Class 9 Maths: Number Systems, Polynomials, Coordinate Geometry, Linear Equations, Euclid's Geometry & Lines and Angles: 38 MCQs with answers

$\sqrt{5}$

$\sqrt{5}$ cannot be written as $\frac{p}{q}$ with integers $p, q$ and $q \neq 0$, so it is irrational. The others are rational.

3

The degree is the highest power of the variable, which is $3$ here.

$7$

In $(x, y)$, $x$ is the abscissa. So the abscissa is $7$.

Complementary angles

Complementary angles sum to $90^\circ$; supplementary angles sum to $180^\circ$.

The fifth postulate

Euclid's fifth postulate deals with parallel lines and is called the parallel postulate.

True

$\sqrt{2}$ is irrational — its proof uses the method of contradiction, assuming $\sqrt{2} = \frac{p}{q}$ in lowest terms and deriving that both $p$ and $q$ must be even.

3

Natural numbers are defined as positive integers starting from 1, so 3 is a natural number.

4

The degree of a polynomial is determined by the highest power of the variable, which is 4 in this case.

Abscissa

In the ordered pair \( (x, y) \), \( x \) is known as the abscissa, while \( y \) is the ordinate.

They are always equal.

Vertically opposite angles are formed when two lines intersect and they are always equal.

2x + 3y = 6

A linear equation in two variables is of the form \( ax + by + c = 0 \), and \( 2x + 3y = 6 \) fits this form.

2

The square root of 4 is 2, since \( 2 imes 2 = 4 \).

They can be expressed as a fraction of two integers.

Rational numbers can be expressed as a fraction \( rac{p}{q} \) where \( p \) and \( q \) are integers and \( q eq 0 \).

Supplementary angles

Angles that add up to \( 180^\circ \) are called supplementary angles.

It is quadratic.

A polynomial of degree 2 is classified as a quadratic polynomial.

If a straight line falls on two straight lines, they meet on that side.

Euclid's fifth postulate states that if a straight line falls on two straight lines and makes the interior angles on the same side less than two right angles, the two lines will meet on that side.

Rational numbers

Rational numbers are defined as numbers that can be expressed in the form \( \frac{p}{q} \) where \( q \neq 0 \).

2

The degree of a polynomial is the highest power of the variable, which in this case is \(2\).

The origin

The point \((0, 0)\) is known as the origin, where the x-axis and y-axis intersect.

\( 2x + 3y = 6 \)

A linear equation in two variables is of the form \( ax + by + c = 0 \), which \( 2x + 3y = 6 \) satisfies.

Supplementary angles

Angles that sum to \( 180^\circ \) are known as supplementary angles.

Monomial

A polynomial with exactly one term is called a monomial.

They are always equal.

Vertically opposite angles are formed when two lines intersect and they are always equal.

The ordinate

In the ordered pair \((x, y)\), \( y \) represents the ordinate, while \( x \) is the abscissa.

They can be expressed as \( \frac{p}{q} \) where \( q \neq 0 \).

Rational numbers can be expressed in the form \( \frac{p}{q} \) where \( q \neq 0 \).

Degree

The highest power of a variable in a polynomial is called its degree.

$0$

$p(2) = 2^2 - 5(2) + 6 = 4 - 10 + 6 = 0$. So $x - 2$ is a factor.

Infinitely many solutions

Every point on the line satisfies the equation, so there are infinitely many solutions.

$70^\circ$

Co-interior angles are supplementary, so the other angle is $180^\circ - 110^\circ = 70^\circ$.

$2x^2 + 3x - 7$

A quadratic polynomial has degree $2$. Only $2x^2 + 3x - 7$ has degree $2$.

Quadrant II

In Quadrant II, $x$ is negative and $y$ is positive, which matches $(-4, 3)$.

$\frac{5}{9}$

$\frac{5}{9}$ is of the form $\frac{p}{q}$ with $q \neq 0$, so it is rational. The others are irrational.

$(1, 3)$

Substituting $(1, 3)$: $1 + 3 = 4$, which satisfies the equation.

$p(3) = 0$

By the Factor Theorem, $x - a$ is a factor of $p(x)$ if and only if $p(a) = 0$. Here $a = 3$.

$40$

Vertically opposite angles are equal, so $2x = 80$, giving $x = 40$.

It is always a straight line

A linear equation in two variables always graphs as a straight line.

2

To find \( a + b \), we first set up the equations from \( p(1) = 0 \) and \( p(-1) = 0 \). From \( p(1) = 2(1)^3 - 3(1)^2 + a(1) + b = 0 \), we get \( 2 - 3 + a + b = 0 \) or \( a + b = 1 \). From \( p(-1) = 2(-1)^3 - 3(-1)^2 + a(-1) + b = 0 \), we get \( -2 - 3 - a + b = 0 \) or \( b - a = 5 \). Solving these two equ…

3

For two lines to be parallel, their slopes must be equal. The slope of the first line \( 2x + 3y - 6 = 0 \) can be found by rewriting it in slope-intercept form: \( y = -rac{2}{3}x + 2 \), giving a slope of \( -rac{2}{3} \). For the second line \( 4x + ky - 12 = 0 \), rewriting gives \( y = -rac{4}{k}x + rac{12}{k}…