IB Mathematics Applications & Interpretation Topic SL 2.1—equations of a Line Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic SL 2.1—equations of a Line Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic SL 2.1—equations of a Line with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 2.1—equations of a Line and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SL & HLPaper 1

The line $L_{1}$ has equation $y = 2 x - 5$ and the line $L_{2}$ has equation $x + y = 4$ .

The line $L_{3}$ passes through $P$ and is perpendicular to $L_{1}$ .

Find the coordinates of $P$ , the point of intersection of $L_{1}$ and $L_{2}$ .

[3]

Write down the gradient of $L_{3}$ .

[1]

Find the equation of $L_{3}$ , giving your answer in the form $y = m x + c$ .

[3]

Question 2

SL & HLPaper 1

The line $L_{1}$ has equation $4 x - 3 y + 12 = 0$ .

The line $L_{2}$ is parallel to $L_{1}$ and passes through the point $P (6, - 1)$ .

Write the equation of $L_{1}$ in the form $y = m x + c$ .

[2]

Write down the gradient and the $y$ -intercept of $L_{1}$ .

[2]

Find the equation of $L_{2}$ , giving your answer in the form $a x + b y + d = 0$ , where $a$ , $b$ , $d \in Z$ .

[2]

Question 3

SLPaper 1

The straight line passing through the points $(- 3, 2)$ and $(1, - 6)$ intersects the line $x - y = 1$ at the point $P$ . Find the coordinates of $P$ .

[5]

Question 4

SL & HLPaper 1

The points $A$ and $B$ have coordinates $A (- 3, 5)$ and $B (7, - 1)$ .

Find the coordinates of $M$ , the midpoint of $[A B]$ .

[2]

Find the gradient of the line through $A$ and $B$ .

[2]

Find the equation of the line through $A$ and $B$ , giving your answer in the form $y = m x + c$ .

[2]

Question 5

SL & HLPaper 2

The line $L_{1}$ has equation $y = x + 1$ and the point $A$ has coordinates $A (2, 3)$ .

The point $C$ has coordinates $C (6, - 5)$ . The midpoint of $[A C]$ is $M$ .

The line $L_{2}$ is perpendicular to $[A C]$ and passes through $M$ .

The point $D$ is the intersection of $L_{1}$ and $L_{2}$ .

The point $B$ is such that $A B C D$ is a rhombus.

Show that $A$ lies on $L_{1}$ .

[2]

Find the coordinates of $M$ .

[2]

Find the length of $[A C]$ . Give your answer in the form $p q$ , where $p$ , $q \in Z^{+}$ .

[2]

Show that the equation of $L_{2}$ is $y = \frac{1}{2} x - 3$ .

[4]

Find the coordinates of $D$ .

[2]

Find the area of the rhombus $A B C D$ .

[2]

IB Mathematics Applications & Interpretation SL 2.1—equations of a Line Questionbank

IB Mathematics Applications & Interpretation SL 2.1—equations of a Line Questionbank

Unlock all 16 questions with a free account

IB Mathematics Applications & Interpretation SL 2.1—equations of a Line Questionbank

IB Mathematics Applications & Interpretation SL 2.1—equations of a Line Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 2.1—equations of a Line Questionbank

Unlock all 16 questions with a free account