EmSAT Achieve (UAE) · Mathematics

Algebra, Equations and Coordinate Geometry

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

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Solve for $x$ : $3 (2 x - 5) - 4 = 2 (x + 7) + 1$ .
What is the slope of the line perpendicular to $4 x - 8 y = 15$ ?
What is the distance between the points $(- 2, 7)$ and $(4, - 1)$ in the Cartesian plane?
Find the vertex of the parabola $f (x) = 3 x^{2} - 12 x + 5$ .
What is the center and radius of the circle $x^{2} + y^{2} + 6 x - 10 y + 9 = 0$ ?
What are the solutions to the quadratic equation $2 x^{2} - 5 x - 3 = 0$ ?
What is the solution set of the inequality $∣3 x - 4∣ < 11$ ?
For which value of $c$ does the system of equations have infinitely many solutions?
${4 x - 6 y = 10 6 x - 9 y = c$
What is the remainder when $f (x) = 2 x^{4} - 3 x^{2} + 5 x - 8$ is divided by $(x + 2)$ ?
What is the equation of the line with $x$ -intercept $(4, 0)$ and $y$ -intercept $(0, - 6)$ in standard form $A x + B y = C$ (with $A > 0$ and coprime integers)?
What is the midpoint of the line segment joining $(- 7, 9)$ and $(3, - 5)$ ?
Which expression represents the complete factorization of $8 x^{3} - 27$ over the real numbers?
What is the value of $k$ such that the line $k x + 3 y = 7$ is parallel to the line $2 x - y = 5$ ?
Solve for $x$ : $\frac{2}{x - 3} - \frac{1}{x} = \frac{5}{x ( x - 3 )}$ .
What is the product of the solutions to the quadratic equation $3 x^{2} - 11 x + 6 = 0$ ?
What is the radius of the circle with equation $2 x^{2} + 2 y^{2} - 8 x + 12 y - 6 = 0$ ?
What is the determinant of the $2 \times 2$ matrix $M = (73 - 4 2)$ ?
Find all real solutions to $3 x + 1 = x - 3$ .
What is the directrix of the parabola $y^{2} = 12 x$ ?
Which ordered pair $(x, y)$ satisfies the linear system?
${3 x + 2 y = 16 2 x - 3 y = - 11$
What is the domain of $f (x) = 2 x - 6 + \frac{1}{x - 5}$ ?
What is the equation of the line passing through $(- 1, 4)$ and $(3, - 2)$ ?
What is the focal length of the parabola $(x - 1)^{2} = 8 (y + 2)$ ?
What is the solution of the quadratic inequality $x^{2} - 4 x - 12 > 0$ ?
If $f (x) = \frac{2 x - 1}{x + 3}$ for $x \neq = - 3$ , what is the formula for the inverse function $f^{- 1} (x)$ ?
What is the coefficient of $x^{3}$ in the binomial expansion of $(2 x - 3)^{5}$ ?
What is the sum of the infinite geometric series $8 + \frac{8}{3} + \frac{8}{9} + \frac{8}{27} + \dots$ ?
What are all solutions to $2 cos^{2} (x) - cos (x) - 1 = 0$ in the interval $[0, 2 π)$ ?

Algebra, Equations and Coordinate Geometry

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