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Composite Functions Exam Practice: Guide with Examples & Solutions, Schemes and Mind Maps of Mathematics
A comprehensive set of practice exercises on composite functions, designed to help students prepare for exams. It includes a variety of questions covering different aspects of composite functions, such as finding the value of a composite function, solving equations involving composite functions, and understanding the properties of composite functions. Each question is accompanied by a detailed solution, providing step-by-step explanations and clear reasoning. An excellent resource for students seeking to solidify their understanding of composite functions and improve their exam preparation.
Typology: Schemes and Mind Maps
2024/2025
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Independent practice
Composite Functions Exam Practice
Q1.
g( x ) = a ร bx^ where a and b are constants.
g(0) = 8 and g(3) = 343 Work out the value of g(1) (Total 4 marks)
Q2.
f( x ) = x^2 + 6 x
g( x ) = 2 x + 4
(a) Show that fg( x ) = 4 x^2 + 28 x + 40
(3)
(b) Solve fg( x ) = โ
(3) (Total 6 marks)
Q3.
f( x ) = 3 x and g( x ) = x^2
Circle the expression for fg( x )
3 x^2 9 x^2 3 x^3 9 x^4
(Total 1 mark)
Q4.
For all values of x , f( x ) = 2 x^2 + 3 g( x ) = x + 4
(a) Show that fg( x ) = 2 x^2 + 16 x + 35
(2)
Mark schemes
Q1.
8 = a ร b^0 or a = 8
oe M
343 = their 8 ร b^3
oe M1dep oe M1dep 28 A Additional Guidance The first M1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts [4]
Q2.
(a) (2 x + 4)^2 + 6(2 x + 4)
may be seen in a grid M
4 x^2 + 8 x + 8 x + 16 + 12 x + 24
or 4 x^2 + 16 x + 16 + 12 x + 24
fully expanded expression with terms summed allow one omission or one arithmetic error M1dep
4 x^2 + 8 x + 8 x + 16 + 12 x + 24
or 4 x^2 + 16 x + 16 + 12 x + 24
and
4 x^2 + 28 x + 40
A Additional Guidance
4 x^2 + 16 + 12 x + 24 is two errors
(b) 4 x^2 + 28 x + 45 (= 0)
must be correct
M
(2 x + 5)(2 x + 9) (= 0)
or (2 x + 7)^2 โ 49 + 45 (= 0)
or or or oe implies first M M1dep
( x =) โ2.5 and ( x =) โ4.
oe fraction or decimal
SC2 (x =) [โ1.63, โ1.629] and (x =) [โ5.371, โ5.37]
A Additional Guidance
SC2 from using 4 x^2 + 28 x + 35 (= 0)
Trial and improvement with both answers correct and chosen from any list M1M1A Trial and improvement with one answer correct M0M0A [6]
Q3.
3 x^2
B [1]
Q4.
(a) 2( x + 4)^2 + 3
M
2 x^2 + 16 x + 32 + 3
= 2 x^2 + 16 x + 35
A
(b) 2 x^2 + 3 + 4 or 2 x^2 + 7
B
x^2 + 16 x + 35 = their (2 x^2 + 7)
M