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Grade 9

11.04 Loops in code

Worksheet
Loops
1

Consider the following pseudocode:

a

Find the initial value of a.

b

Find the final value of a.

c

Find the value of \text{OUTPUT}.

\text{START} \\ \text{SET } a = 9 \\ \text{SET sum = 0} \\ \text{WHILE } a \gt 3\\ \quad \text{sum = sum} + a\\ \quad a = a - 1 \\ \text{END WHILE} \\ \text{PRINT sum} \\ \text{END}

2

For each of the following pseudocodes:

i

Find the initial value of a.

ii

Find the \text{OUTPUT} of the code.

a

\text{START} \\ \text{SET } a = 2 \\ \text{SET sum} = 0 \\ \text{WHILE a < 9} \\ \quad \text{sum = sum} + a \\ \quad a = a + 1 \\ \text{END WHILE} \\ \text{PRINT sum} \\ \text{END}

b

\text{START} \\ \text{SET } a = 3 \\ \text{SET sum} = 0 \\ \text{SET } n = 0 \\ \text{WHILE } a \lt 12 \\ \quad \text{sum = sum + a} \\ \quad a = a + 1 \\ \quad n = n + 1 \\ \text{END WHILE} \\ \text{PRINT sum / } n \\ \text{END}

3

Find the final value, n, for the following pseudocode:

\text{START} \\ \text{SET } a = 4 \\ \text{SET } n = 0 \\ \text{WHILE } a \gt 1 \\ \quad \text{sum = sum + a} \\ \quad a = a \, / \, 2 \\ \quad n = n + 1 \\ \text{END WHILE} \\ \text{END}

4

Determine the value that is printed at the end of the following pseudocodes:

a

\text{START} \\ \text{SET } a = 19 \\ \text{WHILE } a \gt 5 \\ \quad a = a - 1 \\ \text{END WHILE} \\ \text{PRINT } a \\ \text{END}

b

\text{START} \\ \text{SET } a = 1 \\ \text{WHILE } a \lt 24\\ \quad \text{PRINT } a \\ \quad a = a * 2 \\ \text{END WHILE} \\ \text{END}

c

\text{START} \\ \text{SET } a = 5 \\ \text{WHILE } a \lt 7 \\ \quad \text{PRINT } a \\ \quad a = a + 1 \\ \text{END WHILE} \\ \text{END}

d

\text{START} \\ \text{SET } a = 2 \\ \text{WHILE } a \lt 10 \\ \quad \text{PRINT } a \\ \quad a = a + 2 \\ \text{END WHILE} \\ \text{END}

e

\text{START} \\ \text{SET } a = 5 \\ \text{WHILE } a \lt 20 \\ \quad \text{PRINT } a \\ \quad a = a * 2 \\ \text{END WHILE} \\ \text{END}

5

Consider the algorithm represented by the flow chart:

Arrange the following lines of pseudocode in the correct order for the algorithm.

StepCode
A\text{WHILE } a \gt 4
B\text{END WHILE}
C\text{PRINT } a
D\text{SET } a = 4
Ea = a - 1
6

Consider the algorithm represented by the flow chart:

Arrange the following lines of pseudocode in the correct order for the algorithm.

StepCode
Aa = a + 1
B\text{SET } a = 4
C\text{WHILE } a \neq 5
D\text{PRINT sum}
E\text{sum = sum} + a
F\text{END WHILE}
G\text{SET sum}=0
7

Consider the algorithm for finding the sum of the first n natural numbers represented by the flow chart.

a

Find the output of this algorithm if n=4.

b

Arrange the following lines of pseudocode for adding the first 50 natural numbers in the correct order for the algorithm.

StepCode
A\text{sum = } a + \text{sum}
B\text{PRINT sum}
C\text{SET } a=1
Da=a+1
E\text{GO TO LINE } 3
F\text{SET sum}=0
G\text{IF } a=50 \text{ THEN GO TO LINE } 7
8

The factorial of a non-negative integer n is given by n! = n \times (n-1) \times (n-2) \times .... \times 2 \times 1. For example, 5! = 5 \times 4 \times 3 \times 2 \times 1=120.

Consider the algorithm for finding n! represented by the flow chart:

a

Find the output of this algorithm if n=6.

b

Arrange the following lines of pseudocode in the correct order for finding 50!.

StepCode
Ap = p * a
Ba = a + 1
C\text{PRINT } p
D\text{SET } a = 1
E\text{IF } a=50 \text{ THEN GO TO LINE } 7
F\text{SET } p=1
G\text{GO TO LINE } 3
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Outcomes

9.C2.1

Use coding to demonstrate an understanding of algebraic concepts including variables, parameters, equations, and inequalities.

9.C2.2

Create code by decomposing situations into computational steps in order to represent mathematical concepts and relationships, and to solve problems.

9.C2.3

Read code to predict its outcome, and alter code to adjust constraints, parameters, and outcomes to represent a similar or new mathematical situation.

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