Exponents Powers and Roots
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 62 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

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

1QuestionLaws of Exponents for Integer PowersAssessment Practice
3 marks~5 minCriterion D
In atmospheric science, particle masses are often expressed as powers of ten. The mass of a dust particle is approximately 10−610^{-6} kg and the mass of a grain of sand is approximately 10−410^{-4} kg.
a
Deduce how many times heavier a grain of sand is than a dust particle. Apply the quotient law of exponents and show all steps. [1]
b
A scientist collects 10310^3 dust particles and 10310^3 grains of sand. Deduce the total combined mass of both samples, showing your working. [1]
c
The scientist claims these power-of-ten values give a sufficiently accurate model for comparing particle masses. Critique this claim, giving one specific mathematical reason. [1]
Question diagram

Solutions

2QuestionLaws of Exponents for Integer PowersAssessment Practice
3 marks~5 minCriterion B
The intensity of light decreases as it travels from a source. A photographer measures the relative intensity of a lamp at several distances.

Distance (m): 2, 4, 8, 162, \ 4, \ 8, \ 16

Relative intensity: 16, 4, 1, 0.2516, \ 4, \ 1, \ 0.25
a
Express each relative intensity as a power of 2. [1]
b
Express each distance as a power of 2, then deduce the relationship between the exponent of the distance and the exponent of the relative intensity. [1]
c
A subject is positioned 32 m from the lamp. The photographer requires a relative intensity of at least 0.10.1 for a usable photograph. Using laws of exponents, calculate the relative intensity at 32 m and advise the photographer whether the subject should be moved closer. [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=2xy = 2^x, where yy is the population size (thousands) and xx is time in hours. Population B decays and is modelled by y=12xy = \dfrac{1}{2^x}.
a
Show that 12x=2−x\dfrac{1}{2^x} = 2^{-x}, stating the law of exponents used. [1]
b
Describe the geometric transformation that maps the graph of y=2xy = 2^x onto the graph of y=2−xy = 2^{-x}, explaining how the change in exponent produces this transformation. [2]
c
At x=3x = 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

(16a−4b681c−8d12)−34\left( \frac{16a^{-4}b^{6}}{81c^{-8}d^{12}} \right)^{-\frac{3}{4}}

where aa, bb, cc, dd represent measurable physical parameters, all positive and non-zero.
a
Show that the expression simplifies to 27a3d98b92c6\dfrac{27a^{3}d^{9}}{8b^{\frac{9}{2}}c^{6}}, stating each law of exponents you apply. [4]
b
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

Questions 5-66

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 66.

+62 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade