How do you substitute a negative value?

Put it in brackets, for example b=-2 gives 3b^2=3(-2)^2=12.

Terms with exactly the same letters and powers.

Algebraic expressions and substitutionIB MYP Maths Extended: Flashcards

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What is a coefficient?

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What is a coefficient?: The number multiplied by a letter, for example 5 in $5x$ .
What does $3a$ mean?: $3\times a$ .
What does $a^2$ mean?: $a\times a$ , not $2\times a$ .
How do you substitute a negative value?: Put it in brackets, for example $b=-2$ gives $3b^2=3(-2)^2=12$ .
What are like terms?: Terms with exactly the same letters and powers.
Simplify $5x+3y-2x+4y$ .: $3x+7y$
Can $3x+2y$ be simplified?: No, $x$ and $y$ are unlike terms.
Expand $3(2x-5)$ .: $6x-15$
Expand $-2(x-4)$ .: $-2x+8$
Expand $(x+3)(x+5)$ .: $x^2+8x+15$
Expand $(x+4)^2$ .: $x^2+8x+16$
Expand $(x-3)(x+3)$ .: $x^2-9$

Exam questions on Algebraic expressions and substitution

A taxi company in Nairobi charges $C=50+30d$ shillings for a journey of $d$ kilometres.
A second journey is twice as long as one of $d$ km, so it is $2d$ km. Write a simplified expression for the total cost, in shillings, of one journey of $d$ km and one journey of $2d$ km.2 marks
Let $a=3$ , $b=-2$ and $c=5$ .
Find the value of $\frac{c-b}{a-b}$ .2 marks
A school hall is a rectangle of length $(2x+3)$ metres and width $(x+4)$ metres. A square stage of side $x$ metres is built inside the hall.
Show that the area of the hall is $2x^2+11x+12$ square metres.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).