Kit Library / Mathematics / General Mathematics
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. The bites below come from this kit — swipe through them in the app.
💡 Key Idea
All numbers you know fit here.
The real number system includes all numbers on the number line. It is divided into rational and irrational numbers. Rational numbers can be written as a fraction $\frac{p}{q}$ where $q \neq 0$. Irrational numbers cannot be expressed as a simple fraction; their decimal expansions are non-terminating and non-…
↳ Every real number is either rational or irrational.
📖 Definition
Expressions with many terms.
A polynomial is an expression of the form $a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0$, where $a_i$ are real numbers and $n$ is a non-negative integer. The degree is the highest power of the variable. For example, $3x^2 - 5x + 2$ has degree 2.
↳ Degree tells you the highest exponent in a polynomial.
➗ Formula
Shortcuts for expanding expressions.
↳ Memorize these identities to factor and expand quickly.
⚙️ Process
Find the point of intersection.
↳ The solution is the ordered pair $(x, y)$ that satisfies both equations.
⭐ Important Fact
Plotting points on a plane.
The Cartesian plane is divided into four quadrants by the x-axis and y-axis. A point is written as $(x, y)$. The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.
↳ Coordinates tell you exactly where a point is.
➗ Formula
Area from three sides.
↳ Use Heron's formula when you know all three sides.
📖 Definition
Relationships between angles.
↳ Angle relationships help solve geometric problems.
⚙️ Process
Same shape, same size.
Two triangles are congruent if their corresponding sides and angles are equal. Common criteria: SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle), AAS (angle-angle-side), and RHS (right angle-hypotenuse-side).
↳ Congruent triangles are identical in every way.
➗ Formula
Half base times height.
↳ This works for any triangle when you know base and height.
⭐ Important Fact
Round and round.
↳ Remember the formulas for circumference and area.
⚙️ Process
3D shapes and their measures.
For a cuboid of length $l$, breadth $b$, height $h$: surface area = $2(lb + bh + hl)$, volume = $l \times b \times h$. For a cylinder of radius $r$ and height $h$: curved surface area = $2\pi rh$, total surface area = $2\pi r(r+h)$, volume = $\pi r^2 h$.
↳ Know the formulas for common solids.
🛠️ Application
Summarizing data.
↳ These measures describe central tendency.
🚫 Warning
Don't cancel across addition.
In algebra, you cannot cancel terms that are added or subtracted. For example, $\frac{x+2}{2} \neq x+1$. You can only cancel common factors in a product.
↳ Cancel factors, not terms.
🎯 Exam Tip
Method marks matter.
In board exams, writing clear steps can earn you partial credit even if the final answer is wrong. Always show your work, especially in geometry and algebra.
↳ Step-by-step solutions maximize your score.
This kit covers essential 9th grade math topics including the real number system, polynomials, linear equations, coordinate geometry, geometry, mensuration, and statistics. It provides key formulas, definitions, and prob…
Full explanation, worked examples & memory tricks in the app
All 17 questions, laddered from warm-up to topper-level, each with its answer and the reasoning behind it.
Q1. Which of the following is an irrational number?
BeginnerC · $\sqrt{2}$
$\sqrt{2}$ cannot be expressed as a fraction of two integers, so it is irrational. The others are rational.
Q2. What is the value of $(2^3)^2$?
BeginnerB · $2^6$
Using the power of a power rule: $(a^m)^n = a^{m \times n}$, so $(2^3)^2 = 2^{3 \times 2} = 2^6$.
Q3. The point $(0, -4)$ lies on which axis?
BeginnerB · y-axis
A point with x-coordinate 0 lies on the y-axis. Here, $(0, -4)$ is on the negative y-axis.
Q4. Which of the following is a linear equation in two variables?
BeginnerC · $2x + 3y = 6$
A linear equation in two variables has the form $ax + by + c = 0$ where $a$ and $b$ are not both zero. $2x + 3y = 6$ fits this form.
Q5. What is the area of a triangle with base $8$ cm and height $5$ cm?
BeginnerD · $20$ cm$^2$
Area of a triangle = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 5 = 20$ cm$^2$.
Q6. The mean of the numbers $2, 4, 6, 8, 10$ is:
BeginnerB · $6$
Mean = $\frac{2+4+6+8+10}{5} = \frac{30}{5} = 6$.
Q7. The value of $(x + y)^2$ is:
BeginnerB · $x^2 + 2xy + y^2$
Using the identity: $(x + y)^2 = x^2 + 2xy + y^2$.
Q8. What is the probability of getting a head when a fair coin is tossed once?
BeginnerC · $\frac{1}{2}$
A fair coin has two equally likely outcomes: head or tail. So, probability of head = $\frac{1}{2}$.
Q9. The sum of the angles of a quadrilateral is:
BeginnerC · $360^\circ$
The sum of interior angles of a quadrilateral is always $360^\circ$.
Q10. Every integer is a rational number.
BeginnerA · True
Any integer $n$ can be written as $\frac{n}{1}$, so it is rational.
Q11. The degree of a non-zero constant polynomial is 1.
BeginnerB · False
The degree of a non-zero constant polynomial is 0, not 1.
Q12. If $p(x) = 2x^2 - 3x + 1$, what is $p(2)$?
IntermediateD · $3$
Substitute $x=2$: $p(2) = 2(2)^2 - 3(2) + 1 = 8 - 6 + 1 = 3$.
Q13. In triangle $ABC$, if $AB = AC$, then which angles are equal?
IntermediateD · $\angle B = \angle C$
In an isosceles triangle, angles opposite equal sides are equal. Since $AB = AC$, the angles opposite them, $\angle C$ and $\angle B$, are equal.
Q14. Which of the following is a polynomial?
IntermediateB · $x^2 + 2x + 1$
A polynomial has non-negative integer exponents. $x^2 + 2x + 1$ is a polynomial; the others involve division by a variable or fractional exponents.
Q15. If two lines are parallel, their slopes are:
IntermediateB · Equal
Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals.
Q16. Which of the following is a quadratic polynomial?
IntermediateC · $x^2 - 5x + 6$
A quadratic polynomial has degree 2. $x^2 - 5x + 6$ has degree 2.
Q17. If $a > b$ and $b > c$, then which is true?
IntermediateB · $a > c$
By transitivity of inequality, if $a > b$ and $b > c$, then $a > c$.
18 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Word Match
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True False
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Memory Match
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Flashcard Battle
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Speed Quiz
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Guess Term
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Sequence Builder
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Revision Battle
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