MATHNASIUM JOB ASSESSMENT EXAM ACTUAL EXAM 2026 | ALL QUESTIONS AND
CORRECT ANSWERS | JUST RELEASED
Question 1
What is the correct formula for the area of a trapezoid?
A) A = lw
B) A = bh
C) A = (1/2)h(b1 + b2)
D) A = (1/2)bh
E) A = pi x r^2
Correct Answer: C) A = (1/2)h(b1 + b2)
Rationale: The area of a trapezoid is calculated by taking the average of the two parallel
bases (b1 and b2) and multiplying by the height (h). Geometrically, this is equivalent to
transforming the trapezoid into a rectangle with a width equal to the average of the bases.
Question 2
How many feet are in 3.5 miles?
A) 15,840 feet
B) 18,480 feet
C) 5,280 feet
D) 17,600 feet
E) 21,120 feet
Correct Answer: B) 18,480 feet
Rationale: There are exactly 5,280 feet in one mile. To find the number of feet in 3.5 miles,
you multiply 3.5 by 5,280. Calculation: 3 * 5280 = 15,840; 0.5 * 5280 = 2,640. Total: 15,840
+ 2,640 = 18,480.
Question 3
Which formula represents the Pythagorean Theorem for a right triangle with legs a and b and
hypotenuse c?
A) a + b = c
B) a^2 + b^2 = c^2
C) (1/2)ab = c
D) a^2 - b^2 = c^2
E) sqrt(a+b) = c
Correct Answer: B) a^2 + b^2 = c^2
Rationale: The Pythagorean Theorem states that in any right-angled triangle, the area of
the square whose side is the hypotenuse is equal to the sum of the areas of the squares
whose sides are the two legs. This is a fundamental principle in Euclidean geometry used to
find missing side lengths.
Question 4
How many centimeters are in 5 inches?
A) 10.54 cm
, 2
B) 12.70 cm
C) 15.24 cm
D) 2.54 cm
E) 11.25 cm
Correct Answer: B) 12.70 cm
Rationale: One inch is defined as exactly 2.54 centimeters. To convert inches to centimeters,
you multiply the number of inches by 2.54. Calculation: 5 * 2.54 = 12.70.
Question 5
What is the value of i^63?
A) i
B) -i
C) 1
D) -1
E) 0
Correct Answer: B) -i
Rationale: Powers of the imaginary unit 'i' follow a cycle of four: i^1 = i, i^2 = -1, i^3 = -i,
and i^4 = 1. To find i^63, divide 63 by 4. The remainder is 3 (since 60 is a multiple of 4).
Therefore, i^63 is equivalent to i^3, which is -i.
Question 6
A circle has a diameter of 10 units. What is its area?
A) 10pi
B) 100pi
C) 25pi
D) 5pi
E) 20pi
Correct Answer: C) 25pi
Rationale: The formula for the area of a circle is A = pi * r^2. If the diameter is 10, the
radius (r) is half of that, which is 5. Plugging this into the formula: A = pi * (5)^2 = 25pi.
Question 7
How do you calculate the sum of the interior angles of a polygon with 'n' sides?
A) 180n
B) 180(n - 2)
C) 360(n - 2)
D) 180(n + 2)
E) 90(n - 2)
Correct Answer: B) 180(n - 2)
Rationale: A polygon with 'n' sides can be divided into (n - 2) triangles by drawing
, 3
diagonals from a single vertex. Since each triangle's angles sum to 180 degrees, the total
interior angle sum for the polygon is 180 * (n - 2).
Question 8
What is the volume of a cone with radius 'r' and height 'h'?
A) V = pi * r^2 * h
B) V = (4/3)pi * r^3
C) V = (1/2)pi * r^2 * h
D) V = (1/3)pi * r^2 * h
E) V = 2pi * r * h
Correct Answer: D) V = (1/3)pi * r^2 * h
Rationale: The volume of a cone is exactly one-third the volume of a cylinder with the same
base and height. The area of the base is pi * r^2, so the volume of the cone is (1/3) * base *
height.
Question 9
In a 30-60-90 triangle, if the shortest leg is x, what is the length of the hypotenuse?
A) x * sqrt(3)
B) x * sqrt(2)
C) 2x
D) x + 30
E) x / 2
Correct Answer: C) 2x
Rationale: The side lengths of a 30-60-90 triangle follow the ratio 1 : sqrt(3) : 2. The shortest
leg (opposite the 30° angle) is x, the longer leg (opposite the 60° angle) is x*sqrt(3), and the
hypotenuse (opposite the 90° angle) is always twice the length of the shortest leg.
Question 10
Which of the following is the Quadratic Formula?
A) x = (-b ± sqrt(b^2 - 4ac)) / 2a
B) x = (b ± sqrt(b^2 + 4ac)) / 2a
C) x = -b / 2a
D) x = (-b ± sqrt(a^2 - 4bc)) / 2
E) x = (-c ± sqrt(b^2 - 4ac)) / 2a
Correct Answer: A) x = (-b ± sqrt(b^2 - 4ac)) / 2a
Rationale: The quadratic formula is derived from completing the square on the general
quadratic equation ax^2 + bx + c = 0. It provides the solutions (roots) for any quadratic
equation, where 'a' is the leading coefficient, 'b' the linear coefficient, and 'c' the constant.
Question 11
What is the Greates Common Factor (GCF) of 24 and 36?
CORRECT ANSWERS | JUST RELEASED
Question 1
What is the correct formula for the area of a trapezoid?
A) A = lw
B) A = bh
C) A = (1/2)h(b1 + b2)
D) A = (1/2)bh
E) A = pi x r^2
Correct Answer: C) A = (1/2)h(b1 + b2)
Rationale: The area of a trapezoid is calculated by taking the average of the two parallel
bases (b1 and b2) and multiplying by the height (h). Geometrically, this is equivalent to
transforming the trapezoid into a rectangle with a width equal to the average of the bases.
Question 2
How many feet are in 3.5 miles?
A) 15,840 feet
B) 18,480 feet
C) 5,280 feet
D) 17,600 feet
E) 21,120 feet
Correct Answer: B) 18,480 feet
Rationale: There are exactly 5,280 feet in one mile. To find the number of feet in 3.5 miles,
you multiply 3.5 by 5,280. Calculation: 3 * 5280 = 15,840; 0.5 * 5280 = 2,640. Total: 15,840
+ 2,640 = 18,480.
Question 3
Which formula represents the Pythagorean Theorem for a right triangle with legs a and b and
hypotenuse c?
A) a + b = c
B) a^2 + b^2 = c^2
C) (1/2)ab = c
D) a^2 - b^2 = c^2
E) sqrt(a+b) = c
Correct Answer: B) a^2 + b^2 = c^2
Rationale: The Pythagorean Theorem states that in any right-angled triangle, the area of
the square whose side is the hypotenuse is equal to the sum of the areas of the squares
whose sides are the two legs. This is a fundamental principle in Euclidean geometry used to
find missing side lengths.
Question 4
How many centimeters are in 5 inches?
A) 10.54 cm
, 2
B) 12.70 cm
C) 15.24 cm
D) 2.54 cm
E) 11.25 cm
Correct Answer: B) 12.70 cm
Rationale: One inch is defined as exactly 2.54 centimeters. To convert inches to centimeters,
you multiply the number of inches by 2.54. Calculation: 5 * 2.54 = 12.70.
Question 5
What is the value of i^63?
A) i
B) -i
C) 1
D) -1
E) 0
Correct Answer: B) -i
Rationale: Powers of the imaginary unit 'i' follow a cycle of four: i^1 = i, i^2 = -1, i^3 = -i,
and i^4 = 1. To find i^63, divide 63 by 4. The remainder is 3 (since 60 is a multiple of 4).
Therefore, i^63 is equivalent to i^3, which is -i.
Question 6
A circle has a diameter of 10 units. What is its area?
A) 10pi
B) 100pi
C) 25pi
D) 5pi
E) 20pi
Correct Answer: C) 25pi
Rationale: The formula for the area of a circle is A = pi * r^2. If the diameter is 10, the
radius (r) is half of that, which is 5. Plugging this into the formula: A = pi * (5)^2 = 25pi.
Question 7
How do you calculate the sum of the interior angles of a polygon with 'n' sides?
A) 180n
B) 180(n - 2)
C) 360(n - 2)
D) 180(n + 2)
E) 90(n - 2)
Correct Answer: B) 180(n - 2)
Rationale: A polygon with 'n' sides can be divided into (n - 2) triangles by drawing
, 3
diagonals from a single vertex. Since each triangle's angles sum to 180 degrees, the total
interior angle sum for the polygon is 180 * (n - 2).
Question 8
What is the volume of a cone with radius 'r' and height 'h'?
A) V = pi * r^2 * h
B) V = (4/3)pi * r^3
C) V = (1/2)pi * r^2 * h
D) V = (1/3)pi * r^2 * h
E) V = 2pi * r * h
Correct Answer: D) V = (1/3)pi * r^2 * h
Rationale: The volume of a cone is exactly one-third the volume of a cylinder with the same
base and height. The area of the base is pi * r^2, so the volume of the cone is (1/3) * base *
height.
Question 9
In a 30-60-90 triangle, if the shortest leg is x, what is the length of the hypotenuse?
A) x * sqrt(3)
B) x * sqrt(2)
C) 2x
D) x + 30
E) x / 2
Correct Answer: C) 2x
Rationale: The side lengths of a 30-60-90 triangle follow the ratio 1 : sqrt(3) : 2. The shortest
leg (opposite the 30° angle) is x, the longer leg (opposite the 60° angle) is x*sqrt(3), and the
hypotenuse (opposite the 90° angle) is always twice the length of the shortest leg.
Question 10
Which of the following is the Quadratic Formula?
A) x = (-b ± sqrt(b^2 - 4ac)) / 2a
B) x = (b ± sqrt(b^2 + 4ac)) / 2a
C) x = -b / 2a
D) x = (-b ± sqrt(a^2 - 4bc)) / 2
E) x = (-c ± sqrt(b^2 - 4ac)) / 2a
Correct Answer: A) x = (-b ± sqrt(b^2 - 4ac)) / 2a
Rationale: The quadratic formula is derived from completing the square on the general
quadratic equation ax^2 + bx + c = 0. It provides the solutions (roots) for any quadratic
equation, where 'a' is the leading coefficient, 'b' the linear coefficient, and 'c' the constant.
Question 11
What is the Greates Common Factor (GCF) of 24 and 36?
