IB Mathematics Analysis and Approaches Topic SL 2.1—equations of Straight Lines, Parallel and Perpendicular Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 2.1—equations of Straight Lines, Parallel and Perpendicular Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 2.1—equations of Straight Lines, Parallel and Perpendicular 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 Straight Lines, Parallel and Perpendicular and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

A line through $A (- 4, 3)$ with gradient $m$ intersects $C:\ y=x^2+8x$ at points $P$ and $Q$ . The distance $P Q = 11$ .

Show the $x$ -coordinates satisfy $x^2+(8-m)x+(-4m-3)=0.$

[4]

Determine the condition on $m$ for two distinct intersections.

[2]

Show $(x_{P} - x_{Q})^{2} = m^{2} + 76$ .

[3]

Solve for $m$ using $P Q = 11$ .

[4]

Question 2

SLPaper 1

The points $A (3, 2), B (7, 2)$ , and $C (3, 8)$ are shown in the diagram below.

Find the equation of the perpendicular bisector of the line segment $[A B]$ .

[2]

Find the equation of the perpendicular bisector of the line segment $[A C]$ .

[2]

Write down the coordinates of the point of intersection $P$ of the two bisectors, and show that $P$ is the midpoint of the line segment $[B C]$ .

[3]

Find the equation of the perpendicular bisector $L$ of the line segment $[B C]$ , in the form $a x + b y + d = 0$ , where $a, b, d \in Z$ .

[3]

Show that the line $L$ does not pass through point $A$ .

[2]

Question 3

SLPaper 2

A line $L$ passes through $A (1, 4)$ with gradient $m$ . It meets the parabola $C:\ y=x^2-2x-3$ at two points $P, Q$ . The distance $P Q = 6$ .

Show that the $x$ -coordinates of $P, Q$ satisfy $x^2-(m+2)x+(m-7)=0.$

[4]

State the condition on $m$ for two distinct intersections.

[2]

Show that $(x_{P} - x_{Q})^{2} = m^{2} + 32$ .

[4]

Using $P Q = 6$ , form an equation in $m$ and solve.

[5]

Question 4

SLPaper 2

A line through $A (3, 1)$ with gradient $m$ meets $C:\ y=x^2-6x-2$ at $P, Q$ . The distance $P Q = 7$ .

Show that the $x$ -coordinates of $P$ and $Q$ satisfy $x^2-(m+6)x+(3m-3)=0.$

[4]

Show that the line intersects the curve at two distinct points for all real $m$ .

[2]

Show that $(x_{P} - x_{Q})^{2} = m^{2} + 48$ .

[3]

Find the value(s) of $m$ given that $P Q = 7$ .

[5]

Question 5

SLPaper 1

Let $A (- 2, 5)$ and $B (4, 9)$ be two points in the Cartesian plane.

Calculate the gradient of the line through points $A$ and $B$ .

[2]

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

[1]

Determine the equation of the line that is perpendicular to $[A B]$ and passes through point $M$ .

[2]

Calculate the distance between points $A$ and $M$ .

[2]

IB Mathematics Analysis and Approaches SL 2.1—equations of Straight Lines, Parallel and Perpendicular Questionbank

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IB Mathematics Analysis and Approaches SL 2.1—equations of Straight Lines, Parallel and Perpendicular Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 2.1—equations of Straight Lines, Parallel and Perpendicular Questionbank

Unlock all 14 questions with a free account