VertexMath · MTH1W · Free worksheet

Coding with Python Review

Try each problem first. You don’t need to finish everything.

Core path ~55 min Full sheet ~1 h 45 min

Recommended: K1–K5, then one A and one T problem

K = Knowledge & Understanding · A = Application · T = Thinking · Boss = Challenge

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Quick reference

Assignment: $\texttt{x\ =\ x\ +\ 3}$ computes the right side first, then stores it in $\texttt{x}$ . $\texttt{=}$ stores a value; $\texttt{==}$ tests whether two values are equal.
Operators: $\texttt{/}$ always gives a $\texttt{float}$ , $\texttt{//}$ gives the whole-number quotient, $\texttt{\%}$ the remainder, and $\texttt{**}$ a power (not $\texttt{\textasciicircum{}}$ ).
Input: $\texttt{input()}$ always returns a $\texttt{str}$ . Convert it with $\texttt{int()}$ or $\texttt{float()}$ before you calculate.
Loops and branches: $\texttt{range(a,\ b)}$ starts at $\texttt{a}$ and stops before $\texttt{b}$ . In an $\texttt{if}$ / $\texttt{elif}$ / $\texttt{else}$ chain, only the first true branch runs.

Show your work on separate paper. Show your work in the dot-grid space.

Core Skills (K)

Variables · Operators · Data Types · Loops · Conditionals

K1 Trace the Variables

Determine what each program prints.

a)
$\texttt{a\ =\ 7}$
$\texttt{b\ =\ a}$
$\texttt{a\ =\ 2}$
$\texttt{print(a,\ b)}$
b)
$\texttt{x\ =\ 4}$
$\texttt{x\ =\ x\ +\ 3}$
$\texttt{x\ =\ 2\ *\ x}$
$\texttt{print(x)}$
c)
$\texttt{p\ =\ 3}$
$\texttt{q\ =\ 8}$
$\texttt{p\ =\ q}$
$\texttt{q\ =\ p}$
$\texttt{print(p,\ q)}$

Stuck? Peek at a hint

Work line by line: the right side is computed first, then stored in the variable on the left, replacing what was there.

K2 Python Operators

Evaluate each pair of expressions in Python.

a)
$\texttt{23\ //\ 4}$ and $\texttt{23\ \%\ 4}$
b)
$\texttt{12\ /\ 4}$ and $\texttt{2\ **\ 5}$
c)
$\texttt{1\ /\ 2\ *\ 8}$ and $\texttt{1\ /\ (2\ *\ 8)}$

Stuck? Peek at a hint

Python does $\texttt{*}$ , $\texttt{/}$ , $\texttt{//}$ and $\texttt{\%}$ from left to right, after brackets and $\texttt{**}$ .

K3 Numbers or Text?

Determine the value and the data type ( $\texttt{int}$ , $\texttt{float}$ or $\texttt{str}$ ) of each result.

a)
$\texttt{"12"\ +\ "3"}$
b)
$\texttt{int("12")\ +\ 3}$
c)
The user types $\texttt{4}$ when this program runs.
$\texttt{n\ =\ input("Enter\ a\ number:\ ")}$
$\texttt{print(n\ *\ 3)}$

Stuck? Peek at a hint

Quotation marks make a $\texttt{str}$ . Check whether $\texttt{int()}$ or $\texttt{float()}$ has turned the text into a number before you calculate.

K4 Loops and range

Determine what each program prints.

a)
$\texttt{for\ i\ in\ range(4):}$
$\texttt{\ \ \ \ print(i\ *\ 2)}$
b)
$\texttt{for\ i\ in\ range(3,\ 12,\ 4):}$
$\texttt{\ \ \ \ print(i)}$
c)
$\texttt{total\ =\ 0}$
$\texttt{for\ k\ in\ range(1,\ 5):}$
$\texttt{\ \ \ \ total\ =\ total\ +\ k\ *\ k}$
$\texttt{print(total)}$

Stuck? Peek at a hint

List the values of the loop variable first: $\texttt{range(a,\ b)}$ starts at $\texttt{a}$ and stops before $\texttt{b}$ .

K5 Branching

Determine what this program prints for each input.
$\texttt{t\ =\ float(input("Temperature:\ "))}$
$\texttt{if\ t\ >\ 25:}$
$\texttt{\ \ \ \ print("hot")}$
$\texttt{elif\ t\ >\ 10:}$
$\texttt{\ \ \ \ print("mild")}$
$\texttt{else:}$
$\texttt{\ \ \ \ print("cold")}$

a)
The user types $\texttt{30}$ .
b)
The user types $\texttt{25}$ .
c)
The user types $\texttt{10}$ .

Stuck? Peek at a hint

Test the conditions from the top. Python runs the first branch whose condition is $\texttt{True}$ and skips the rest.

Real World (A)

Math Library · While Loops · Branching in Context

A1 Ladder Check

A hardware store's app uses this program to find how high a ladder reaches up a wall.
$\texttt{import\ math}$
$\texttt{ladder\ =\ float(input("Ladder:\ "))}$
$\texttt{base\ =\ float(input("Base:\ "))}$
$\texttt{h\ =\ math.sqrt(ladder**2\ -\ base**2)}$
$\texttt{print("Reaches",\ round(h,\ 2),\ "m")}$

a)
A 5 m ladder stands with its base 1.4 m from a wall. Determine the output. How high up the wall does the ladder reach?
b)
A painter always sets the base one quarter of the ladder's length from the wall. Rewrite the $\texttt{base}$ line so the program calculates it instead of asking. Then determine the output for a 6 m ladder.
c)
Someone types a ladder length of 3 and a base of 4. What happens when the program runs, and what does it mean for the ladder?

Stuck? Peek at a hint

The ladder, the wall and the ground form a right triangle, and the ladder is the hypotenuse.

A2 Saving for a Bike

Maya has $50 and saves $35 every week for a $480 bike. Her program counts the weeks.
$\texttt{savings\ =\ 50}$
$\texttt{weeks\ =\ 0}$
$\texttt{while\ savings\ <\ 480:}$
$\texttt{\ \ \ \ savings\ =\ savings\ +\ 35}$
$\texttt{\ \ \ \ weeks\ =\ weeks\ +\ 1}$
$\texttt{print(weeks,\ savings)}$

a)
Determine the output. What does it tell Maya?
b)
Maya already has $500 when she starts, so the first line becomes $\texttt{savings\ =\ 500}$ . Determine the output and what it means.
c)
A friend calculates $\dfrac{480-50}{35}\approx 12.29$ and says Maya needs 12.29 weeks. Who is right, Maya's program or her friend?

Stuck? Peek at a hint

Track $\texttt{savings}$ and $\texttt{weeks}$ each time the loop runs, and test the condition before every pass.

A3 Electricity Bill

An Ontario utility charges 10 cents per kWh for the first 600 kWh in a month, and 12 cents per kWh for each kWh above 600. This program prints the bill in dollars.
$\texttt{kwh\ =\ float(input("Energy\ used\ (kWh):\ "))}$
$\texttt{if\ kwh\ <=\ 600:}$
$\texttt{\ \ \ \ cost\ =\ 0.10\ *\ kwh}$
$\texttt{else:}$
$\texttt{\ \ \ \ cost\ =\ 60\ +\ 0.12\ *\ (kwh\ -\ 600)}$
$\texttt{print(round(cost,\ 2))}$

a)
Determine the output for 450 kWh and for 900 kWh. What do the outputs mean?
b)
A family's bill was $120. How much energy did they use?
c)
The meter reader types $-50$ by mistake. Determine the output. Does it make sense for the bill? Write an $\texttt{if}$ condition that would catch this kind of mistake.

Stuck? Peek at a hint

In (b), $120 is an output of the program, so work backwards from the branch that gives bills over $60.

Think It Through (T)

Error Analysis · Building Code from a Graph

T1 Spot the Flaw

A student wants to add $1+2+3+4$ :
$\texttt{for\ n\ in\ range(1,\ 5):}$
$\texttt{\ \ \ \ total\ =\ 0}$
$\texttt{\ \ \ \ total\ =\ total\ +\ n}$
$\texttt{print(total)}$
"My trace table shows that the total ends at 10, so the program prints 10."

$n$	$1$	$2$	$3$	$4$
$\texttt{total}$	$1$	$3$	$6$	$10$

a)
Determine what the program actually prints.
b)
Identify the line that causes the problem, explain why, and fix the program.
c)
To add the whole numbers from 1 to 100, the student starts the fixed loop with $\texttt{for\ n\ in\ range(1,\ 100):}$ instead. Determine what it prints, and correct the loop.

Stuck? Peek at a hint

Trace the program one pass at a time, writing down $\texttt{total}$ after every line inside the loop.

T2 Build It from the Graph

The graph shows the cost $C$ , in dollars, to ship a parcel of mass $m$ kilograms, for $0<m\le 6$ .

a)
Write a program that reads $\texttt{m}$ and prints $\texttt{C}$ , using $\texttt{if}$ , $\texttt{elif}$ and $\texttt{else}$ .
b)
Determine the cost of a 3 kg parcel and of a 3.2 kg parcel from the graph.
c)
A student's program uses $\texttt{if\ m\ <\ 1:}$ as its first condition and $\texttt{elif\ m\ <=\ 3:}$ after it. Find the mass for which it disagrees with the graph.

Stuck? Peek at a hint

A closed dot means that endpoint belongs to the piece, which matches $\texttt{<=}$ ; an open dot matches $\texttt{<}$ .

Boss Level

Optional challenge

Count Without Running

$\texttt{count\ =\ 0}$
$\texttt{for\ n\ in\ range(1,\ 1001):}$
$\texttt{\ \ \ \ if\ n\ \%\ 3\ ==\ 0\ or\ n\ \%\ 5\ ==\ 0:}$
$\texttt{\ \ \ \ \ \ \ \ count\ =\ count\ +\ 1}$
$\texttt{print(count)}$

a)
Determine the output without running the program.
b)
The $\texttt{or}$ is changed to $\texttt{and}$ . Determine the new output.
c)
With $\texttt{or}$ again, $\texttt{1001}$ is replaced by a whole number $\texttt{N}$ . Find the smallest $\texttt{N}$ for which the program prints $\texttt{100}$ .

Stuck? Peek at a hint

Count the multiples of 3 and the multiples of 5 separately, then look for the numbers you counted twice.

Answer key

Final answers only. Try first, then check.

Core Skills

a) $\texttt{2\ 7}$
b) $\texttt{14}$
c) $\texttt{8\ 8}$

a) $\texttt{5}$ and $\texttt{3}$
b) $\texttt{3.0}$ and $\texttt{32}$
c) $\texttt{4.0}$ and $\texttt{0.0625}$

a) $\texttt{"123"}$ , a $\texttt{str}$
b) $\texttt{15}$ , an $\texttt{int}$
c) $\texttt{444}$ ( $\texttt{n}$ is the $\texttt{str}$ $\texttt{"4"}$ )

a) $\texttt{0}$ , $\texttt{2}$ , $\texttt{4}$ , $\texttt{6}$ (one per line)
b) $\texttt{3}$ , $\texttt{7}$ , $\texttt{11}$ (one per line)
c) $\texttt{30}$

a) $\texttt{hot}$
b) $\texttt{mild}$
c) $\texttt{cold}$

Real World

a) $\texttt{Reaches\ 4.8\ m}$ : the ladder reaches 4.8 m up the wall.
b) $\texttt{base\ =\ ladder\ /\ 4}$ ; $\texttt{Reaches\ 5.81\ m}$
c) Python stops with a $\texttt{ValueError}$ : $3^2-4^2=-7$ , and $\texttt{math.sqrt}$ cannot take the square root of a negative number. A 3 m ladder cannot reach a wall 4 m away.

a) $\texttt{13\ 505}$ : Maya can buy the bike after 13 weeks, with $505 saved ($25 left over).
b) $\texttt{0\ 500}$ : the loop never runs, so she can buy the bike today.
c) The program: Maya adds $35 once a week, so after 12 weeks she has $470, which is not enough. She needs 13 whole weeks.

a) $\texttt{45.0}$ and $\texttt{96.0}$ : bills of $45.00 and $96.00
b) 1100 kWh (from $60+0.12(k-600)=120$ )
c) $\texttt{-5.0}$ : the family would be paid $5, which is impossible because energy used cannot be negative. e.g. $\texttt{if\ kwh\ <\ 0:}$ then print a warning instead of a bill.

Think It Through

a) $\texttt{4}$
b) $\texttt{total\ =\ 0}$ runs on every pass, so the running total restarts each time. Move $\texttt{total\ =\ 0}$ above the $\texttt{for}$ line.
c) $\texttt{4950}$ (it stops at 99); use $\texttt{range(1,\ 101)}$ to get $\texttt{5050}$

a) e.g.
$\texttt{m\ =\ float(input("Mass\ (kg):\ "))}$
$\texttt{if\ m\ <=\ 1:}$
$\texttt{\ \ \ \ C\ =\ 8}$
$\texttt{elif\ m\ <=\ 3:}$
$\texttt{\ \ \ \ C\ =\ 12}$
$\texttt{else:}$
$\texttt{\ \ \ \ C\ =\ 20}$
$\texttt{print(C)}$
b) $12 and $20
c) $m=1$ : the graph gives $8, the student's program gives $12

Boss Level

Boss

a) $\texttt{467}$
b) $\texttt{66}$
c) $N=216$

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Most testedWhat does this program print?
$\texttt{total\ =\ 0}$
$\texttt{for\ k\ in\ range(1,\ 6):}$
$\texttt{\ \ \ \ total\ =\ total\ +\ k}$
$\texttt{print(total)}$ (card 7)

1Variables and print

$\texttt{score\ =\ score\ +\ 5}$

Use $\texttt{=}$ stores the right side's value on the left; $\texttt{==}$ tests if two values are equal.

Tip $\texttt{print("x")}$ shows x, not its value.

Trap $\texttt{a\ =\ 4}$ , $\texttt{b\ =\ a}$ , $\texttt{a\ =\ 9}$ : $\texttt{b}$ is still $\texttt{4}$ , not $\texttt{9}$ .

2Operators

Order: brackets, $\texttt{**}$ , then $\texttt{*\ /\ //\ \%}$ , then $\texttt{+\ -}$ .

$\texttt{7\ /\ 2}$	$\texttt{3.5}$ (float)
$\texttt{7\ //\ 2}$	$\texttt{3}$ (quotient)
$\texttt{7\ \%\ 2}$	$\texttt{1}$ (remainder)
$\texttt{7\ **\ 2}$	$\texttt{49}$ (power)

Tip $\texttt{round(x,\ 2)}$ : 2 decimals. $\texttt{\#}$ starts a comment.

Trap $1/(2k)$ is $\texttt{1\ /\ (2\ *\ k)}$ ; $\texttt{1\ /\ 2\ *\ k}$ is half of $k$ .

3Data types and input

$\texttt{age\ =\ int(input("Age:\ "))}$

Use $\texttt{input()}$ gives a $\texttt{str}$ : convert it before you calculate.

$\texttt{int}$	whole: $\texttt{42}$
$\texttt{float}$	decimal: $\texttt{4.0}$
$\texttt{str}$	text: $\texttt{"42"}$

TrapType $\texttt{6}$ into $\texttt{n\ =\ input()}$ : $\texttt{n\ *\ 2}$ is $\texttt{"66"}$ , not $\texttt{12}$ .

Trap $\texttt{int(4.9)}$ is $\texttt{4}$ , not $\texttt{5}$ ; $\texttt{int("4.9")}$ is a ValueError.

4The math library

$\texttt{import\ math}$

$\texttt{math.sqrt(x)}\;\to\;\sqrt{x}$

$\texttt{math.pi}\;\to\;3.14159\ldots$

ExampleLegs $5$ and $12$ :
$\texttt{math.sqrt(5**2\ +\ 12**2)}$
gives $\texttt{13.0}$ .

Trap $\texttt{3\ \textasciicircum{}\ 2}$ is $\texttt{1}$ , not $\texttt{9}$ . A power is $\texttt{3\ **\ 2}$ .

5 $\texttt{for}$ loops

$\texttt{for\ i\ in\ range(...):}$ runs once per value.

$\texttt{range(5)}$	$0,1,2,3,4$
$\texttt{range(2,\ 6)}$	$2,3,4,5$
$\texttt{range(1,\ 10,\ 3)}$	$1,4,7$

Trap $\texttt{range(1,\ 8)}$ stops at $\texttt{7}$ . For $\texttt{8}$ , use $\texttt{range(1,\ 9)}$ .

6 $\texttt{while}$ loops

UseTests before each pass; stops once $\texttt{False}$ .

ExamplePrints $\texttt{81}$ :
$\texttt{n\ =\ 1}$
$\texttt{while\ n\ <\ 50:}$
$\texttt{\ \ \ \ n\ =\ n\ *\ 3}$
$\texttt{print(n)}$

TrapSaving $40 a week for $300, the loop counts 8 weeks, not $300\div40=7.5$ .

7Running total

ExamplePrints $\texttt{15}$ ( $1+2+3+4+5$ ):
$\texttt{total\ =\ 0}$
$\texttt{for\ k\ in\ range(1,\ 6):}$
$\texttt{\ \ \ \ total\ =\ total\ +\ k}$
$\texttt{print(total)}$

TipProduct? Start at $\texttt{1}$ .

Trap $\texttt{total\ =\ 0}$ inside the loop resets it each pass: it prints $\texttt{5}$ , not $\texttt{15}$ .

8Conditional statements

UseOnly the first true branch runs.

$\texttt{if\ mark\ >=\ 80:}$	$\texttt{"A"}$
$\texttt{elif\ mark\ >=\ 70:}$	$\texttt{"B"}$
$\texttt{else:}$	$\texttt{"C"}$

TipA nested $\texttt{if}$ runs only if the outer test is $\texttt{True}$ .

TrapFor $\texttt{mark\ =\ 80}$ , $\texttt{mark\ >\ 80}$ is $\texttt{False}$ . Use $\texttt{>=}$ when the endpoint counts.

9Loops with branches

UseIn a loop, $\texttt{n\ \%\ 4\ ==\ 0}$ finds multiples of $4$ .

Example$500 at 4% for 3 years: $\texttt{m\ =\ m\ *\ 1.04}$ , 3 times, gives $\texttt{562.43}$ .

TrapAt 10¢/kWh, $-80$ kWh prints a bill of $\texttt{-8.0}$ . Check inputs with $\texttt{if}$ first.

Which tool?

You know how many times to repeat for loop

Repeat until a goal is reached while loop

Pick one action from several if / elif / else

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Core Skills (K)

K1 Trace the Variables

K2 Python Operators

K3 Numbers or Text?

K4 Loops and range

K5 Branching

Real World (A)

A1 Ladder Check

A2 Saving for a Bike

A3 Electricity Bill

Think It Through (T)

T1 Spot the Flaw

T2 Build It from the Graph

Boss Level

Count Without Running

Answer key

Core Skills

Real World

Think It Through

Boss Level

Coding with Python Cheat Sheet

Unit Summary

Build your own

Phone card

1Variables and print

2Operators

3Data types and input

4The math library

5for\texttt{for}for loops

6while\texttt{while}while loops

7Running total

8Conditional statements

9Loops with branches

Which tool?

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5 $\texttt{for}$ loops

6 $\texttt{while}$ loops