EmSAT Achieve (UAE) · Mathematics

Functions, Logarithms and Exponential Models

29 practice questions, each with the answer and an explanation.

Practise Functions, Logarithms and Exponential Models now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 29 questions

Evaluate $lo g_{2} (64) - lo g_{3} (\frac{1}{27})$ .
Solve for $x$ : $5^{2 x + 1} = 12 5^{x - 1}$ .
If $f (x) = x^{2} - 3$ and $g (x) = 2 x + 1$ , what is $(f \circ g) (2)$ ?
What is the horizontal asymptote of the rational function $f (x) = \frac{6 x ^{3} - 5 x + 2}{2 x ^{3} + 7 x ^{2} - 1}$ ?
What is the vertical asymptote of the logarithmic function $f (x) = ln (2 x - 8)$ ?
What is the inverse function of $f (x) = 2 e^{3 x - 1}$ ?
If $lo g_{a} (x) = 3$ and $lo g_{a} (y) = 5$ , what is the value of $lo g_{a} (\frac{x ^{2}}{y})$ ?
A radioactive substance decays according to $A (t) = A_{0} e^{- 0.05 t}$ , where $t$ is measured in days. After how many days will the sample decay to half its initial amount?
What is the domain of the function $f (x) = lo g_{3} (x^{2} - 4 x - 12)$ ?
What is the value of $x$ satisfying $lo g_{2} (x + 3) + lo g_{2} (x - 3) = 4$ ?
Which of the following functions has a graph that is symmetric with respect to the origin?
What is the range of $f (x) = 4 - 3 e^{2 x}$ ?
If $lo g (2) \approx 0.3010$ and $lo g (3) \approx 0.4771$ , what is the approximate value of $lo g (18)$ ?
What is the value of $\sum_{n = 1}^{4} (3^{n} - 2)$ ?
What is the domain of the function $g (x) = \frac{1}{l n ( x - 2 )}$ ?
Solve for $x$ : $e^{2 x} - 5 e^{x} + 6 = 0$ .
If $f (x) = 3 x - 2$ and $g (x) = \frac{x + 2}{3}$ , which statement is true about $f$ and $g$ ?
What is the value of $lo g_{4} (32)$ ?
Which function exhibits exponential decay for all $x > 0$ ?
Solve for $x$ : $lo g_{3} (x) + lo g_{9} (x) = 6$ .
What is the asymptote of the graph of $f (x) = 5 - 2^{x + 3}$ ?
If $f (x) = \frac{x ^{2} - 16}{x - 4}$ , what is the removable discontinuity (hole) in the graph of $f$ ?
Which expression is equivalent to $\frac{e ^{4 x} - e ^{- 4 x}}{2}$ ?
What is the value of $x$ if $3 \cdot 2^{x} = 96$ ?
Evaluate the definite integral $\int_{0}^{π /2} x cos (x) d x$ .
What is the value of $(1 + i 3)^{6}$ using De Moivre's theorem?
What is the solution to the differential equation $\frac{d y}{d x} = 2 x y$ with initial condition $y (0) = 3$ ?
What is the inverse of the matrix $A = (3512)$ ?
What is the focal length $c$ of the ellipse defined by $9 x^{2} + 25 y^{2} = 225$ ?

Keep practising

More EmSAT Achieve (UAE) topics

Trigonometry, Vectors and Complex Numbers29 questions
Algebra, Equations and Coordinate Geometry28 questions
Differential Calculus and Probability Distributions28 questions
Grammar, Syntax and Sentence Structure26 questions
Reading Comprehension and Text Analysis26 questions
Mechanics and Thermodynamics26 questions
Waves, Electromagnetism and Modern Physics26 questions
Matter, Atomic Structure and Chemical Bonding26 questions

All EmSAT Achieve (UAE) practice →

Ready for the full EmSAT Achieve (UAE) test?

Take a mock test EmSAT Achieve (UAE) hub