CAIE IGCSE Mathematics Extended E2.4 Indices Ii

Covered syllabus points

E2.4.1 Understand and use indices (positive, zero, negative and fractional).E2.4.2 Understand and use the rules of indices

[Maximum number: 6]

(a)

Simplify $\left(\frac{x^{2}}{4}\right)^{\frac{3}{2}}$ .

[ 2 ]

[ $\pm$ ] $\frac{x^3}{8}$ final answer
B1 for $\frac{x^3}{k}$ or $\frac{x^k}{8}$

(b)

$16^{x} \times\left(\frac{1}{2}\right)^{x}=4^{x+3}$

Find the value of x.

[ 4 ]

6 nfww
B3 for 4x-x=2(x+3) oe
or for correctly combining to a single base on each side with no brackets in the powers
OR M1 for $(2^4)^x$ or $(2^{-1})^x$ or $2^{2(x+3)}$ or better seen
M1 for correctly forming a linear equation in x from their powers of their consistent base

[Maximum number: 1]

f(x)=1-3x $g(x)=(x-1)^2$ $h(x)=\frac3x,\ x\ne0$

h(x^n)=3 x^7

Find the value of n.

n=

[Maximum number: 1]

$2p^{1/3}=6$
Find the value of p.
p=

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CAIE IGCSE Mathematics Extended E2.4 Indices Ii Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question 3