Exercises for Question Type 3: Finding points of intersection of two different functions

Question 1

Skill question

Determine the points where the circle $x^{2} + y^{2} = 25$ meets the line $y = x + 1$ .

[6]

Question 2

Skill question

Find the intersection points of $y = 2 x^{2} + x$ and $y = 3 x + 4$ .

[6]

Question 3

Skill question

Determine where the curves $y = x^{2} - 4$ and $y = 4 x + 2$ intersect.

[6]

Question 4

Skill question

Find the intersection of the circle $x^{2} + y^{2} = 9$ and the line $y = 2 x - 3$ .

[5]

Question 5

Skill question

Find the values of $x$ in the interval $0 \leq x \leq 2 π$ for which the graph of $y = sin x$ intersects the line $y = \frac{1}{2}$ .

[3]

Question 6

Skill question

Determine the intersection points of $y = x^{2} - 4$ and $y = 3 x$ .

[5]

Question 7

Skill question

Solve for the intersection of $y = ∣ x ∣$ and $y = x - 2$ .

[5]

Question 8

Skill question

Find all intersection points of $y = ∣ x - 1∣$ and $y = x + 2$ .

[5]

Question 9

Skill question

Find the coordinates of the intersection point of the graphs of $y = x^{3}$ and $y = x^{2} + 2$ .

[3]

Question 10

Skill question

Determine where the parabola $y = 3 x - x^{2}$ intersects the horizontal line $y = 2$ .

[4]

Question 11

Skill question

Find the points of intersection of the functions $y = 2 x + 3$ and $y = x^{2} - 1$ .

[5]

Question 12

Skill question

Find all intersection points of $y = ln x$ and $y = x - 1$ .

[5]

IB Mathematics Applications & Interpretation Question Type 3: Finding Points of Intersection of Two Different Functions Exercises