DP IB Maths: AA SL

Topic Questions

2.1 Linear Functions & Graphs

1a
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3 marks

The equation of a line l subscript 1 is 2 x minus y plus 6 equals 0.

For the line l subscript 1 find:

(i)
the y-intercept

(ii)
the x-intercept

(iii)
the gradient.
1b
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3 marks

A new line, l subscript 2 comma intersects the x-axis at (4, 0) and is perpendicular to l subscript 1.

Find:

(i)
the gradient of the line l subscript 2

(ii)
the equation of the line l subscript 2 Give your answer in the form a x plus b y plus d equals 0, where a comma space b and d are integers.

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2a
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2 marks

The coordinates of point A are open parentheses 2 comma space 8 close parentheses and the coordinates of point B are open parentheses negative 8 comma space 2 close parenthesesM is the midpoint of open square brackets A B close square brackets.

Find the coordinates of M.

2b
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2 marks

The line l subscript 1passes through A and B.

Find the gradient of l subscript 1.

2c
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3 marks

Find the equation of the line l subscript 1. Give your answer in the form a x plus b y plus d equals 0, where a comma space b and d are integers.

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3a
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2 marks

The coordinates of point A are open parentheses 1 comma space 7 close parentheses and the coordinates of point B are open parentheses 5 comma space 5 close parentheses. M is the midpoint of open square brackets A B close square brackets.

Find the coordinates of M.

3b
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2 marks

The line l subscript 1 passes through the points A and B.

Find the equation of l subscript 1. Give your answer in the form of space y equals m x plus c.

3c
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3 marks

A new line, l subscript 2, is the perpendicular bisector to l subscript 1.

Find the equation of l subscript 2. Give your answer in the form of y equals m x plus c.

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4a
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2 marks

Plumber A charges a fixed fee of $25 plus $15 per hour.

Using t for the number of hours a job takes, and C subscript A for the total cost of a job, in dollars, from Plumber A, write down an equation connecting t and C subscript A.

4b
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2 marks

A job takes the plumber seven hours.

Calculate the total cost of the job.

4c
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2 marks

Plumber B charges a fixed fee of $20 plus $16 per hour.

Using t for the number of hours a job takes, and C subscript B for the total cost of a job, in dollars, from Plumber B, write down an equation connecting t and C subscript B.

4d
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3 marks

Determine which plumber would be the cheapest for a job taking six hours.

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5a
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2 marks

The diagram below shows the line l subscript 1, which intersects the y-axis at Aopen parentheses 0 comma 10 close parentheses  and the x-axis at Bopen parentheses 5 comma 0 close parentheses.

q5-2-1-medium-linear-functions-and-graphs

Find the equation of l subscript 1. end subscript Give your answer in the form of y equals m x plus c.

5b
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2 marks

Find the length of [AB].

5c
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2 marks

A second line, l subscript 2 is parallel to l subscript 1 and intersects the x-axis at Copen parentheses 8 comma 0 close parentheses.

Find the equation of l subscript 2 Give your answer in the form a x plus b y plus d equals 0, where a comma space b and d are integers.

5d
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1 mark

Find the coordinates where l2  intersects the y-axis.

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6a
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4 marks

Photocopy shop A charges $122 for 115 copies, and $190 for 200 copies.

Assuming a linear relationship, find

(i)
the price for 180 copies

(ii)
how many copies could be made for $385.20.
6b
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3 marks

Photocopy shop B charges $0.82 per copy and a fixed fee of $25.50.

State which photocopy shop is cheaper to make 220 copies.

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7a
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2 marks

A family can be supplied with electricity by two companies that have different pricing structures:

                      Company A: Fixed fee of $25/month and $0.2 per kWh consumed.

                      Company B: Fixed fee of $10/month and $0.22 per kWh consumed.

Determine the equation of the cost function for both companies, where the total monthly cost y is a function of the monthly electricity consumption x in kWh.

7b
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4 marks

Calculate the monthly energy consumption that results in the same monthly cost from both companies.

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8a
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2 marks

Ardie’s monthly expenditure, C space open parentheses x close parentheses comma is a linear function of his monthly income, x. Ardie’s monthly expenditure is $1000 when his monthly income is $1200 and his monthly expenditure increases by $60 for every $150 increase in his monthly income.

Write an expression connecting Ardie’s monthly expenditure, C space open parentheses x close parentheses comma with his monthly income, x.

8b
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2 marks

Calculate Ardie’s monthly expenditure when his monthly income is $1885. Give your answer to the nearest dollar.

8c
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2 marks

Find Ardie’s monthly income when his monthly expenditure is $1070. Give your answer to the nearest dollar.

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9a
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1 mark

The diagram below represents a mountain with a west facing slope and an east facing slope labelled W and E respectively.

Horizontal scale: 1 unit represents 100 m.

Vertical scale: 1 unit represents 100 m.

q9-2-1-medium-linear-functions-and-graphs

Find the gradient of the west facing slope.

9b
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6 marks

The gradient of the east facing slope in the diagram is  negative 3 over 10.

Find the total distance to hike over the mountain in km.

9c
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1 mark

Suggest a reason as to why the actual total distance hiked may be greater than the distance found in part (b).

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10a
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4 marks

The straight lines l subscript 1 and l subscript 2 are shown in the diagram below l subscript 1 intercepts the x-axis at open parentheses 17 comma space 0 close parentheses and the y-axis at open parentheses 0 comma 17 close parentheses and l subscript 2  intercepts the x-axis at open parentheses 2 comma space 0 close parentheses and the y-axis at open parentheses 0 comma space minus 1 close parentheses.

q10-2-1-medium-linear-functions-and-graphs

Giving your answer in the form y equals m x plus c, find:

(i)
the equation of l subscript 1

(ii)
the equation of l subscript 2.
10b
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4 marks

Find the area of the shaded region.

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11a
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3 marks

A line passing through the origin O, is perpendicular to a line with equation x thin space plus space y space equals space 16.
The two lines meet at point RP is a point such that OP : PR = 3 : 1.

Find the equation of the perpendicular line and hence, the co-ordinates of point R.

11b
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2 marks

Find the coordinates of P.

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