Egyptian Scholastic Test (EST) · EST Mathematics

Algebra, Linear Systems and Functions

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

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If $3 x - 5 = 2 (x + 4) - 7$ , what is the value of $x$ ?
A line in the xy-plane passes through the points $(2, 5)$ and $(6, 13)$ . What is the slope-intercept equation of this line?
Solve the system of equations for $y$ : \begin{cases} 2x + 3y = 12 \\ x - y = 1 \end{cases}
If $f (x) = 2 x^{2} - 3 x + 4$ , what is the value of $f (- 2)$ ?
Which of the following functions has a graph that does NOT intersect the x-axis?
If $\frac{2}{x - 3} = \frac{4}{2 x + 1}$ , what is the value of $x$ ?
A theater sells adult tickets for $12 each and student tickets for $8 each. If a total of 150 tickets were sold for $1,520, how many adult tickets were sold?
What is the vertex of the parabola defined by $y = x^{2} - 6 x + 11$ ?
If $f (x) = 3 x - 1$ and $g (x) = x^{2} + 2$ , what is the value of $(g \circ f) (2)$ ?
For what value of $c$ will the equation $4 x^{2} + 12 x + c = 0$ have exactly one real repeated solution?
If $2^{3 x - 1} = 32$ , what is the value of $x$ ?
Which of the following represents the domain of the function $h (x) = \frac{1}{2 x - 8}$ ?
A car depreciates in value by 15% each year. If its initial purchase price was $24,000, which function models its value $V(t) $a f t er$ t$ years?
What is the inverse function $f^{- 1} (x)$ of $f (x) = \frac{3 x - 4}{2}$ ?
If $∣2 x - 3∣ < 7$ , which interval represents all possible values of $x$ ?
What are the solutions to the quadratic equation $x^{2} - 4 x - 5 = 0$ ?
If a line has an x-intercept of $(4, 0)$ and a y-intercept of $(0, - 6)$ , what is the slope of the line?
Simplify the rational expression $\frac{x ^{2} - 9}{x ^{2} + 5 x + 6}$ for all valid $x$ .
If $g (x) = 5 - 2 x$ , what is the value of $g (a + 1) - g (a)$ ?
What is the sum of the solutions to the equation $2 x^{2} - 8 x + 3 = 0$ ?
If $lo g_{2} (x) + lo g_{2} (x - 2) = 3$ , what is the real value of $x$ ?
A system of two linear equations has no solutions. What must be true about their graphs in the xy-plane?
If $f (x) = k x^{3}$ and $f (2) = 24$ , what is the value of $f (- 1)$ ?
What is the range of the quadratic function $f (x) = - (x - 3)^{2} + 7$ ?
If $\frac{x}{3} + \frac{y}{4} = 1$ , what is the slope of this line?
Solve for $x$ : $3 x + 1 = 4$ .
What is the center and radius of the circle defined by $x^{2} + y^{2} - 6 x + 8 y = 0$ ?
If $x$ and $y$ satisfy the system $x^{2} + y^{2} = 25$ and $y - x = 1$ , what are the real solutions $(x, y)$ ?
A population of bacteria grows according to $P (t) = P_{0} e^{k t}$ . If population triples in 4 hours, what is $k$ ?
What is the sum of all distinct roots of $(x^{2} - 5 x + 6) (x^{2} - 7 x + 12) = 0$ ?
What is the vertex of the parabola $f (x) = - 2 x^{2} + 8 x - 3$ ?
Find all solutions of $∣5 x + 4∣ = 11$ .
If $3 x + 1 y = - 9$ and $- 2 x + 3 y = - 5$ , what is the value of $x$ ?
Evaluate $lo g_{3} 3 + lo g_{3} 9$ .
A colony of 200 bacteria multiplies by 2 every hour. How many bacteria are there after 5 hours?
A price of 150 pounds is increased by 10% and then reduced by 30%. What is the final price?
The graph of $y = f (x)$ is moved 4 units to the right and 3 units up. What is the equation of the new graph?
After a 50% increase a price is 225 pounds. What was the original price?
The graph of $y = f (x)$ is moved 3 units to the right and 4 units up. What is the equation of the new graph?
A price of 120 pounds is increased by 20% and then reduced by 20%. What is the final price?
What is the domain of $f (x) = 3 x - 4$ ?
If $- 2 x + 4 y = 10$ and $4 x + 4 y = - 8$ , what is the value of $y$ ?
Solve for $x$ : $3 x - 10 = - 3 x + 56$ .
What are the solutions of $x^{2} + 5 x + 6 = 0$ ?
If $- 3 x + 3 y = 36$ and $3 x + 1 y = - 8$ , what is the value of $x$ ?
A price of 40 pounds is increased by 25% and then reduced by 30%. What is the final price?
A colony of 200 bacteria multiplies by 3 every hour. How many bacteria are there after 3 hours?
Find all solutions of $∣5 x - 3∣ = 16$ .
What is the sum of the roots of $2 x^{2} + 4 x - 16 = 0$ ?
Solve $lo g_{5} (x + 12) = 4$ .
Evaluate $lo g_{2} 2 + lo g_{2} 2$ .
Find all solutions of $∣3 x + 6∣ = 13$ .
A price of 800 pounds is increased by 20% and then reduced by 25%. What is the final price?
What is the solution set of $x^{2} - 7 x - 18 < 0$ ?
If $f (x) = 5 x - 7$ and $g (x) = 4 x - 1$ , what is $f (g (3))$ ?
Find all solutions of $∣5 x + 4∣ = 15$ .
What is the minimum value of $f (x) = x^{2} + 10 x + 3$ ?
Solve for $x$ : $5 x + 12 = 3 x + 36$ .
Find all solutions of $∣3 x + 4∣ = 5$ .
Solve $lo g_{10} (x + 6) = 4$ .
A price of 200 pounds rises by 25%. What is the new price?
Solve for $x$ : $5 x + 8 = 2 x + 5$ .
What is the solution set of $x^{2} + x - 20 > 0$ ?
A price of 80 pounds is increased by 10% and then reduced by 30%. What is the final price?
Solve for $x$ : $6 x + 2 = - 4 x + 62$ .
Solve $lo g_{2} (x + 7) = 5$ .
What is the sum of the roots of $3 x^{2} + 9 x - 54 = 0$ ?
After a 10% increase a price is 550 pounds. What was the original price?
After a 15% increase a price is 920 pounds. What was the original price?
A coat costing 400 pounds is sold with a 20% discount. What is the sale price?
What is the product of the roots of $3 x^{2} + 15 x - 18 = 0$ ?
If $- 3 x - 1 y = - 16$ and $- 1 x + 2 y = 11$ , what is the value of $x$ ?
After a 30% increase a price is 1040 pounds. What was the original price?
A price of 60 pounds is increased by 20% and then reduced by 20%. What is the final price?
A price of 40 pounds is increased by 30% and then reduced by 10%. What is the final price?

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