Exercises for Question Type 3: Converting between different forms

Question 1

Skill question

Convert the Cartesian equation of the line $3 x + 4 y = 12$ into parametric form $x = x_{0} + a t$ , $y = y_{0} + b t$ .

[3]

Question 2

Skill question

Convert the equation $2 x - 5 y + 10 = 0$ to slope-intercept form $y = m x + c$ .

[2]

Question 3

Skill question

Convert the factorised form $y = (x + 1) (x - 4)$ into standard form $y = a x^{2} + b x + c$ .

[2]

Question 4

Skill question

Convert the quadratic $y = 2 x^{2} - 8 x + 5$ into vertex form $y = a (x - h)^{2} + k$ .

[3]

Question 5

Skill question

Convert the equation $y = 3 x + 7$ to standard form $A x + B y + C = 0$ .

[2]

Question 6

Skill question

Convert the vertex-form quadratic $y = 3 (x - 2)^{2} + 4$ into standard form $y = a x^{2} + b x + c$ .

[2]

Question 7

Skill question

Convert the circle $x^{2} + y^{2} - 4 x + 6 y - 12 = 0$ into centre-radius form $(x - h)^{2} + (y - k)^{2} = r^{2}$ .

[3]

Question 8

Skill question

Factorise the quadratic $y = x^{2} - 6 x + 8$ into the form $y = (x - p) (x - q)$ .

[2]

Question 9

Skill question

Express the equation of the circle $(x - 3)^{2} + (y + 2)^{2} = 25$ in the form $x^{2} + y^{2} + D x + E y + F = 0$ .

[3]

Question 10

Skill question

Convert the parametric line $x = 2 t + 1$ , $y = - 3 t + 4$ into a single Cartesian equation in $x$ and $y$ .

[4]

Question 11

Skill question

Express $lo g_{2} (16) = x$ in exponential form and find $x$ .

[2]

IB Mathematics Analysis and Approaches Question Type 3: Converting Between Different Forms Exercises