In this document goes over the one of eighty topics you need to go over in maths this will help give you a better understanding of the topic you are working on in maths. I believe it will help you become a master in areas of maths where you were struggling. In this document it goes over linear func...
𝑦 is a linear function of 𝑥 if it can be expressed in the form 𝑦 = 𝑚𝑥 + 𝑐.
The graph of 𝑦 against 𝑥 is then a straight line, where 𝑚 is the gradient of the
line and 𝑐 is the value of 𝑦 when 𝑥 is zero and is the intercept on the 𝑦-axis.
A straight line of gradient 𝑚 passing through the point (𝑥! , 𝑦! ) has equation
𝑦 − 𝑦! = 𝑚(𝑥 − 𝑥! )
Lines that are parallel have the same gradient.
Two lines with gradients 𝑚! and 𝑚" are perpendicular if
𝑚! 𝑚" = −1
The mid-point of (𝑥! , 𝑦! ) and (𝑥" , 𝑦" ) is
𝑥! + 𝑥" 𝑦! + 𝑦"
, , .
2 2
The perpendicular bisector of two points 𝐴 and 𝐵 is the line that passes
through the midpoint of 𝐴 and 𝐵 and is perpendicular to 𝐴𝐵.
To determine where a line crosses the 𝑥-axis, substitute 𝑦 = 0 and solve the
resulting equation. To determine where a line crosses the 𝑦-axis, substitute
𝑥 = 0 and solve the resulting equation.
,A-Level Maths Key Assignment 01 Linear Functions
DAY ONE
1. Find the equation of the straight line passing through these points, in the
form 𝑦 = 𝑚𝑥 + 𝑐:
a. (0,3) and (2,7)
b. (1,4) and (2,6)
c. (5,4) and (10,19)
d. (1, −5) and (−4,0)
e. (1,2) and (−2,1)
f. (−3, −2) and (−1,2)
2. Determine the gradient of each of the following straight lines:
a. 𝑦 = 6𝑥 − 9
b. 𝑦 = 5 − 3𝑥
#$%&
c. 𝑦 =
"
d. 2𝑦 + 4𝑥 = 7
3. Rearrange the equation 12𝑥 − 9𝑦 = 11 into the form 𝑦 = 𝑚𝑥 + 𝑐, where
𝑚 and 𝑐 are rational numbers.
4. Which…
a. …of these lines are parallel to the line 𝑦 = 4𝑥 − 2?
i. 𝑦 = 2 − 4𝑥
ii. 𝑦 = 4𝑥 + 8
iii. 4𝑥 + 𝑦 + 6 = 0
iv. −8𝑥 + 2𝑦 − 7 = 0
b. …of these lines are parallel to the line 2𝑥 + 3𝑦 − 4 = 0?
i. 3𝑥 − 2𝑦 + 1 = 0
"
ii. 𝑦 = 𝑥 + 6
'
iii. 4𝑥 + 6𝑦 + 3 = 0
"
iv. 𝑦 = − 𝑥
'
, A-Level Maths Key Assignment 01 Linear Functions
5. Give the mid-point of each of these pairs of points.
a. (4,4) and (6,10)
b. (3,1) and (7,8)
c. (2,5) and (9,1)
d. (4, −2) and (8,4)
e. (−1,3) and (3, −1)
f. (−4,5) and (−1, −2)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller MRMath. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.86. You're not tied to anything after your purchase.
