IB Math Studies Yr 1

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4-9 Linear Functions Test Review

Unit 4 Linear Functions Test Review Directions: Complete each question to the best of your ability. You may use your notes. Be sure to clearly mark your

answers and work. Unless otherwise stated leave all answers as exact or rounded to 3 significant figures.

To receive full credit, you must complete the following:

Show all of your work Check your work using the answer key. Show evidence of checking your work

(correct any mistakes IN A DIFFERENT COLOR)

1. In the diagram, the lines L1 and L2 are parallel.

(a) What is the gradient of L1?

(c) Write down the equation of L2 in the form ax + by + c = 0.

x

y

L

L

1

2

6

4

2

–2

–4

–6

–6 –4 –2 0 2 4 6

IB Math Studies Yr 1

2. The straight line, 𝐿1, has equation 𝑦 = −0.5𝑥 − 2.

(a) Write down the y intercept of 𝐿1.

(b) Write down the gradient of 𝐿1.

The line 𝐿2 is perpendicular to 𝐿1 and passes through the point (3, 7).

(c) Write down the gradient of line 𝐿2.

(d) Find the equation of 𝐿2. Give your answer in the form 𝑎𝑥 + 𝑏𝑦 + 𝑑 = 0 where a, b, and d are all integers.

3. The gradients of several lines are as follows:

Line a b c d e f g h

Gradient −2 −1.2 1.5 5

−6

1

2

5

6

3

2 −4

2

(a) Find two pairs of lines that are parallel to each other.

(b) Find any two pairs of lines that are perpendicular to each other.

IB Math Studies Yr 1

4. The following diagram shows a straight line l.

(a) Find the equation of the line l.

The line n is parallel to l and passes through the point (0, 8).

(b) Write down the equation of the line n.

(c) The line n crosses the horizontal axis at the point P. Find the coordinates of P.

10

8

6

4

2

0

0 1 2 3 4 5 6x

y l

IB Math Studies Yr 1

5. The lines L1 and L2 are shown on the set of axes below.

Diagram not drawn to scale

The coordinates of A and C are (7, 4) and (3, 0), respectively.

M is the midpoint of the line segment [AC].

(a) Write down the coordinates of M.

The line L1 passes through the point M and the point B (0, 4).

(b) Write down the equation of L1.

(c) Find the length of each line segment below. Round each to three significant figures.

(i) MC;

(ii) AB.

IB Math Studies Yr 1

6. The following diagram shows the lines l1 and l2, which are perpendicular to each other.

Diagram not to scale

(a) Calculate the gradient of line 𝑙2.

(b) Write the equation of line 𝑙2 in the form ax + by + d = 0 where a, b and d are integers, and a > 0.