30 practice questions on writing-algebraic-expressions from the Expressions using Letter-Numbers section of the UPSC Prelims syllabus. 30 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.
Find the value of $5xy$ when $x=2$ and $y=3$.
Correct answer: A - $30$
The expression means $5\times x\times y$, so substituting gives $5\times 2\times 3=30$. The value $10$ multiplies by $x$ alone, $15$ multiplies by $y$ alone, and $523$ simply joins the digits together.
A taxi fare is given by $50+9d$, where $d$ is the distance in kilometres. Which part of this expression does not change with the distance?
Correct answer: A - $50$
The number $50$ is a constant term, so it stays the same however far the journey goes. The term $9d$ grows with the distance, $d$ is the distance itself and clearly changes, and the whole expression changes because $9d$ does.
The perimeter of a rectangle is $2l+2b$. If the length is $3$ metres more than the breadth, which expression gives the perimeter using $b$ alone?
Correct answer: B - $4b+6$
Writing the length as $b+3$ gives a perimeter of $2(b+3)+2b=2b+6+2b=4b+6$. The expression $4b+3$ counts the extra three metres only once, $2b+6$ leaves out one pair of sides, and $4b+12$ doubles that extra length too many times.
What is the coefficient of $y$ in the term $y$?
Correct answer: B - $1$
Writing $y$ on its own means one lot of $y$, so the coefficient is $1$ even though it is not written down. A coefficient of $0$ would wipe the term out, a letter is not its own coefficient, and every term does have one.
Which of these is the correct short form of $9\times t$?
Correct answer: A - $9t$
The number is written first and the letter straight after it with no sign between, giving $9t$. Writing $t9$ reverses the accepted order, and the last two options change the operation altogether.
In the expression $4x+9$, which part is the constant term?
Correct answer: D - $9$
A constant term carries no letter, so its value never changes, and here that term is $9$. The term $4x$ changes as $x$ changes, $4$ is only the coefficient inside that term, and $x$ is the variable itself.
Ravi's savings are $8w$ rupees and Sita's are $5w$ rupees, where $w$ is the number of weeks they have been saving. What do the coefficients tell you?
Correct answer: C - Ravi saves ₹$8$ a week and Sita saves ₹$5$ a week
In each expression the letter $w$ counts the weeks, so the coefficient is the amount saved per week: ₹$8$ for Ravi and ₹$5$ for Sita. The number of weeks is $w$, the totals are the whole expressions, and the weekly gap between them is ₹$3$, not ₹$8$.
Write "$6$ subtracted from twice a number $p$" as an expression.
Correct answer: D - $2p-6$
Twice the number is $2p$, and subtracting six from that gives $2p-6$. The expression $6-2p$ subtracts the other way round, $2(p-6)$ subtracts before doubling, and $6p-2$ swaps the two numbers.
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