This is done especially for my O Levels (Secondary 3 and 4) A Maths girls.
One of my student (Jasmine, yes its you!) showed me one good question on modulus function and got me thinking.
Decided to do up some basic “MUST KNOW” points for this topic and some questions for practice to ensure you folks got the technique for solving modulus function problems. 🙂
Modulus function MUST KNOWS
i. |a| = |−a|
SO |a−b| = |b−a| (we need to form common factors to be brought out)
ii. |a| ≥ 0
( Obviously right? Hee. You must get it before talking about other techiques to solve modulus functions)
SO |a| = a if a ≥ 0
But then this property is important in removing the modulus sign which is our objective when solving modulus functions questions.
e.g. |5 − 3| + |3 − 5| = 5 − 3 + |5 − 3| = 2(5) – 2(3)
iii. |ab| = |a||b|
Always remember to keep the mod sign when expanding
iv. |a/b| = |a|/|b|
Look out to form common factors too.
v. |a|2 = a2
We can remove the mod sign by ‘squaring both sides’.
But the mod sign stays for odd powers
|a|3 ≠ a3!
Please complete these questions and hand up to me next lesson! 😀
Modulus function Questions
1) | 3x-5 | + 2 |10-6x| = 25
2) |21x + 28||3x-4| = 28
3) |9a2 +24a+16| = 9
4) 5x = | x2 +6|
5) | -4x2/5-x| = |10-2x/8 |
6) |√ 3 x | = |-2x-3/ √3 |
7) |x + √5||x − √5| = −6x
Have a great weekend!! 🙂