FormulaWon

11+ · Practice Sheet 35

Sheet code: ELEVEN-PLUS-S35 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
For the quadratic 4x² + 3x + 7 = 0, find the sum and product of its roots.
Formula:Vieta's Formulas (roots)
$\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$
View formula →
2.
Quantitative Aptitude
An item is bought for £700 and sold for £910. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
View formula →
3.
Quantitative Aptitude
Divide £1,376 between two people in the ratio 6:2. How much does each receive?
Formula:Sharing in a Ratio
$\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$
View formula →
4.
Mathematics
If f(x) = 2x³ + 1x² + 1x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
View formula →
5.
Quantitative Aptitude
Divide £524 between two people in the ratio 2:2. How much does each receive?
Formula:Sharing in a Ratio
$\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$
View formula →
6.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
View formula →
7.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
View formula →
8.
Quantitative Aptitude
An item is bought for £900 and sold for £1,125. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
View formula →
9.
Mathematics
Find the sum of the first 17 terms of an AP with first term 4 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
View formula →
10.
Quantitative Aptitude
Find the compound interest on £6,000 at 10% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
View formula →
11.
Quantitative Aptitude
Pipe A fills a tank in 6 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
View formula →
12.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
View formula →
13.
Quantitative Aptitude
The sum of the ages of two people is 82 years, and one is 6 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
View formula →
14.
Mathematics
Find term number 6 of a geometric progression with first term 3 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
View formula →
15.
Quantitative Aptitude
The marked price of an item is £1,200. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
View formula →
16.
Quantitative Aptitude
Two varieties costing £33 and £63 per kg are mixed to give a mixture worth £53 per kg. Find the mixing ratio.
Formula:Alligation (Mixtures)
$\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$
View formula →
17.
Mathematics
Find the sum of the first 17 terms of an AP with first term 5 and common difference 8.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
View formula →
18.
Mathematics
In an arithmetic progression with first term 12 and common difference 10, find term number 8.
Formula:AP nth Term
$a_n = a + (n-1)d$
View formula →
19.
Mathematics
If f(x) = 1x³ + 1x² + 1x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
View formula →
20.
Mathematics
Find term number 7 of a geometric progression with first term 4 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
View formula →

Go to full solutions for this sheet