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Class 8 & 9 Mathematics Foundations: Algebra, Geometry, Probability & Proportional Reasoning: 16 MCQs with answers

All 16 multiple-choice questions from this kit, free and with no sign-up.

Full kit · everything Flashcards · 20 Quick Revision · 15

Warm-up · 7 questions

Q1. A point on the Cartesian plane is written as an ordered pair. Which of the following correctly represents the point with x-coordinate 4 and y-coordinate $-3$?

Beginner
A $(-4, 3)$
B $(3, -4)$
C $(-3, 4)$
D $(4, -3)$
Show the answer

D · $(4, -3)$

An ordered pair is written as $(x, y)$, so x = 4 and y = -3 gives $(4, -3)$. Swapping the numbers gives a different point.

Q2. In which quadrant does the point $(-5, 2)$ lie?

Beginner
A Quadrant III
B Quadrant I
C Quadrant IV
D Quadrant II
Show the answer

D · Quadrant II

The signs are $(-, +)$, which matches Quadrant II (top-left).

Q3. What are the coordinates of the origin?

Beginner
A $(1, 1)$
B $(1, 0)$
C $(0, 1)$
D $(0, 0)$
Show the answer

D · $(0, 0)$

The origin is where the x-axis and y-axis meet, at $(0, 0)$.

Q4. A point lies on the y-axis. Which statement must be true?

Beginner
A It lies in Quadrant I.
B Its x-coordinate is 0.
C Its y-coordinate is 0.
D Both coordinates are positive.
Show the answer

B · Its x-coordinate is 0.

Any point on the y-axis has not moved horizontally, so its x-coordinate is 0.

Q5. To plot $(2, -5)$, you start at the origin. What is the correct sequence of moves?

Beginner
A 5 up, then 2 right
B 5 down, then 2 right
C 2 right, then 5 down
D 2 left, then 5 up
Show the answer

C · 2 right, then 5 down

Always move along the x-axis first (2 right), then parallel to the y-axis (5 down).

Q6. Which of these points lies in Quadrant III?

Beginner
A $(-3, 4)$
B $(3, -4)$
C $(3, 4)$
D $(-3, -4)$
Show the answer

D · $(-3, -4)$

Quadrant III has sign pattern $(-,-)$, so $(-3, -4)$ is correct.

Q7. The distance formula $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ is derived directly from the Pythagorean theorem.

Beginner
A True
B False
Show the answer

A · True

The distance formula $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ is derived directly from the Pythagorean theorem.

Building up · 6 questions

Q8. A student plots the point $(0, 6)$ and labels it as lying in Quadrant I. What is the error?

Intermediate
A The point actually lies in Quadrant II.
B Points on an axis belong to no quadrant.
C There is no error; $(0,6)$ is in Quadrant I.
D The point should be $(6, 0)$ instead.
Show the answer

B · Points on an axis belong to no quadrant.

Since the x-coordinate is 0, the point lies on the y-axis, and axis points belong to no quadrant.

Q9. Find the distance between $A(1, 2)$ and $B(4, 6)$.

Intermediate
A $3$
B $5$
C $4$
D $7$
Show the answer

B · $5$

Horizontal gap = 3, vertical gap = 4, so distance = $\sqrt{3^2+4^2} = \sqrt{25} = 5$.

Q10. Find the midpoint of the segment joining $A(1, 2)$ and $B(4, 6)$.

Intermediate
A $(3, 4)$
B $(5, 8)$
C $(2, 3)$
D $(2.5, 4)$
Show the answer

D · $(2.5, 4)$

Midpoint = $\left(\frac{1+4}{2}, \frac{2+6}{2}\right) = (2.5, 4)$.

Q11. Which statement explains why the distance formula uses squares of the differences?

Intermediate
A So the distance is always positive and rational.
B So the answer is always a perfect square.
C So the order of subtraction does not affect the result.
D So the formula works only in Quadrant I.
Show the answer

C · So the order of subtraction does not affect the result.

Squaring removes the sign, making $(x_2-x_1)^2 = (x_1-x_2)^2$; hence distance from A to B equals distance from B to A.

Q12. A point has a negative x-coordinate and a positive y-coordinate. Which quadrant is it in, and what does that mean visually?

Intermediate
A Quadrant I; it is up and to the right of the origin.
B Quadrant III; it is down and to the left of the origin.
C Quadrant IV; it is down and to the right of the origin.
D Quadrant II; it is up and to the left of the origin.
Show the answer

D · Quadrant II; it is up and to the left of the origin.

Signs $(-, +)$ place the point in Quadrant II, which is up and to the left of the origin.

Q13. A student computes the distance between $(2, 3)$ and $(5, 7)$ as $\sqrt{(5-2)^2 + (7-3)}$. What mistake did they make?

Intermediate
A They subtracted in the wrong order.
B They forgot to square the second difference.
C They should have added the coordinates first.
D They used the midpoint formula instead.
Show the answer

B · They forgot to square the second difference.

The distance formula squares both differences: $\sqrt{(5-2)^2 + (7-3)^2}$. Only the first difference was squared here.

Topper level · 3 questions

Q14. Assertion (A): The points $(3, 5)$ and $(5, 3)$ are different points on the Cartesian plane. Reason (R): In an ordered pair, the order of the coordinates matters.

Advanced
A Both A and R are true, and R correctly explains A.
B A is false but R is true.
C A is true but R is false.
D Both A and R are true, but R does not explain A.
Show the answer

A · Both A and R are true, and R correctly explains A.

Because the pair is ordered, swapping coordinates gives a different location; R is exactly the reason A holds.

Q15. Consider the statements: I. $(0, 4)$ lies on the y-axis. II. $(0, 4)$ lies in Quadrant I. III. $(0, 4)$ belongs to no quadrant. Which combination is correct?

Advanced
A I, II and III
B II and III only
C I and III only
D I and II only
Show the answer

C · I and III only

Since x = 0, the point is on the y-axis (I true) and therefore belongs to no quadrant (III true); II is false.

Q16. Points $P(-2, 3)$ and $Q(4, 3)$ are given. A student claims the midpoint is $(1, 3)$. Which reasoning best justifies this?

Advanced
A The midpoint must lie in Quadrant I because both x-values differ.
B Averaging x-coordinates gives 1 and y-coordinates stay 3.
C The distance between P and Q is 6, so the midpoint is $(1,3)$.
D The signs cancel, so the midpoint is the origin.
Show the answer

B · Averaging x-coordinates gives 1 and y-coordinates stay 3.

Midpoint = $\left(\frac{-2+4}{2}, \frac{3+3}{2}\right) = (1, 3)$; averaging each coordinate is the correct reasoning.

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