Unit 1

Question 1

What is the discriminant?

Answer 1

b² - 4ac

Question 1

Two distinct real roots?

Answer 1

b² - 4ac > 0

Question 2

Two real roots?

Answer 2

b² - 4ac => 0

Question 3

One real root?

Answer 3

b² - 4ac = 0

Question 4

No roots?

Answer 4

b² - 4ac < 0

Question 5

What is remainder theorum?

Answer 5

When f(x) is divided by the polynomial x - a, the remainder of the calculation is f(a)

Question 6

What is factor theorum?

Answer 6

If f(a) = 0 then x - a is a factor of the f(x)

Question 7

What are the types of proof?

Answer 7

• proof by deduction
• proof by exhaustion
• disproof by counter example

Question 8

What is the length of a line?

Answer 8

√(x2 - x1)² + (y2 - y1)²

Question 9

What are the two equations for lines?

Answer 9

y = mx + c
y - y1 = m(x - x1)

Question 10

What is the midpoint of a line?

Answer 10

(y1 + y2 / 2, x1 + x2 / 2)

Question 11

What is the gradient of a line?

Answer 11

y2 - y1 / x2 - x1

Question 12

What is the sine rule?

Answer 12

a/sinA = b/sinB = c/sinC or vice versa

Question 13

What is the cosine rule?

Answer 13

a² = b² + c² - 2bccosA
or cosA = b² + c² - a² / 2bc

Question 14

What is the area of a triangle?

Answer 14

1/2 ab sinC

Question 15

What are the circle theorems?

Answer 15

1. the angle in a semi circle is a right angle
2. the perpendicular from the centre to a chord bisects the chord
3. the radius of a circle at a given point on its circumference is perpendicular to the tangent to the circle at that point

Question 16

What are the trig identities?

Answer 16

sin²θ + cos²θ = 1
sin²θ = 1 - cos²θ
tanθ = sinθ/cosθ

Question 17

What is the symbol for “is a member of”?

Answer 17

A big curved E

Question 18

What are the symbols for the set of all integers and the set of all positive integers?

Answer 18

A big Z and a big Z with a +

Question 19

What is the symbol for the set of all real numbers?

Answer 19

A big R

Question 20

What does it mean when numbers are in curly brackets?

Answer 20

That all the numbers within it are included e.g. {1,2,3,4,5} 1, 2, 3, 4 and 5 are all included.

Question 21

What does it mean when numbers are in square brackets?

Answer 21

That the numbers from the first number to the second number are included, including the first and second number e.g. [1,5] numbers 1-5 are included as well as 1 and 5.

Question 22

What does it mean when numbers are in regular brackets?

Answer 22

That the numbers from the first number to the second number are included, NOT including the first and second number e.g. (1,5) numbers 1-5 are included MINUS 1 and 5.

Question 23

What are the log laws?

Answer 23

1. log(xy) = log(x) + log(y)
2. log(x/y) = log(x) - log(y)
3. nlog(x) = log(x^n)

Question 24

What are concentric circles?

Answer 24

Circles that have the same centre point.

Question 25

How can you prove that 2 circles don't touch?

Answer 25

d > r1 + r2

Question 26

How can you prove that 2 circles touch externally?

Answer 26

d = r1 + r2

Question 27

How can you prove that 2 circles meet at 2 distinct points?

Answer 27

d < r1 + r2

Question 28

How can you prove that two circles touch internally?

Answer 28

d = r1 - r2

Question 29

How can you prove that 2 circles don't touch, but one is within the other?

Answer 29

d < r1 - r2

Question 30

How do you know when to use the sine rule?

Answer 30

- when there are 2 angles and 1 side - when there are 2 sides and a non included angle

Question 31

How do you know when to use the cosine rule?

Answer 31

- when there are 3 sides - when there are 2 sides and an included angle

Question 32

What transformation is f(x+a)?

Answer 32

Horizontal translation of f(x) (negative is right, positive is left)

Question 33

What transformation is f(x) + a?

Answer 33

Vertical translation of f(x) (positive up, negative down)

Question 34

What transformation is f(ax)?

Answer 34

Horizontal stretch of a scale factor of 1/a, so you multiply the x co-ords by 1/a

Question 35

What transformation is af(x)?

Answer 35

A vertical stretch of a scale factor of a, so you multiply the y co-ords by a

Question 36

What transformation is f(-x)?

Answer 36

Change the x co-ords, reflection in the y axis

Question 37

What transformation is -f(x)?

Answer 37

Change in y co-ords, reflection in the x axis

Question 38

How do you differentiate using first principles?

Answer 38

f(x+h) - f(x) / h

Question 39

How do you differentiate?

Answer 39

- multiply power by coefficient of x - decrease the power by 1

Question 40

How do you integrate?

Answer 40

- increase the power by 1 - divide by the new power - add + c (if needed)

Question 41

What are differentiation and integration used for?

Answer 41

Differentiation: finding the gradient of a curve Integration: finding the area under a curve

Question 42

What is a normal?

Answer 42

A line perpendicular to a tangent

Question 43

How do you determine whether a stationary point is minimum or maximum?

Answer 43

If the second differential > 0, it is a minimum. If the second differential < 0, it is a maximum.