Egyptian Scholastic Test (EST) · EST Mathematics

Advanced Mathematics, Geometry and Data Analysis

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

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All 75 questions

A circle in the xy-plane has equation $(x - 3)^{2} + (y + 2)^{2} = 25$ . What are the coordinates of its center and its radius?
In right triangle $A B C$ , angle $C = 9 0^{\circ}$ . If $sin A = \frac{3}{5}$ , what is the value of $cos A$ ?
What is the area of an equilateral triangle with side length $8 cm$ ?
A cylinder has a radius of $3 cm$ and a height of $10 cm$ . What is its total volume?
What is the median of the dataset ${4, 8, 12, 15, 19, 22, 27}$ ?
Two similar triangles have corresponding side lengths in the ratio $2 : 5$ . If the smaller triangle has an area of $24 cm^{2}$ , what is the area of the larger triangle?
In a standard normal distribution, approximately what percentage of data values lie within two standard deviations of the mean (between $μ - 2 σ$ and $μ + 2 σ$ )?
What is the distance between the two points $(1, - 3)$ and $(4, 1)$ in the Cartesian plane?
What is the measure of each interior angle of a regular hexagon?
If a box contains 5 red balls, 3 blue balls, and 2 green balls, what is the probability of randomly drawing a ball that is NOT green?
In the circle with center $O$ , central angle $∠ A O B = 6 0^{\circ}$ intercepts an arc $A B$ . If the radius of the circle is $6 cm$ , what is the length of arc $A B$ ?
What is the value of $tan (4 5^{\circ}) + cos (6 0^{\circ})$ ?
A survey of 200 high school students revealed that 120 play football, 90 play basketball, and 40 play both sports. How many students play NEITHER sport?
What is the slope of a line that is perpendicular to the line with equation $3 x - 4 y = 8$ ?
A cone and a cylinder have identical base radii of $4 cm$ and identical heights of $9 cm$ . What is the ratio of the volume of the cone to the volume of the cylinder?
In a dataset of 5 distinct positive integers, the mean is 12, the median is 10, and the mode does not exist. If the smallest integer is 4, what is the greatest possible value of the largest integer?
What is the equation of the line passing through $(0, 0)$ with an angle of inclination of $4 5^{\circ}$ ?
What is the surface area of a sphere with radius $r = 3 cm$ ?
In a triangle, two sides have lengths $7 cm$ and $10 cm$ . According to the triangle inequality theorem, which could be the length of the third side?
What is the sum of the angles in a quadrilateral?
A standard 6-sided die is rolled twice. What is the probability that the sum of the two rolls is equal to 7?
If the variance of a dataset is 16, what is its standard deviation?
In right triangle $D E F$ , the hypotenuse $D F = 13$ and leg $D E = 5$ . What is the length of leg $E F$ ?
What is the midpoint of the segment connecting $(- 2, 7)$ and $(6, - 1)$ ?
A rectangular garden has length 15 meters and width 10 meters. If a uniform pathway of width $x$ surrounds the garden, what expression represents the total area including the pathway?
What is the value of $sin^{2} (3 0^{\circ}) + cos^{2} (3 0^{\circ})$ ?
Evaluate $\frac{3 + 4 i}{1 - 2 i}$ in standard rectangular form $a + bi$ .
What is the area of a triangle with vertices at $(0, 0)$ , $(4, 1)$ , and $(2, 5)$ ?
What is the solution set of $\frac{x - 3}{x + 2} \geq 0$ ?
If a line has equation $3 x - 4 y = 12$ , what is the equation of the line perpendicular to it passing through $(1, 2)$ ?
In a set of 5 distinct positive integers, the median is 8, the unique mode does not exist, and the mean is 9. What is the greatest possible integer in the set if all are distinct?
In an arithmetic sequence $a_{3} = - 7$ and $a_{7} = - 27$ . What is $a_{13}$ ?
A car drives to a town at 60 km/h and returns by the same road at 90 km/h. What is its average speed for the round trip?
A data set has mean 23. Each value is multiplied by 4 and then 7 is added. What is the new mean?
In how many ways can 11 people stand in a row if two particular people must stand next to each other?
What is the remainder when $3 x^{3} - 2 x^{2} - 3 x + 4$ is divided by $x + 3$ ?
A fair coin is tossed 8 times. What is the probability of exactly 7 heads?
What is the total surface area of a cuboid measuring 2 cm by 7 cm by 4 cm?
In a race with 12 runners, how many different orders are possible for first, second and third place?
Convert 54 km/h to metres per second.
In an arithmetic sequence $a_{4} = 3$ and $a_{7} = 12$ . What is $a_{14}$ ?
A fair coin is tossed 5 times. What is the probability of exactly 2 heads?
Machine A finishes a job in 10 hours and machine B in 40 hours. Working together, how long do they take?
A fair coin is tossed 7 times. What is the probability of exactly 6 heads?
Machine A finishes a job in 12 hours and machine B in 4 hours. Working together, how long do they take?
In an arithmetic sequence $a_{5} = 18$ and $a_{12} = 46$ . What is $a_{15}$ ?
What is the centre of the circle $x^{2} + y^{2} + 2 x - 6 y - 54 = 0$ ?
In how many ways can 6 people stand in a row if two particular people must stand next to each other?
A circle has radius 11 cm. What is its circumference, in terms of $π$ ?
What is the volume of a cone of base radius 14 cm and height 6 cm? (Use $π = \frac{22}{7}$ .)
What is the remainder when $3 x^{3} + 6 x - 5$ is divided by $x + 4$ ?
In triangle $A B C$ , $∠ A = 4 5^{\circ}$ , $∠ B = 3 0^{\circ}$ and $a = 102$ . Find $b$ .
A fair coin is tossed 4 times. What is the probability of exactly 2 heads?
What is the radius of the circle $x^{2} + y^{2} - 6 x - 2 y - 71 = 0$ ?
In an arithmetic sequence $a_{3} = 15$ and $a_{8} = 55$ . What is $a_{13}$ ?
What is the sum of the first 7 terms of the geometric sequence with first term 5 and common ratio 3?
What is the total surface area of a cuboid measuring 9 cm by 5 cm by 5 cm?
Convert 108 km/h to metres per second.
A circle has radius 10 cm. What is its circumference, in terms of $π$ ?
A team of 2 men and 1 women is chosen from 7 men and 6 women. How many teams are possible?
What is the centre of the circle $x^{2} + y^{2} + 10 x + 2 y - 38 = 0$ ?
What is the centre of the circle $x^{2} + y^{2} + 10 x + 10 y - 14 = 0$ ?
In an arithmetic sequence $a_{6} = 1$ and $a_{11} = 6$ . What is $a_{19}$ ?
Find the median of 30, 30, 29, 18, 30, 35, 26, 26.
What is the radius of the circle $x^{2} + y^{2} - 4 x + 8 y + 16 = 0$ ?
What is the centre of the circle $x^{2} + y^{2} - 2 x - 10 y - 10 = 0$ ?
Machine A finishes a job in 6 hours and machine B in 12 hours. Working together, how long do they take?
From a point 50 m from the foot of a building on level ground, the angle of elevation of the top is $4 5^{\circ}$ . How high is the building, in metres (eye height ignored)?
A fair coin is tossed 6 times. What is the probability of exactly 2 heads?
A data set has standard deviation 6. Each value is multiplied by 2 and then 6 is added. What is the new standard deviation?
In an arithmetic sequence $a_{4} = 30$ and $a_{12} = 86$ . What is $a_{19}$ ?
If $θ$ is acute and $sin θ = \frac{7}{25}$ , what is $tan θ$ ?
10 litres of a 10% solution are mixed with 20 litres of a 60% solution. What is the concentration of the mixture?
Group A has 23 students with mean score 64; group B has 13 students with mean score 58. What is the combined mean, rounded to two decimals?
In an arithmetic sequence $a_{4} = 8$ and $a_{12} = - 8$ . What is $a_{17}$ ?

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