Algorithms and flowchartsIB MYP Maths Extended: Subtopic test

1. 1
   An algorithm is written in steps. Step 1: Set $n=5$ and $total=0$. Step 2: Add $n$ to $total$. Step 3: Reduce $n$ by $1$. Step 4: If $n>0$, go back to Step 2; otherwise output $total$ and stop.

   (a)

   What does the algorithm output?

   [1 mark]

   • A$10$
   • B$15$
   • C$5$
   • D$14$

   (b)

   How many times is Step 2 carried out?

   [1 mark]

   • A$4$
   • B$6$
   • C$15$
   • D$5$

   (c)

   Step 1 is changed to set $n=8$. Find the new output.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A flowchart takes a number $x$ as its input. Process: double $x$ and subtract $3$ to get $y$. Decision: if $y>10$, output the word "Large"; otherwise output $y$.

   (a)

   What is the output when $x=4$?

   [1 mark]

   • A$5$
   • B"Large"
   • C$8$
   • D$11$

   (b)

   What is the output when $x=6.5$?

   [1 mark]

   • A"Large"
   • B$13$
   • C$10$
   • D$16$

   (c)

   Find the smallest whole number input that gives the output 'Large'.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A sequence is generated by an algorithm. Step 1: Set the first term $u_1=3$. Step 2: To get the next term, multiply the previous term by $2$ and then add $1$. Step 3: Repeat Step 2 until the terms needed have been found.

   (a)

   Use the algorithm to find the first five terms of the sequence.

   [3 marks]

   (b)

   Continue the algorithm to find the first term that is greater than $500$, and state its position in the sequence.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An algorithm solves equations of the form $ax+b=c$. Step 1: Input $a$, $b$ and $c$. Step 2: Subtract $b$ from $c$. Step 3: Divide the result by $a$. Step 4: Output the answer as $x$.

   (a)

   (i) Use the algorithm with $a=3$, $b=5$ and $c=29$ to find $x$.
   (ii) Explain why the algorithm fails when $a=0$.

   [6 marks]

   (b)

   Write the steps of an algorithm to solve $px+q=rx+s$, where $p\ne r$. Use your algorithm to solve $5x+7=2x+22$ and verify your answer.

   [6 marks]

   Total for question 4: 12 marks

End of questions