Composite Functions: A High School Mathematics Exercise, Schemes and Mind Maps of Mathematics

A series of exercises focused on composite functions in mathematics. It includes examples, practice problems, and a clear explanation of the concept. Designed for high school students learning about composite functions and provides a structured approach to understanding this important mathematical concept.

Typology: Schemes and Mind Maps

2024/2025

Uploaded on 02/13/2025

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bg1
13 February 2025
Do now
Composite functions -
expressions
1 MWB: Work out the value of gf (2) =
2 g(x) = 16 โ€“ xโ€ƒโ€ƒh(x) = x3
Findโ€ƒโ€ƒgh(-1) =
3 S is the centre of the circle. Find the value of the angle x..
4A, B and C are points on a circle, centre O. BD is a tangent
to the circle. OCD is a straight line. Find the value of x
5a = 65 to the nearest integer
Give the upper bound of a
6b = 30 to 1 significant figure
Give the lower bound of b
7 Calculator: Work out the upper bound forโ€ƒโ€ƒ2a2 โ€“ b2
You must show your working.
Do next
๐Ÿ.๐Ÿ“
7955.5
๐‘ผ๐‘ฉ=๐Ÿ”๐Ÿ“ .๐Ÿ“
๐’™=๐Ÿ”๐Ÿ“ยฐ ,
17
17
๐’š=๐Ÿ๐Ÿ”ยฐ ,
๐’š
L
The๎˜†nth term of a sequence is
Work out the sum of the 1st and 6th terms
pf3
pf4
pf5
pf8
pf9
pfa

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13 February 2025

Do now expressions 1 MWB: Work out the value of gf (2) = 2 g(x) = 16 โ€“ x h(x) = x 3 Find gh(-1) = 3 S is the centre of the circle. Find the value of the angle x.. 4 A , B and C are points on a circle, centre O. BD is a tangent to the circle. OCD is a straight line. Find the value of x 5 a = 65 to the nearest integer Give the upper bound of a 6 b = 30 to 1 significant figure Give the lower bound of b 7 Calculator: Work out the upper bound for 2 a 2

  • b 2 You must show your working. Do next ๐Ÿ. ๐Ÿ“

๐‘ผ๐‘ฉ = ๐Ÿ”๐Ÿ“. ๐Ÿ“ ๐’™ = ๐Ÿ”๐Ÿ“ ยฐ , 17 17 ๐’š = ๐Ÿ๐Ÿ” ยฐ , ๐’š L The n th term of a sequence is Work out the sum of the 1st and 6th terms

Learning Objectives To know:

  • (^) How to use composite functions
  • How to write a composite function as a single expression

New Learning ๐‘” ( ๐‘ฅ )= 2 + 3 ๐‘ฅ f^ (^ ๐‘ฅ^ )= ๐‘ฅ 2 ๐‘”๐‘“ ( ๐‘ฅ )= ๐‘” ( ๐‘ฅ 2 ) ยฟ 2 + 3 ( ๐‘ฅ 2 ) ๐‘“๐‘” ( ๐‘ฅ )ยฟ^2 +^3 ๐‘ฅ 2

I Do

Find the composite function of gg

We Do

Find the composite function of gf

CFU

CFU

CfU gf(x)

Independent practice