The World of Algorithms: CBSE Class 9 Mathematics practice questions

Practise 50 questions on The World of Algorithms, free, with an explanation for each answer.

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Sample questions

In Step 3 of the addition algorithm, one column has two digits and a carry. What is the largest total that one such column can have?

1. 18
2. 19
3. 20
4. 10

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B. 19

The biggest digit is $9$ and the biggest carry is $1$, so the largest column total is $9 + 9 + 1 = 19$. Writing the units digit $9$ and carrying $1$ shows the carry can never be more than $1$. $18$ forgets the incoming carry; $20$ would need a carry of $2$, which never happens; $10$ is a possible column total (for example $5 + 5$) but not the largest.

Follow the column-addition steps exactly to add $4857 + 3968$.

1. 8725
2. 7715
3. 8815
4. 8825

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D. 8825

Units: $7 + 8 = 15$, write $5$, carry $1$. Tens: $5 + 6 + 1 = 12$, write $2$, carry $1$. Hundreds: $8 + 9 + 1 = 18$, write $8$, carry $1$. Thousands: $4 + 3 + 1 = 8$. Answer $8825$. $7715$ is what you get by forgetting every carry; $8725$ forgets the carry into the hundreds; $8815$ forgets the carry from the units column into the tens.

Using the column algorithm, add the 5-digit number $48936$ to the 3-digit number $275$. Which is the correct result?

1. 76436
2. 48211
3. 49211
4. 49201

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C. 49211

Units $6+5=11$ (write 1, carry 1); tens $3+7+1=11$ (write 1, carry 1); hundreds $9+2+1=12$ (write 2, carry 1); thousands $8+0+1=9$; ten-thousands $4$. Result $49211$. $76436$ comes from aligning the left ends ($48936 + 27500$); $48211$ stops adding once $275$ runs out and drops the carry; $49201$ forgets the carry from the units column.

Topics covered

• Where the carry is written
• Adding 4-digit numbers
• Numbers of different lengths
• Why the carry is at most 1
• Steps of the addition algorithm
• Why the last step is needed
• Time to add by columns
• Counting vs columns
• Adding decimals
• Tracing the divisors algorithm
• Divisors in pairs
• Examining fewer numbers
• Order of the list of divisors
• Reading a flowchart: the decision
• Reading a flowchart: the loop
• Flowchart symbols
• Counting loop tests
• Following the flowchart
• Common divisors list
• Elements of one list not in another
• Facts about the divisors algorithm
• Efficiency of gcd scans
• Bound on common divisors
• Tracing the common-divisor scan
• Reading a flowchart: update step
• Which k update d
• Counting tests in a scan
• Which pairs have gcd 6
• Why Euclid's reduction works
• Tiling picture of m - n
• Counting subtraction reductions
• Slow case of subtraction
• Computing a gcd with Euclid's method
• Counting divisions
• Next pair in the remainder method
• Chain of reductions
• Stopping test
• Loop in Euclid's algorithm
• Where the answer is produced
• Why Step 1 reverses
• Tracing the flowchart
• Remainders
• Speed of the subtraction algorithm
• Why remainders are faster
• Remainder method for a hard case
• An algorithm for lcm
• prime(n) using divisors(n)
• primedivisors(n)
• Prime factorisation as a list
• History of algorithms

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More CBSE Class 9 Mathematics chapters

• Orienting Yourself: The Use of Coordinates
• Introduction to Linear Polynomials
• The World of Numbers
• Exploring Algebraic Identities
• I’m Up and Down, and Round and Round
• Measuring Space: Perimeter and Area
• The Mathematics of Maybe: Introduction to Probability
• Predicting What Comes Next: Exploring Sequences and Progressions
• Propositions and Their Converses
• How Quantities Combine: Understanding Data
• Quadrilaterals
• Two Variables, One Line
• Math of Space: Surface Area and Volume