AKU MBBS Admission Test Mathematical Reasoning Syllabus

State the quadratic formula for solving ax² + bx + c = 0.

x = [−b ± √(b² − 4ac)] ÷ (2a).

What is the discriminant of a quadratic, and what do its values tell you about the roots?

Discriminant D = b² − 4ac. D > 0: two distinct real roots; D = 0: one repeated real root; D < 0: no real roots (two complex roots).

For ax² + bx + c = 0, what are the sum and product of the roots?

Sum of roots = −b/a. Product of roots = c/a.

How do you solve a quadratic equation by factoring?

Write it as ax² + bx + c = 0, factor into (px + q)(rx + s) = 0, then set each factor to zero and solve, using the zero-product property.

What is the method for solving a system of two linear equations by substitution?

Solve one equation for one variable, substitute that expression into the other equation to get one equation in one variable, solve it, then back-substitute to find the second variable.

When you multiply or divide both sides of an inequality by a negative number, what must you do?

Reverse (flip) the direction of the inequality sign. E.g. −2x < 6 becomes x > −3.

What is the difference between strict inequalities (<, >) and inclusive inequalities (≤, ≥) on a number line?

Strict (<, >) use an open circle and exclude the endpoint. Inclusive (≤, ≥) use a closed/filled circle and include the endpoint.

How do you express the solution of |x| < a (a > 0) as a compound inequality?

|x| < a means −a < x < a. Correspondingly |x| > a means x < −a or x > a.

What is the formal definition of a function in terms of inputs and outputs?

A function is a relation that assigns to each input (element of the domain) exactly one output (element of the range).

What are the domain and range of a function?

Domain is the set of all permissible input (x) values. Range is the set of all resulting output (y) values.

What is the vertical line test, and what does it determine?

If any vertical line crosses a graph more than once, the graph is not a function. It tests whether each x maps to only one y.

In the line y = mx + c, what do m and c represent?

m is the slope (gradient, rise over run) and c is the y-intercept (where the line crosses the y-axis).

What is the shape of the graph of y = ax² + bx + c, and what determines its opening direction?

It is a parabola. If a > 0 it opens upward (minimum vertex); if a < 0 it opens downward (maximum vertex).

How do you find the x-axis of symmetry / vertex x-coordinate of the parabola y = ax² + bx + c?

x = −b/(2a). Substitute this back into the equation to get the vertex's y-coordinate.

Strategy: how should you translate the word-problem phrase 'is', 'of', and 'per' into mathematics?

'is' means equals (=), 'of' means multiply (×), and 'per' means divide (÷) or 'for each'.

What is the sum of the interior angles of a triangle, and of angles on a straight line?

Interior angles of a triangle sum to 180°. Angles on a straight line also sum to 180°.

Define complementary and supplementary angles.

Complementary angles sum to 90°. Supplementary angles sum to 180°.

Classify triangles by their sides: scalene, isosceles, equilateral.

Scalene: all three sides (and angles) different. Isosceles: two equal sides and two equal base angles. Equilateral: all three sides equal and all angles 60°.

State the Pythagorean theorem and when it applies.

In a right-angled triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle) and a, b are the other two sides.

What is the relationship between angles when two parallel lines are cut by a transversal (corresponding and alternate angles)?

Corresponding angles are equal, alternate (Z) angles are equal, and co-interior (allied) angles are supplementary (sum to 180°).

Give the area and perimeter formulas for a rectangle.

Area = length × width. Perimeter = 2 × (length + width).

Give the area formulas for a triangle and a circle, and the circumference of a circle.

Triangle area = ½ × base × height. Circle area = πr². Circumference = 2πr (or πd).

What is the formula for the volume of a cube, a rectangular box (cuboid), and a cylinder?

Cube: side³. Cuboid: length × width × height. Cylinder: πr²h.

What is the formula for the volume of a sphere and a cone?

Sphere: (4/3)πr³. Cone: (1/3)πr²h.

What is the distance formula between two points (x₁, y₁) and (x₂, y₂)?

Distance = √[(x₂ − x₁)² + (y₂ − y₁)²].

What is the midpoint formula for the segment joining (x₁, y₁) and (x₂, y₂)?

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2).

What is the slope (gradient) formula between two points, and what are the slopes of horizontal and vertical lines?

Slope m = (y₂ − y₁)/(x₂ − x₁). A horizontal line has slope 0; a vertical line has an undefined slope.

What is the slope relationship for two parallel lines and for two perpendicular lines?

Parallel lines have equal slopes (m₁ = m₂). Perpendicular lines have slopes that multiply to −1 (m₁ × m₂ = −1, i.e. negative reciprocals).

Define mean, median and mode.

Mean = sum of all values ÷ number of values. Median = the middle value when data is ordered. Mode = the value that occurs most frequently.

How do you find the median when there is an even number of data values?

Order the data, then take the average (mean) of the two middle values.

What is the range of a data set, and how is it calculated?

Range = largest value − smallest value; it measures the spread of the data.

What is the basic probability formula for a single event with equally likely outcomes?

P(event) = (number of favourable outcomes) ÷ (total number of possible outcomes). It ranges from 0 (impossible) to 1 (certain).

What is the probability of the complement of an event A?

P(not A) = 1 − P(A).

For two independent events A and B, what is the probability that both occur (the multiplication rule)?

P(A and B) = P(A) × P(B), when the events are independent.

For two mutually exclusive events A and B, what is the probability that either occurs (the addition rule)?

P(A or B) = P(A) + P(B), when the events cannot happen at the same time. For non-exclusive events, subtract P(A and B).

When reading a chart to find a percentage of a total (e.g. a pie chart), how do you convert a sector's angle to a value?

Value = (sector angle ÷ 360°) × total. Equivalently, percentage of total = sector angle ÷ 360° × 100.

When interpreting a line graph, what does a steeper slope indicate compared to a flatter slope?

A steeper slope indicates a faster rate of change (greater increase or decrease per unit), while a flatter slope indicates a slower rate of change; a horizontal segment means no change.

What is the fundamental relationship among distance, speed and time?

Distance = Speed × Time. Therefore Speed = Distance ÷ Time and Time = Distance ÷ Speed.

In work-rate problems, if one worker takes a hours and another takes b hours alone, how long do they take together?

Combined rate = 1/a + 1/b jobs per hour, so time together = 1 ÷ (1/a + 1/b) = ab/(a + b) hours.

How do you find average speed for a whole journey when speeds over segments differ?

Average speed = total distance ÷ total time. It is NOT simply the average of the speeds.

How do you convert a speed from km/h to m/s?

Multiply by 1000/3600, which simplifies to multiplying by 5/18. (To go m/s to km/h, multiply by 18/5.)

List the basic metric length and mass conversions: km to m, m to cm, kg to g.

1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 g = 1000 mg.

What is rounding to estimate, and how do you round a number to a given place value?

Look at the digit immediately to the right of the rounding place: if it is 5 or more, round up; if it is 4 or less, round down (keep the digit). Estimation replaces numbers with convenient rounded values for quick calculation.

What is the order of operations (BODMAS/PEMDAS) for evaluating expressions?

Brackets/Parentheses, Orders/Exponents (powers and roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

In a logical numerical pattern, how do you identify whether the rule is arithmetic or based on a repeated operation?

Check the differences between consecutive terms: constant difference indicates adding/subtracting (arithmetic); constant ratio indicates multiplying/dividing (geometric); changing differences may indicate squares, cubes, or alternating rules.

1 litre equals how many millilitres, and 1 cubic metre equals how many litres?

1 litre = 1000 millilitres. 1 cubic metre (m³) = 1000 litres. Also 1 litre = 1000 cm³.

How do you find what percentage one number is of another?

Percentage = (part ÷ whole) × 100. E.g. 15 out of 60 is (15/60) × 100 = 25%.