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Air University Entry Test Quantitative Syllabus
The Quantitative syllabus for Air University Entry Test in full: 4 chapters and 17 topics, every one listed below, plus 51 Quantitative flashcards with answers.
Quantitative syllabus: all 4 chapters
Expand any chapter to see its topics and sub-topics.
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Arithmetic
5 topics- Number systems
- Ratio and proportion
- Percentages
- Profit, loss and discount
- Average, speed and time
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Algebra
4 topics- Linear equations
- Quadratic equations
- Algebraic expressions and factorization
- Inequalities
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Geometry
5 topics- Lines and angles
- Triangles and polygons
- Circles
- Area, perimeter and volume
- Coordinate geometry
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Data Interpretation
3 topics- Tables and charts
- Graphs
- Basic statistics and averages
Air University Entry Test Quantitative flashcards — 51 questions with answers
What are natural numbers?
The counting numbers starting from 1: 1, 2, 3, 4, ... (positive integers, excluding 0).
What are whole numbers?
The natural numbers together with 0: 0, 1, 2, 3, ...
Define a prime number and give the only even prime.
A natural number greater than 1 with exactly two factors (1 and itself). The only even prime is 2.
What is a rational number?
Any number expressible as p/q where p and q are integers and q is not 0 (e.g. 3/4, -2, 0.5).
What is an irrational number? Give an example.
A real number that cannot be written as a ratio of two integers; its decimal is non-terminating and non-repeating. Example: square root of 2, or pi.
State the test for divisibility by 3.
A number is divisible by 3 if the sum of its digits is divisible by 3.
State the test for divisibility by 9.
A number is divisible by 9 if the sum of its digits is divisible by 9.
State the test for divisibility by 11.
A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is 0 or a multiple of 11.
What is the relationship between HCF and LCM of two numbers a and b?
HCF(a,b) x LCM(a,b) = a x b.
What is a ratio, and how is the ratio a:b expressed as a fraction?
A ratio compares two quantities of the same kind by division; a:b is written as the fraction a/b.
What is a proportion, and what is the key cross-multiplication property?
A proportion states two ratios are equal: a/b = c/d. Cross-multiplication gives a x d = b x c (product of means = product of extremes).
In direct proportion, how do two quantities behave?
They increase or decrease together so their ratio stays constant: y = kx, meaning y/x is constant.
In inverse proportion, how do two quantities behave?
As one increases the other decreases so their product stays constant: xy = k.
How do you divide an amount N in the ratio a:b?
First part = N x a/(a+b); second part = N x b/(a+b).
How do you convert a fraction or decimal to a percentage?
Multiply by 100 and add the percent sign (e.g. 0.25 x 100 = 25%).
How do you express x% of a quantity Q?
x% of Q = (x/100) x Q.
What is the percentage increase or decrease formula?
Percentage change = (change in value / original value) x 100.
If a value increases by x% then decreases by x%, what is the net effect?
A net decrease of (x squared)/100 percent (never returns to the original).
Define profit and loss in terms of cost price (CP) and selling price (SP).
Profit = SP - CP when SP > CP; Loss = CP - SP when CP > SP.
What are the formulas for profit percent and loss percent?
Profit% = (Profit/CP) x 100; Loss% = (Loss/CP) x 100. Both are calculated on the cost price.
Show the other 31 Quantitative flashcards
What is discount, and on what value is it calculated?
Discount is a reduction on the marked price (MP). Discount = MP - SP, and Discount% = (Discount/MP) x 100, calculated on the marked price.
How are marked price, discount and selling price related?
SP = MP x (1 - discount%/100), i.e. SP = MP - Discount.
What is the formula for the average of n quantities?
Average = (sum of all quantities) / (number of quantities).
State the basic relationship between speed, distance and time.
Speed = Distance / Time; so Distance = Speed x Time and Time = Distance / Speed.
How do you convert speed from km/h to m/s?
Multiply by 5/18 (since 1 km/h = 1000 m / 3600 s = 5/18 m/s).
What is the formula for average speed over a whole journey?
Average speed = Total distance / Total time (not the simple mean of the speeds).
For two equal distances covered at speeds x and y, what is the average speed?
Average speed = 2xy / (x + y) (the harmonic mean).
What is a linear equation in one variable, and how many solutions does it have?
An equation of the form ax + b = 0 (a not 0); the degree is 1 and it has exactly one solution, x = -b/a.
What does the slope-intercept form y = mx + c tell you?
m is the slope (gradient) of the line and c is the y-intercept (where the line crosses the y-axis).
What is the formula for the slope of a line through points (x1,y1) and (x2,y2)?
Slope m = (y2 - y1) / (x2 - x1).
When does a system of two linear equations have a unique solution, no solution, or infinitely many?
Unique: a1/a2 not equal to b1/b2 (lines intersect). No solution: a1/a2 = b1/b2 not equal to c1/c2 (parallel). Infinite: a1/a2 = b1/b2 = c1/c2 (same line).
What is the standard form of a quadratic equation?
ax squared + bx + c = 0, where a, b, c are constants and a is not 0.
State the quadratic formula.
x = (-b plus or minus the square root of (b squared - 4ac)) / (2a).
What is the discriminant of a quadratic, and what does its value indicate?
D = b squared - 4ac. If D > 0: two distinct real roots; D = 0: one repeated real root; D < 0: no real (complex) roots.
For ax squared + bx + c = 0, what are the sum and product of the roots?
Sum of roots = -b/a; Product of roots = c/a.
State the difference of squares factorization.
a squared - b squared = (a - b)(a + b).
Expand (a + b) squared and (a - b) squared.
(a + b) squared = a squared + 2ab + b squared; (a - b) squared = a squared - 2ab + b squared.
What is the factorization of a cubed + b cubed?
a cubed + b cubed = (a + b)(a squared - ab + b squared).
What is the factorization of a cubed - b cubed?
a cubed - b cubed = (a - b)(a squared + ab + b squared).
What is a polynomial, and how is its degree defined?
An algebraic expression of terms with non-negative integer powers of variables; its degree is the highest power of the variable present.
What happens to an inequality when you multiply or divide both sides by a negative number?
The direction of the inequality sign reverses (e.g. -2x < 6 becomes x > -3).
What is the difference between a strict inequality and a non-strict inequality?
Strict (< or >) excludes the boundary value; non-strict (less-than-or-equal or greater-than-or-equal) includes the boundary value.
What does |x| < a (a > 0) mean as a compound inequality?
It means -a < x < a (x lies between -a and a).
What is a complementary pair of angles and a supplementary pair?
Complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees.
What are vertically opposite angles, and what is their key property?
The pairs of opposite angles formed when two lines intersect; vertically opposite angles are always equal.
When a transversal cuts two parallel lines, what is true of alternate interior angles and corresponding angles?
Alternate interior angles are equal, and corresponding angles are equal.
What is the sum of the interior angles of a triangle?
180 degrees.
State the Pythagorean theorem.
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c squared = a squared + b squared.
What is the formula for the sum of interior angles of a polygon with n sides?
Sum of interior angles = (n - 2) x 180 degrees.
What are the formulas for the area and circumference of a circle of radius r?
Area = pi x r squared; Circumference = 2 x pi x r.
What is the relationship between an inscribed angle and the central angle subtending the same arc?
The inscribed angle is half the central angle subtending the same arc.
Air University Entry Test Quantitative FAQ
What is in the Air University Entry Test Quantitative syllabus?
Air University Entry Test Quantitative is split into 4 chapters: Arithmetic, Algebra, Geometry and Data Interpretation. Together they contain 17 topics.
How many chapters are in Air University Entry Test Quantitative?
4 chapters, containing 17 topics. The largest chapter is Arithmetic, with 5 topics.
Are there flashcards for Air University Entry Test Quantitative?
Yes — a 51-card Quantitative deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.