Package deal
EDEXCEL PUPRE MATHS EXAM PACK|GUARANTEED SUCCESS
EDEXCEL PUPRE MATHS EXAM PACK|GUARANTEED SUCCESS
[Show more]EDEXCEL PUPRE MATHS EXAM PACK|GUARANTEED SUCCESS
[Show more]Cosine Rule - Know 2 sides, and the angle in between. You want the missing side. 
a² = b² + c² - 2bcCosA 
 
 
 
Cosine Rule - Know 3 sides. You want an angle. 
Cos A = (b² + c² - a²) ÷ 2bc 
 
 
 
Sine Rule - Know 2 angles and a side. You want the missing side. 
(a ÷ SinA) = (b ÷ SinB) = (c ...
Preview 2 out of 7 pages
Add to cartCosine Rule - Know 2 sides, and the angle in between. You want the missing side. 
a² = b² + c² - 2bcCosA 
 
 
 
Cosine Rule - Know 3 sides. You want an angle. 
Cos A = (b² + c² - a²) ÷ 2bc 
 
 
 
Sine Rule - Know 2 angles and a side. You want the missing side. 
(a ÷ SinA) = (b ÷ SinB) = (c ...
Equation of a straight line 
y - y₁ = m(x - x₁) 
 
 
 
Distance between two points 
d = √(x₂ - x₁)² + (y₂ - y₁)² 
 
 
 
Integration by substitution 
∫f(x) = ∫f(x) × (dx÷du) 
 
 
 
Integration by parts 
∫u (dv÷dx) = uv - ∫v (du÷dx) 
 
 
 
Trapezium Rule 
A = ½h (y₀ + 2(...
Preview 2 out of 6 pages
Add to cartEquation of a straight line 
y - y₁ = m(x - x₁) 
 
 
 
Distance between two points 
d = √(x₂ - x₁)² + (y₂ - y₁)² 
 
 
 
Integration by substitution 
∫f(x) = ∫f(x) × (dx÷du) 
 
 
 
Integration by parts 
∫u (dv÷dx) = uv - ∫v (du÷dx) 
 
 
 
Trapezium Rule 
A = ½h (y₀ + 2(...
What are the turning point co-ordinates in f(x)=a(x+p)^2 +q 
(-p,q) 
 
 
 
How many roots are there if the discriminent > 0? 
Two distinct roots 
 
 
 
How many roots are there if the discriminent = 0? 
One/repeated root 
 
 
 
How many roots are there if the discriminent < 0? 
no real roots 
...
Preview 2 out of 5 pages
Add to cartWhat are the turning point co-ordinates in f(x)=a(x+p)^2 +q 
(-p,q) 
 
 
 
How many roots are there if the discriminent > 0? 
Two distinct roots 
 
 
 
How many roots are there if the discriminent = 0? 
One/repeated root 
 
 
 
How many roots are there if the discriminent < 0? 
no real roots 
...
fg(x) 
apply g first then f 
 
 
 
Functions f(x) and f^-1(x) 
reflections of each other in the line y = x 
 
 
 
Domain of f(x) 
Range of f^-1(x) 
 
 
 
Range of f(x) 
Domain of f^-1(x) 
 
 
 
y = |f(x)| 
reflection of y = f(x) for x>0 in the x-axis 
 
 
 
y = f(|x|) 
reflection of y = f(x) for ...
Preview 1 out of 2 pages
Add to cartfg(x) 
apply g first then f 
 
 
 
Functions f(x) and f^-1(x) 
reflections of each other in the line y = x 
 
 
 
Domain of f(x) 
Range of f^-1(x) 
 
 
 
Range of f(x) 
Domain of f^-1(x) 
 
 
 
y = |f(x)| 
reflection of y = f(x) for x>0 in the x-axis 
 
 
 
y = f(|x|) 
reflection of y = f(x) for ...
Base 
The number that is going to be raised to a power. 
 
 
 
Exponent 
The number that is used as a reference for the power 
 
 
 
Add the powers 
Multiplying numbers with powers - rule 
 
 
 
Subtract the powers 
Dividing numbers with powers - rule 
 
 
 
Multiply the powers 
Multiplying numbers ...
Preview 1 out of 2 pages
Add to cartBase 
The number that is going to be raised to a power. 
 
 
 
Exponent 
The number that is used as a reference for the power 
 
 
 
Add the powers 
Multiplying numbers with powers - rule 
 
 
 
Subtract the powers 
Dividing numbers with powers - rule 
 
 
 
Multiply the powers 
Multiplying numbers ...
Quadratic equation 
Written as ax²+bx+c=0 where a, b, c and constants. Has 0-2 solutions 
 
 
 
Roots 
- The solutions to an equation 
- The values of x for which f(x)=0 
- Find by factorising x 
 
 
 
Completing the square 
x²+bx = (x+b÷2)²-(b÷2)² 
 
 
 
Completing the square when a≠1 
- Fa...
Preview 1 out of 2 pages
Add to cartQuadratic equation 
Written as ax²+bx+c=0 where a, b, c and constants. Has 0-2 solutions 
 
 
 
Roots 
- The solutions to an equation 
- The values of x for which f(x)=0 
- Find by factorising x 
 
 
 
Completing the square 
x²+bx = (x+b÷2)²-(b÷2)² 
 
 
 
Completing the square when a≠1 
- Fa...
Natural Numbers 
The set of numbers 1, 2, 3, 4, ... Also called counting numbers. 
 
 
 
Integers 
The set of whole numbers and their opposites 
Z⁺ 
Z⁺₀ 
 
 
 
Rational Number 
set of all numbers that can be written as a fraction of two integers 
Q 
 
 
 
irrational numbers 
Numbers that can'...
Preview 4 out of 36 pages
Add to cartNatural Numbers 
The set of numbers 1, 2, 3, 4, ... Also called counting numbers. 
 
 
 
Integers 
The set of whole numbers and their opposites 
Z⁺ 
Z⁺₀ 
 
 
 
Rational Number 
set of all numbers that can be written as a fraction of two integers 
Q 
 
 
 
irrational numbers 
Numbers that can'...
Midpoint 
([x₁+x₂]÷2 , [y₁+y₂]÷2) 
 
 
 
Perpendicular bisector 
The line that passes through the midpoint of another line at 90° 
 
 
 
Finding perpendicular bisectors 
1. Find the midpoint of AB 
2. Find the gradient of AB 
3. Find the negative reciprocal of that 
4. Sub the midpoint an...
Preview 1 out of 2 pages
Add to cartMidpoint 
([x₁+x₂]÷2 , [y₁+y₂]÷2) 
 
 
 
Perpendicular bisector 
The line that passes through the midpoint of another line at 90° 
 
 
 
Finding perpendicular bisectors 
1. Find the midpoint of AB 
2. Find the gradient of AB 
3. Find the negative reciprocal of that 
4. Sub the midpoint an...
Differentiate tan(kx) 
ksec^2(kx) 
 
 
 
Differentiate cos(kx) 
-ksin(kx) 
 
 
 
Differentiate sin(kx) 
kcos(kx) 
 
 
 
Arithmetic sequence 
Un = a + (n - 1)d 
 
 
 
Arithmetic series 
Sn = n/2 (a + d) 
 
 
 
Geometric sequences 
Un = ar^n - 1 
 
 
 
Geometric series 
Sn = a(r^n - 1) / r - 1 
 
 
 
...
Preview 2 out of 6 pages
Add to cartDifferentiate tan(kx) 
ksec^2(kx) 
 
 
 
Differentiate cos(kx) 
-ksin(kx) 
 
 
 
Differentiate sin(kx) 
kcos(kx) 
 
 
 
Arithmetic sequence 
Un = a + (n - 1)d 
 
 
 
Arithmetic series 
Sn = n/2 (a + d) 
 
 
 
Geometric sequences 
Un = ar^n - 1 
 
 
 
Geometric series 
Sn = a(r^n - 1) / r - 1 
 
 
 
...
Contradiction 
A contradiction is a disagreement between two statements, which means that both cannot be true. Proof by contradiction is a powerful technique. 
 
 
 
Proof by contradiction 
To prove a statement by contradiction you start by assuming it is not true. You then use logical steps to show...
Preview 3 out of 19 pages
Add to cartContradiction 
A contradiction is a disagreement between two statements, which means that both cannot be true. Proof by contradiction is a powerful technique. 
 
 
 
Proof by contradiction 
To prove a statement by contradiction you start by assuming it is not true. You then use logical steps to show...
Cubic 
A graph where the highest exponent is 3 
 
 
 
Cubic function 
f(x) = ax³+bx²+cx+d 
 
 
 
Repeated root 
A function where at least 2 of the roots are equal. 
The turning point of the graph is on the x-axis 
E.g. y=(x-3)(x-2)² 
 
 
 
Point of inflection 
A function where all the roots are e...
Preview 1 out of 3 pages
Add to cartCubic 
A graph where the highest exponent is 3 
 
 
 
Cubic function 
f(x) = ax³+bx²+cx+d 
 
 
 
Repeated root 
A function where at least 2 of the roots are equal. 
The turning point of the graph is on the x-axis 
E.g. y=(x-3)(x-2)² 
 
 
 
Point of inflection 
A function where all the roots are e...
Study 
 
AS-level Edexcel Pure Maths - Module 5: Straight line graphs 
 
Share 
In-class activity 
Classic Live 
Checkpoint 
Self-study activity 
Flashcards 
Learn 
Test 
Match 
Profile Picture 
Created by 
Badman892 
Teacher 
 
 
Terms in this set (13) 
 
Original
Preview 1 out of 2 pages
Add to cartStudy 
 
AS-level Edexcel Pure Maths - Module 5: Straight line graphs 
 
Share 
In-class activity 
Classic Live 
Checkpoint 
Self-study activity 
Flashcards 
Learn 
Test 
Match 
Profile Picture 
Created by 
Badman892 
Teacher 
 
 
Terms in this set (13) 
 
Original
Gradient of a line 
(y₂-y₁) ÷ (x₂-x₁) 
 
 
 
Distance between 2 points 
Use pythagoras' theorem 
√[(∆x)²+(∆y)² 
 
 
 
Parallel lines 
- Gradient is equal 
- Y-intercept is different 
 
 
 
Perpendicular lines 
- Gradients multiply to make -1 
- Gradients are a negative reciprocal t...
Preview 1 out of 2 pages
Add to cartGradient of a line 
(y₂-y₁) ÷ (x₂-x₁) 
 
 
 
Distance between 2 points 
Use pythagoras' theorem 
√[(∆x)²+(∆y)² 
 
 
 
Parallel lines 
- Gradient is equal 
- Y-intercept is different 
 
 
 
Perpendicular lines 
- Gradients multiply to make -1 
- Gradients are a negative reciprocal t...
Pascal's triangle 
A triangle where the the two numbers above to make the number below. 
- The numbers are the coefficients of the expansion of (a+b)ⁿ 
- The (n+1)th row gives the coefficients of (a+b)ⁿ 
 
 
 
Binomial 
The sum or difference of two terms 
 
 
 
Expanding brackets 
Multiply ever...
Preview 1 out of 2 pages
Add to cartPascal's triangle 
A triangle where the the two numbers above to make the number below. 
- The numbers are the coefficients of the expansion of (a+b)ⁿ 
- The (n+1)th row gives the coefficients of (a+b)ⁿ 
 
 
 
Binomial 
The sum or difference of two terms 
 
 
 
Expanding brackets 
Multiply ever...
How to calculate the gradient of a line joining 2 points 
y2-y1 / x2-x1 
 
 
 
What are two ways of writing the equations of lines? 
-y=mx+c, where m is the gradient and c is the y intercept 
-ax+by+c, where a b and c are integers 
 
 
 
How can you define a straight line? 
By giving: one point on t...
Preview 1 out of 2 pages
Add to cartHow to calculate the gradient of a line joining 2 points 
y2-y1 / x2-x1 
 
 
 
What are two ways of writing the equations of lines? 
-y=mx+c, where m is the gradient and c is the y intercept 
-ax+by+c, where a b and c are integers 
 
 
 
How can you define a straight line? 
By giving: one point on t...
Quadratic Formula 
 
 
 
Domain 
The set of possible inputs for a function. 
 
 
 
Range 
The set of possible outputs of a function. 
 
 
 
Discriminant 
b² - 4ac > 0 then two distinct real roots. 
 
b² - 4ac = 0 then one repeated real root. 
 
b² - 4ac < 0 then a quadratic function has no ...
Preview 1 out of 2 pages
Add to cartQuadratic Formula 
 
 
 
Domain 
The set of possible inputs for a function. 
 
 
 
Range 
The set of possible outputs of a function. 
 
 
 
Discriminant 
b² - 4ac > 0 then two distinct real roots. 
 
b² - 4ac = 0 then one repeated real root. 
 
b² - 4ac < 0 then a quadratic function has no ...
Simplifying algebraic fractions 
- Factorise the numerator and denominator 
- Collect like terms 
 
 
 
Binomial 
An algebraic expression of the sum or the difference of two terms. E.g. x²-y³ 
 
 
 
Polynomial 
A finite expression with more than 2 terms. E.g. 6x²+24x+48 
 
 
 
Dividend 
The base ...
Preview 1 out of 3 pages
Add to cartSimplifying algebraic fractions 
- Factorise the numerator and denominator 
- Collect like terms 
 
 
 
Binomial 
An algebraic expression of the sum or the difference of two terms. E.g. x²-y³ 
 
 
 
Polynomial 
A finite expression with more than 2 terms. E.g. 6x²+24x+48 
 
 
 
Dividend 
The base ...
How to find a midpoint of a line segment 
Average the x and y coordinates of its end points; (x1+x2/2),(y1+y2/2) 
 
 
 
What's a line segment 
A finite part of a straight line with two distinctive end points 
 
 
 
What's it helpful to do in coordinate geometry? 
Draw a sketch showing the info giv...
Preview 1 out of 2 pages
Add to cartHow to find a midpoint of a line segment 
Average the x and y coordinates of its end points; (x1+x2/2),(y1+y2/2) 
 
 
 
What's a line segment 
A finite part of a straight line with two distinctive end points 
 
 
 
What's it helpful to do in coordinate geometry? 
Draw a sketch showing the info giv...
What's the cosine rule? - correct answer a² = b² + c² - 2bcCosA 
 
cosA=? - correct answer b^2+c^2-a^2/2bc 
 
Sine rule? - correct answer a/sinA = b/sinB = c/sinC ; as well as the inverse 
 
What do you have to watch out for with the sine rule? - correct answer It can sometimes produce 2 possibl...
Preview 1 out of 2 pages
Add to cartWhat's the cosine rule? - correct answer a² = b² + c² - 2bcCosA 
 
cosA=? - correct answer b^2+c^2-a^2/2bc 
 
Sine rule? - correct answer a/sinA = b/sinB = c/sinC ; as well as the inverse 
 
What do you have to watch out for with the sine rule? - correct answer It can sometimes produce 2 possibl...
Gradient 
y2-y1/x2-x1 
 
 
 
Length of a line 
sqrt((x2-x1)^2+(y2-y1)^2) 
 
 
 
Midpoint 
(x1+x2/2, y1+y2/2) 
 
 
 
How do you know if two lines are perpendicular? 
When you multiply the gradients together they should equal -1. The general rule is perpendicular = -1/m. Or you could use Pythagoras to...
Preview 2 out of 8 pages
Add to cartGradient 
y2-y1/x2-x1 
 
 
 
Length of a line 
sqrt((x2-x1)^2+(y2-y1)^2) 
 
 
 
Midpoint 
(x1+x2/2, y1+y2/2) 
 
 
 
How do you know if two lines are perpendicular? 
When you multiply the gradients together they should equal -1. The general rule is perpendicular = -1/m. Or you could use Pythagoras to...
Form of complex numbers 
a + bi 
 
 
 
Real and imaginary parts of z = a + bi 
Re(z) = a, Im(z) = b 
 
 
 
When two complex numbers are equal, what is true 
Their real parts are equal and their imaginary parts are equal 
 
 
 
i² 
-1 
 
 
 
i³ 
-i 
 
 
 
i⁴ 
1 
 
 
 
Determinant for two real roo...
Preview 2 out of 5 pages
Add to cartForm of complex numbers 
a + bi 
 
 
 
Real and imaginary parts of z = a + bi 
Re(z) = a, Im(z) = b 
 
 
 
When two complex numbers are equal, what is true 
Their real parts are equal and their imaginary parts are equal 
 
 
 
i² 
-1 
 
 
 
i³ 
-i 
 
 
 
i⁴ 
1 
 
 
 
Determinant for two real roo...
1 + tan2θ 
= sec2θ 
 
 
 
cot2θ + 1 = cosec2θ 
= cosec2θ 
 
 
 
Sin2θ 
2sinθcosθ 
 
 
 
Cos2θ 
cos²θ-sin²θ 
2cos²θ-1 
1-2sin²θ 
 
 
 
Tan2θ 
2tanθ / (1 - tan²θ) 
 
 
 
How do you write a rational number in a proof? 
a/b 
 
 
 
What does y=|f(x)| do? 
Reflects values below the x-...
Preview 1 out of 3 pages
Add to cart1 + tan2θ 
= sec2θ 
 
 
 
cot2θ + 1 = cosec2θ 
= cosec2θ 
 
 
 
Sin2θ 
2sinθcosθ 
 
 
 
Cos2θ 
cos²θ-sin²θ 
2cos²θ-1 
1-2sin²θ 
 
 
 
Tan2θ 
2tanθ / (1 - tan²θ) 
 
 
 
How do you write a rational number in a proof? 
a/b 
 
 
 
What does y=|f(x)| do? 
Reflects values below the x-...
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
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!
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
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.
Stuvia is a marketplace, so you are not buying this document from us, but from seller GUARANTEEDSUCCESS. Stuvia facilitates payment to the seller.
No, you only buy these notes for CA$86.91. You're not tied to anything after your purchase.
4.6 stars on Google & Trustpilot (+1000 reviews)
81113 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now