Tahsili SAAT (Saudi Arabia) · Mathematics

Functions, Calculus, Vectors and Analytic Geometry

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

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What is the domain of the real-valued function $f (x) = 2 x - 6$ ?
What is the exact value of $sin (15 0^{\circ})$ ?
If $lo g_{2} (x) + lo g_{2} (x - 2) = 3$ , what is the real solution for $x$ ?
What is the derivative $f^{'} (x)$ of the polynomial function $f (x) = 4 x^{3} - 5 x^{2} + 7 x - 9$ evaluated at $x = 1$ ?
What is the value of the definite integral $\int_{0}^{3} (2 x + 1) d x$ ?
Two vectors are given in component form as $u = ⟨ 3, - 4 ⟩$ and $v = ⟨ 4, 3 ⟩$ . What is their dot product $u \cdot v$ ?
What is the coordinates of the vertex of the parabola defined by $y = x^{2} - 6 x + 14$ ?
What is the limit $lim_{x \to 2} \frac{x ^{2} - 4}{x - 2}$ ?
What is the eccentricity $e$ of a circle?
In a geometric sequence where the first term is $a_{1} = 5$ and the common ratio is $r = 2$ , what is the sum of the first 6 terms ( $S_{6}$ )?
What is the solution set of the absolute value inequality $∣2 x - 5∣ < 7$ ?
If a fair six-sided die is rolled twice, what is the probability that the sum of the two numbers is equal to 9?
What is the inverse function $f^{- 1} (x)$ of the bijection $f (x) = 3 x - 7$ ?
What is the distance between the two points $P (2, - 3)$ and $Q (6, 0)$ in the Cartesian plane?
Which of the following functions represents an even function, satisfying $f (- x) = f (x)$ for all $x$ in its domain?
What is the value of $lo g_{3} (81) - lo g_{5} (125)$ ?
What is the period of the trigonometric function $y = 3 sin (4 x)$ ?
What are the asymptotes of the rational function $f (x) = \frac{3 x + 6}{x - 2}$ ?
If a matrix $A = (2154)$ , what is the determinant of $A$ ?
What is the center and radius of the circle defined by the equation $(x - 4)^{2} + (y + 2)^{2} = 36$ ?
What is the solution to the system of linear equations $2 x + y = 7$ and $x - y = 2$ ?
What is the sum of the infinite geometric series $12 + 6 + 3 + 1.5 + \dots$ ?
What is the value of $x$ in the equation $e^{2 x} = 5$ in exact logarithmic terms?
A curve has the equation $y = x^{3} - 3 x$ . At which point does the curve have a local horizontal tangent ( $y^{'} = 0$ )?
What is the magnitude of the 3-dimensional vector $w = ⟨ 2, 3, 6 ⟩$ ?
In how many ways can 5 distinct books be arranged on a single shelf?
Solve for real $x$ : $lo g_{2} (x) + lo g_{2} (x - 2) = 3$ . What is the valid real solution?
What is the equation of the tangent line to the curve $f (x) = x^{3} - 3 x + 2$ at the point where $x = 2$ ?
What is the complete solution set for the compound inequality $∣2 x - 5∣ < 7$ and $x > 0$ ?
What are all the vertical and horizontal asymptotes of the rational function $f (x) = \frac{3 x ^{2} - 12}{x ^{2} - x - 6}$ ?
What is the total area of the finite region enclosed between the parabola $y = x^{2}$ and the line $y = 2 x$ ?

Functions, Calculus, Vectors and Analytic Geometry

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