Egyptian STEM Schools Admissions Assessment · STEM Mathematics and Reasoning

Mathematical Problem Solving and Geometry

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

Practise Mathematical Problem Solving and Geometry now

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

All 75 questions

If a train traveling at $72 km/h$ takes $15 seconds$ to pass a signal pole completely, what is the length of the train?
A regular polygon has an exterior angle measuring $2 4^{\circ}$ . How many sides does this polygon have?
If $x + \frac{1}{x} = 5$ , what is the numerical value of $x^{2} + \frac{1}{x ^{2}}$ ?
A water tank can be filled by Pipe A in 6 hours and by Pipe B in 12 hours. If both pipes are opened simultaneously, how long will it take to fill the empty tank?
In a right triangle, the hypotenuse is $25 cm$ and one leg is $7 cm$ . What is the area of the triangle?
What is the sum of all positive integers from 1 to 100 inclusive?
If $3^{x + 1} + 3^{x} = 36$ , what is the value of $x$ ?
A circle is inscribed in a square of side length $14 cm$ . What is the area of the region inside the square but outside the circle? (Use $π = \frac{22}{7}$ )
If the ratio of the surface areas of two spheres is $9 : 16$ , what is the ratio of their volumes?
A trader marks an item 40% above the cost price and then offers a 20% discount on the marked price. What is the trader's actual percentage profit?
Find the roots of the equation $x^{2} - 7 x + 12 = 0$ .
What is the total number of diagonals in a regular octagon (8-sided polygon)?
If $lo g_{10} (2) = a$ and $lo g_{10} (3) = b$ , express $lo g_{10} (15)$ in terms of $a$ and $b$ .
A cylindrical wire of resistance $8 Ω$ is stretched uniformly to twice its original length without altering its volume. What is its new resistance?
What is the sum of the interior angles of a convex decagon (10-sided polygon)?
A bag contains 4 red, 5 blue, and 6 green marbles. Two marbles are drawn sequentially without replacement. What is the probability that both marbles are red?
If the perimeter of a rectangle is $36 cm$ and its length is twice its width, what is its area?
Solve for $x$ : $2^{x + 3} = 8^{x - 1}$ .
In a group of 60 students, 35 study Physics, 28 study Chemistry, and 12 study both. How many students study NEITHER subject?
What is the angle between the hands of a standard 12-hour clock at precisely 3:30?
What is the value of $12 + 12 + 12 + \dots$ ?
A solid cone has radius $r = 6 cm$ and slant height $l = 10 cm$ . What is its vertical height $h$ ?
If the roots of the quadratic equation $x^{2} + p x + 12 = 0$ are in the ratio $1 : 3$ , what is the positive value of $p$ ?
How many three-digit numbers are divisible by 5?
In a right triangle with acute angle $3 0^{\circ}$ and hypotenuse $16 cm$ , what is the length of the side opposite the $3 0^{\circ}$ angle?
What is the remainder when $2^{50}$ is divided by 7?
What is the smallest positive integer $x$ satisfying the system of congruences: $x \equiv 2 (mod 3)$ , $x \equiv 3 (mod 5)$ , and $x \equiv 2 (mod 7)$ ?
If the roots of $x^{3} - 6 x^{2} + 11 x - 6 = 0$ are $α, β, γ$ , what is the value of $α^{2} + β^{2} + γ^{2}$ ?
In how many ways can 4 boys and 4 girls be seated in a circle such that no two boys sit next to each other?
What is the shortest distance between the origin $(0, 0, 0)$ and the line given by parametric equations $x = 1 + 2 t$ , $y = - 1 + t$ , $z = 2 - t$ ?
A fair coin is flipped repeatedly until two consecutive heads appear. What is the expected number of flips?
If $- 1 x - 1 y = 8$ and $- 3 x + 2 y = 9$ , what is the value of $x$ ?
If $- 2 x + 1 y = - 5$ and $- 2 x + 3 y = - 3$ , what is the value of $x$ ?
Machine A finishes a job in 8 hours and machine B in 24 hours. Working together, how long do they take?
10 litres of a 10% solution are mixed with 20 litres of a 50% solution. What is the concentration of the mixture?
If $3 x + 3 y = - 6$ and $4 x - 3 y = - 29$ , what is the value of $x$ ?
Solve for $x$ : $6 x + 6 = 4 x + 12$ .
What is the sum of the roots of $2 x^{2} - 22 x + 56 = 0$ ?
In triangle $A B C$ , $∠ A = 4 5^{\circ}$ , $∠ B = 3 0^{\circ}$ and $a = 42$ . Find $b$ .
Solve for $x$ : $6 x - 12 = x - 42$ .
If $4 x + 4 y = 12$ and $2 x + 3 y = 5$ , what is the value of $x$ ?
A colony of 500 bacteria multiplies by 2 every hour. How many bacteria are there after 3 hours?
What is the sum of the roots of $2 x^{2} - 8 x - 64 = 0$ ?
A colony of 800 bacteria multiplies by 3 every hour. How many bacteria are there after 5 hours?
If $θ$ is acute and $sin θ = \frac{8}{17}$ , what is $sin 2 θ$ ?
What is the sum of the roots of $2 x^{2} + 6 x + 4 = 0$ ?
In triangle $A B C$ , $∠ A = 6 0^{\circ}$ , $∠ B = 3 0^{\circ}$ and $a = 93$ . Find $b$ .
A price of 40 pounds is increased by 50% and then reduced by 20%. What is the final price?
156 pounds are shared between Sara and Omar in the ratio $4 : 9$ . How much does Omar get?
If $- 3 x - 2 y = - 26$ and $1 x + 3 y = 25$ , what is the value of $x$ ?
A price of 800 pounds is increased by 50% and then reduced by 20%. What is the final price?
If $θ$ is acute and $sin θ = \frac{3}{5}$ , what is $sin 2 θ$ ?
Solve for $x$ : $2 x + 3 = 3 x - 5$ .
The graph of $y = f (x)$ is moved 4 units to the right and 1 units up. What is the equation of the new graph?
If $3 x + 3 y = 6$ and $3 x - 1 y = 26$ , what is the value of $x$ ?
A price of 40 pounds is increased by 15% and then reduced by 20%. What is the final price?
20 litres of a 10% solution are mixed with 10 litres of a 40% solution. What is the concentration of the mixture?
A price of 800 pounds rises by 20%. What is the new price?
What is the total surface area of a cuboid measuring 4 cm by 4 cm by 5 cm?
If $- 1 x - 1 y = 2$ and $3 x - 3 y = 18$ , what is the value of $y$ ?
In triangle $A B C$ , $b = 5$ , $c = 16$ and $∠ A = 12 0^{\circ}$ . Find $a$ .
A plumber charges a fixed fee of 7 pounds plus 3 pounds per hour. What is the cost of a 8-hour job?
A circle has radius 6 cm. What is its circumference, in terms of $π$ ?
A plumber charges a fixed fee of 22 pounds plus 2 pounds per hour. What is the cost of a 7-hour job?
A price of 500 pounds is increased by 20% and then reduced by 30%. What is the final price?
If $- 3 x - 2 y = - 19$ and $1 x + 4 y = 3$ , what is the value of $y$ ?
In triangle $A B C$ , $b = 8$ , $c = 15$ and $∠ A = 6 0^{\circ}$ . Find $a$ .
What is the sum of the roots of $2 x^{2} + 22 x + 56 = 0$ ?
Evaluate $tan^{2} 6 0^{\circ} + sin 9 0^{\circ} - tan 4 5^{\circ}$ .
What is the total surface area of a cuboid measuring 9 cm by 10 cm by 4 cm?
After a 25% increase a price is 75 pounds. What was the original price?
A car drives to a town at 30 km/h and returns by the same road at 60 km/h. What is its average speed for the round trip?
If $- 3 x + 2 y = - 23$ and $- 3 x + 1 y = - 22$ , what is the value of $y$ ?
A circle has radius 5 cm. What is its circumference, in terms of $π$ ?
What is the sum of the roots of $2 x^{2} + 6 x - 8 = 0$ ?

Keep practising

Ready for the full Egyptian STEM Schools Admissions Assessment test?

Take a mock test Egyptian STEM Schools Admissions Assessment hub

Mathematical Problem Solving and Geometry

Practise Mathematical Problem Solving and Geometry now

All 75 questions

Keep practising

More Egyptian STEM Schools Admissions Assessment topics

Ready for the full Egyptian STEM Schools Admissions Assessment test?