Year 1 Pure

Question 1

Irrational numbers

Answer 1

The square root of any number which is not itself a perfect square

Question 2

a^m x a^n

Answer 2

a^(m+n)

Question 3

a^m / a^n

Answer 3

a^(m-n)

Question 4

(a^m)^n

Answer 4

a^mn

Question 5

a^-n

Answer 5

1/(a^n)

Question 6

a^0

Answer 6

1

Question 7

a^(1/n)

Answer 7

nth root of a

Question 8

a^(m/n)

Answer 8

nth root of a^m

Question 9

Describe the shape of a quadratic

Answer 9

Parabola

Question 10

Discriminant

Answer 10

b^2 - 4ac

Question 11

b^2 - 4ac

Answer 11

Discriminant

Question 12

a < x < b

Answer 12

{x:x > a} n {x:x < b}

Question 13

x > b and x < a

Answer 13

{x:x > b} u {x:x < a}

Question 14

Equation of a circle

Answer 14

(x - a)^2 + (x - b)^2 = r^2
Where centre (a,b)

Question 15

Find the midpoint of a circle from 3 points

Answer 15

Find the gradient between two points.
Get the negative reciprocal of this and find the equation from the the midpoint of the two points.
Repeat with two other points
Create a simultaneous equation with this. This is the midpoint.

Question 16

Sin (theta) using cos

Answer 16

Cos ( 90 - theta )

Question 17

Cos ( theta ) using sin

Answer 17

Sin (90 - theta)

Question 18

Trigonometric equation tan (theta)

Answer 18

sin (theta) / cos (theta)

Question 19

Trigonometric equation 1

Answer 19

Sin^2 (theta) + cos^2 (theta) = 1

Question 20

Asymptote

Answer 20

A line which is approached by a curve without ever reaching it

Question 21

y = f(x) + a

Answer 21

Vertical translation

Question 22

y = f(x - a)

Answer 22

Horizontal translation

Question 23

y = af(x)

Answer 23

Vertical stretch

Question 24

y = f(1/a x)

Answer 24

Horizontal stretch

Question 25

Reflection in the x axis

Answer 25

y = -f(x)

Question 26

Reflection in the y axis

Answer 26

y = f(-x)

Question 27

nCr

Answer 27

n! / (r!(n - r)!)

Question 28

Derivative of kx^n

Answer 28

knx^n-1

Question 29

Differentiation

Answer 29

The process of finding the gradient function or derivative or derived function

Question 30

Second derivative

Answer 30

The rate of change of the derivative

Question 31

At a maximum point

Answer 31

dy/dx = 0
d^2y/dx^2 < 0

Question 32

At a minimum point

Answer 32

dy/dx = 0
d^2y/dx^2 > 0

Question 33

Differentiation from first principles

Answer 33

f’(x) = (f(x-a) -f(x)) / a
a -> lim 0

Question 34

Integrate kx^n

Answer 34

(kx / (n+1))^n+1 +c

Question 35

Definite integral

Answer 35

Uses limits to find the area under a portion of a curve

Question 36

Write (r, theta) in component form

Answer 36

(r cos (theta))
(r sin (theta))

Question 37

Position vector

Answer 37

A vector which starts at the origin

Question 38

Unit vector

Answer 38

Has a magnitude of 1

Question 39

a^x = b

Answer 39

Log (a) b = x

Question 40

Log(x) + log(y)

Answer 40

Log(xy)

Question 41

Log(x) - log(y)

Answer 41

Log(x/y)

Question 42

Log(x^n)

Answer 42

n log(x)

Question 43

Log(a) a

Answer 43

1

Question 44

Log(a) 1

Answer 44

0

Question 45

Derivative of e^kx

Answer 45

ke^kx