

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14. 14.

    Mathematics

    Evaluate ∫ from 2 to 4 of 4x^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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15. 15.

    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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16. 16.

    Quantitative Aptitude

    What is 40% of 360?

    Formula:Percentage of a Number

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

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17. 17.

    Mathematics

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

    Formula:GP nth Term

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

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18. 18.

    Quantitative Aptitude

    Divide £2,748 between two people in the ratio 7:5. How much does each receive?

    Formula:Sharing in a Ratio

    $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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19. 19.

    Quantitative Aptitude

    The sum of the ages of two people is 63 years, and one is 5 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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20. 20.

    Mathematics

    In an arithmetic progression with first term 18 and common difference 4, find term number 24.

    Formula:AP nth Term

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

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