Exponents Powers and Roots

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Exponents Powers and Roots — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionLaws of Exponents for Integer PowersConcept Practice

2 marks~3 minCriterion B

Explain why

a^m \cdot a^n = a^{m+n}

holds true, using repeated multiplication in your reasoning. [1]

Support your explanation with the example

2^3 \cdot 2^2

, showing each repeated-multiplication step clearly. [1]

Solutions

2QuestionSquare Roots and Cube RootsAssessment Practice

2 marks~3 minCriterion D

A square concrete slab has an area of

150 \, \text{m}^2

. A foundation measures

12.2 \, \text{m}

wide.

Calculate the side length of the slab, giving your answer to one decimal place. [1]

The construction manager states: "An estimate is good enough — we don't need the exact value." Using your result from part (a), advise the manager whether a one-decimal-place estimate is sufficient to decide if the slab fits the foundation. [1]

Solutions

3QuestionLaws of Exponents for Integer PowersAssessment Practice

4 marks~6 minCriterion C

A biologist models two bacterial populations. Population A grows according to

y = 2^x

, where

y

is the population size (thousands) and

x

is time in hours. Population B decays and is modelled by

y = \dfrac{1}{2^x}

Show that

\dfrac{1}{2^x} = 2^{-x}

, stating the law of exponents used. [1]

Describe the geometric transformation that maps the graph of

y = 2^x

onto the graph of

y = 2^{-x}

, explaining how the change in exponent produces this transformation. [2]

x = 3

hours, Population A has reached 8 thousand. Calculate the size of Population B at the same time, then justify whether this value is a realistic prediction for a decaying bacterial culture. [1]

Solutions

4QuestionSimplifying Expressions with ExponentsAssessment Practice

6 marks~9 minCriterion A

A materials scientist models the thermal conductivity of a composite alloy using the expression

\left( \frac{16a^{-4}b^{6}}{81c^{-8}d^{12}} \right)^{-\frac{3}{4}}

where

a

b

c

d

represent measurable physical parameters, all positive and non-zero.

Show that the expression simplifies to

\dfrac{27a^{3}d^{9}}{8b^{\frac{9}{2}}c^{6}}

, stating each law of exponents you apply. [4]

The scientist states: "Because the outer exponent is negative, the simplified expression must always be less than 1." Critique this claim, justifying your reasoning with a specific numerical counterexample. [2]

Solutions

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