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A-Level Maths · Practice Sheet 49

Sheet code: A-LEVEL-MATHS-S49 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find term number 6 of a geometric progression with first term 6 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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2.
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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3.
Mathematics
Find the sum of the first 5 terms of a GP with first term 4 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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4.
Mathematics
If f(x) = 4x³ + 5x² + 9x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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5.
Quantitative Aptitude
Divide £1,025 between two people in the ratio 3:2. 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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6.
Quantitative Aptitude
Two varieties costing £21 and £97 per kg are mixed to give a mixture worth £41 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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7.
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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8.
Quantitative Aptitude
Find the average of these 8 numbers: 45, 80, 85, 36, 43, 60, 90, 47.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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9.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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10.
Quantitative Aptitude
The sum of the ages of two people is 24 years, and one is 2 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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11.
Quantitative Aptitude
What is 40% of 840?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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12.
Mathematics
Evaluate ∫ from 1 to 3 of 2x^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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13.
Mathematics
Evaluate log base 3 of 729.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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14.
Quantitative Aptitude
Find the average of these 5 numbers: 89, 40, 42, 67, 32.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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15.
Quantitative Aptitude
Find the simple interest on £10,000 at 4% per annum for 5 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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16.
Quantitative Aptitude
A vehicle covers 332 km in 4 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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17.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 5?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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18.
Quantitative Aptitude
Divide £434 between two people in the ratio 3:4. 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.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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20.
Quantitative Aptitude
A vehicle covers 237 km in 3 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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