The Python math Module Class 11: Functions, Constants and the Four Import Forms

Understand The math Module: Functions, Constants and Import Forms

import math
print(math.sqrt(49))        # 7.0
from math import sqrt, pi
print(sqrt(16))             # 4.0
import math as m
print(m.fabs(-3))           # 3.0
from math import *

import math
r = 7
area = math.pi * r * r
print(round(area, 2))      # 153.94
print(math.sqrt(3**2 + 4**2))   # 5.0

The math Module: Functions, Constants and Import Forms: key facts

Import forms

import math	use math.sqrt()
from math import sqrt	use sqrt()
import math as m	use m.sqrt()
from math import star	everything without prefix

Pick one style.

Rounding

• •ceil rounds up
• •floor rounds down
• •ceil(-2.5) = -2
• •floor(-2.5) = -3

Negatives need care.

Return types

• •sqrt returns float
• •pow returns float
• •fabs returns float
• •ceil and floor return int

sqrt(49) is 7.0.

Trigonometry

• •Angles in radians
• •radians = degrees x pi / 180
• •sin(pi/2) = 1.0
• •cos(0) = 1.0

math.pi = 3.141592653589793.

How to answer The math Module: Functions, Constants and Import Forms questions

1. 1Note how the module was imported (prefix or no prefix).
2. 2Evaluate the argument first.
3. 3Apply the function; remember whether it returns an int or a float.
4. 4For ceil and floor with negatives, think of the number line.
5. 5Write the output exactly, for example 7.0, not 7.

The math Module: Functions, Constants and Import Forms in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Tricks to remember The math Module: Functions, Constants and Import Forms

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Ceil climbs, floor falls

  ceil goes up the number line; floor goes down, even for negatives.

  Use it when: ceil and floor.

• Prefix or not

  import math needs math.; from math import sqrt does not.

  Use it when: Import forms.

The math Module: Functions, Constants and Import Forms: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

import math
print(math.sin(math.pi / 2))
print(math.cos(math.pi))
print(math.sin(math.radians(90)))

Where students lose marks in The math Module: Functions, Constants and Import Forms

The slips examiners see most often, and what to write instead.

• ✗Mistake: Forgetting the prefix

  Using sqrt() after import math.

  Wrong working

  sqrt(25)

  Right working

  math.sqrt(25)

  ✓Do this: Use the module name unless from-import was used.

  Usually costs: 1 mark

• ✗Mistake: Writing 7 instead of 7.0

  Ignoring the float result.

  Wrong working

  Output: 7

  Right working

  Output: 7.0

  ✓Do this: sqrt and pow return floats.

  Usually costs: 1/2 mark

• ✗Mistake: ceil and floor mixed for negatives

  Rounding toward zero.

  Wrong working

  floor(-2.5) = -2

  Right working

  floor(-2.5) = -3; ceil(-2.5) = -2

  ✓Do this: Check the number line.

  Usually costs: 1 mark

Practice questions on The math Module: Functions, Constants and Import Forms

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQBoard level

   What is the output of print(math.floor(-3.2)) after import math?
   (a) -3
   (b) -4
   (c) -3.0
   (d) 3

   Hint

   Down the number line.

   Answer

   (b) -4

2. Q2 · 3 marks · Short answerHarder board level

   Give the output: print(math.pow(3, 2), math.ceil(4.2), math.floor(4.8)) after import math. (3 marks)

   Hint

   pow returns a float.

   Answer

   9.0 5 4

3. Q3 · 3 marks · Short answerHarder board level

   Write a program using the math module to read two sides of a right triangle and print the hypotenuse. Give the output for 6 and 8. (3 marks)

   Hint

   sqrt of sum of squares.

   Answer

   import math; a = float(input()); b = float(input()); print(math.sqrt(a * a + b * b)). For 6 and 8: 10.0.

4. Q4 · 1 mark · Assertion-reasonHarder board level

   Assertion (A): After from math import sqrt, the call math.sqrt(9) works.
   Reason (R): from-import does not bring the module name math into the program.
   (a) Both A and R are true, and R is the correct explanation of A.
   (b) Both A and R are true, but R is not the correct explanation of A.
   (c) A is true, but R is false.
   (d) A is false, but R is true.

   Hint

   Name not imported.

   Answer

   (d) A is false, but R is true.

5. Q5 · 4 marks · Short answerHOTS / competency

   A shop packs 47 pens into boxes of 10. Write the code to find the number of boxes using math and also without the math module, and explain which is simpler. (4 marks)

   Hint

   Ceiling of 4.7.

   Answer

   With math: import math; print(math.ceil(47 / 10)) gives 5. Without math: print(-(-47 // 10)) gives 5, or print(47 // 10 + (47 % 10 > 0)) gives 5. The math.ceil version is clearest.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Return type of math.sqrt?Show answer

   float.

2. 2.Value of math.ceil(-2.5)?Show answer

   -2.

3. 3.Value of math.floor(-2.5)?Show answer

   -3.

4. 4.Unit of angles in math.sin?Show answer

   Radians.

5. 5.Which import avoids the prefix?Show answer

   from math import sqrt.

The math Module: Functions, Constants and Import Forms: frequently asked questions