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Class IX Maths SA-1: Number Systems, Polynomials, Coordinate Geometry, Linear Equations & Lines and Angles: 20 MCQs with answers

All 20 multiple-choice questions from this kit, free and with no sign-up.

Full kit · everything Flashcards · 60 Quick Revision · 20

Warm-up · 8 questions

Q1. Which of the following is an example of an irrational number?

Beginner
A $\frac{3}{4}$ B $1.101001000\ldots$ C $0.75$ D $0.\overline{6}$
Show answer & explanation

$1.101001000\ldots$

$1.101001000\ldots$ is non-terminating and non-repeating, so it is irrational. The others are terminating or repeating decimals, hence rational.

Q2. How many rational numbers lie between $\frac{1}{5}$ and $\frac{2}{5}$?

Beginner
A Exactly two B Infinitely many C Exactly one D None
Show answer & explanation

Infinitely many

Between any two rational numbers there are infinitely many rational numbers.

Q3. What is the coefficient of $x$ in $9x^2 + 4x - 6$?

Beginner
A $2$ B $6$ C $9$ D $4$
Show answer & explanation

$4$

The coefficient of $x$ is the number multiplying $x$, which is $4$.

Q4. Which of the following is a quadratic polynomial?

Beginner
A $ax^2 + bx + c$ B $ax^{-2} + bx + c$ C $ax^3 + bx^2 + cx + d$ D $ax + b$
Show answer & explanation

$ax^2 + bx + c$

A quadratic polynomial has degree $2$, so its standard form is $ax^2 + bx + c$.

Q5. If the $y$-coordinate of a point is zero, the point always lies:

Beginner
A In Quadrant II B On the $x$-axis C On the $y$-axis D In Quadrant I
Show answer & explanation

On the $x$-axis

A point with $y = 0$ lies on the $x$-axis.

Q6. What is the standard form of a linear equation in two variables $x$ and $y$?

Beginner
A $ax - by - c = 0$ B $ax + by = c$ C $ax + by = 0$ D $ax + by + c = 0$
Show answer & explanation

$ax + by + c = 0$

The standard form is $ax + by + c = 0$.

Q7. A ray that divides an angle into two equal angles is called:

Beginner
A Angular bisector B Perpendicular bisector C Transversal D Vertex
Show answer & explanation

Angular bisector

An angular bisector divides an angle into two equal angles.

Q8. Every rational number has either a terminating or a repeating decimal expansion, while every irrational number has a non-terminating, non-repeating decimal expansion.

Beginner
A True B False
Show answer & explanation

True

Every rational number has either a terminating or a repeating decimal expansion, while every irrational number has a non-terminating, non-repeating decimal expansion.

Building up · 7 questions

Q9. Which of the following is a rational number?

Intermediate
A $\pi$ B $1.101001000100001\ldots$ C $\sqrt{23}$ D $\sqrt{225}$
Show answer & explanation

$\sqrt{225}$

$\sqrt{225} = 15$, which is rational. $\sqrt{23}$ and $1.101001000\ldots$ are irrational.

Q10. Simplify: $(3 + \sqrt{3})(2 + \sqrt{2})$

Intermediate
A $6 + \sqrt{6}$ B $6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6}$ C $6 + 3\sqrt{2} + 2\sqrt{3}$ D $5 + 3\sqrt{2} + 2\sqrt{3}$
Show answer & explanation

$6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6}$

Using distributive property: $3(2) + 3(\sqrt{2}) + \sqrt{3}(2) + \sqrt{3}(\sqrt{2}) = 6 + 3\sqrt{2} + 2\sqrt{3} + \sqrt{6}$.

Q11. Factorise: $y^2 - 5y + 6$

Intermediate
A $(y + 1)(y - 6)$ B $(y - 2)(y - 3)$ C $(y + 2)(y + 3)$ D $(y - 1)(y - 6)$
Show answer & explanation

$(y - 2)(y - 3)$

Find two numbers that multiply to $6$ and add to $-5$: $-2$ and $-3$. So $y^2 - 5y + 6 = (y-2)(y-3)$.

Q12. Find the value of $k$ if $(x - 1)$ is a factor of $P(x) = kx^2 - 3x + k$.

Intermediate
A $k = 3$ B $k = \frac{1}{2}$ C $k = \frac{3}{2}$ D $k = 1$
Show answer & explanation

$k = \frac{3}{2}$

By Factor Theorem, $P(1) = 0$. So $k(1)^2 - 3(1) + k = 0 \implies 2k - 3 = 0 \implies k = \frac{3}{2}$.

Q13. In which quadrant does the point $(-4, -1)$ lie?

Intermediate
A Quadrant III B Quadrant II C Quadrant I D Quadrant IV
Show answer & explanation

Quadrant III

Both coordinates are negative, so the point lies in Quadrant III.

Q14. Express $5x + 2y = 2$ in the form $ax + by + c = 0$. What is $a + b + c$?

Intermediate
A $-5$ B $5$ C $7$ D $9$
Show answer & explanation

$5$

$5x + 2y - 2 = 0$, so $a=5$, $b=2$, $c=-2$. Then $a+b+c = 5+2-2 = 5$.

Q15. If $x = 0$, find the value of $y$ in $3x + 4y = 12$.

Intermediate
A $y = 4$ B $y = 12$ C $y = 0$ D $y = 3$
Show answer & explanation

$y = 3$

Substitute $x=0$: $4y = 12 \implies y = 3$.

Topper level · 5 questions

Q16. If $x + y + z = 0$, then $x^3 + y^3 + z^3$ equals:

Advanced
A $x^3y^3z^3$ B $xyz$ C $3xyz$ D $0$
Show answer & explanation

$3xyz$

When $x+y+z=0$, the identity $x^3+y^3+z^3-3xyz = \frac{1}{2}(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]$ reduces to $x^3+y^3+z^3 = 3xyz$.

Q17. Given the linear equation $3x + 4y = 12$, if we express it in the form $ax + by + c = 0$, what is the value of $a^2 + b^2 + c^2$?

Advanced
A 25 B 20 C 18 D 16
Show answer & explanation

16

Rearranging $3x + 4y = 12$ gives $3x + 4y - 12 = 0$. Here, $a = 3$, $b = 4$, and $c = -12$. Thus, $a^2 + b^2 + c^2 = 3^2 + 4^2 + (-12)^2 = 9 + 16 + 144 = 169$.

Q18. If $x + y + z = 0$ and $x = 2$, $y = -3$, what is the value of $z^3$?

Advanced
A 8 B -27 C 27 D 0
Show answer & explanation

-27

From $x + y + z = 0$, substituting $x = 2$ and $y = -3$ gives $2 - 3 + z = 0$, leading to $z = 1$. Thus, $z^3 = 1^3 = 1$.

Q19. In a coordinate plane, if the point $A(-4, -6)$ is reflected across the y-axis, what are the coordinates of the reflected point?

Advanced
A (4, -6) B (4, 6) C (-4, 6) D (-6, -4)
Show answer & explanation

(4, -6)

Reflecting across the y-axis changes the sign of the x-coordinate. Therefore, the coordinates of point $A(-4, -6)$ become $(4, -6)$.

Q20. If the angles $\angle AOC$ and $\angle BOC$ are given as $(3x + 10)^\circ$ and $(4x - 26)^\circ$ respectively, what is the value of $x$ if these angles form a linear pair?

Advanced
A 14 B 20 C 18 D 28
Show answer & explanation

28

Since $\angle AOC + \angle BOC = 180^\circ$, we have $3x + 10 + 4x - 26 = 180$. Simplifying gives $7x - 16 = 180$, leading to $7x = 196$, thus $x = 28$.

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