Section 1

Question 1

What is the remainder theorem?

Answer 1

When a polynomial p(x) is divided by (x-a), the remainder is p(a)

Question 2

Formula for the sum of the first n natural numbers

Answer 2

1/2n (n+1)

Question 3

Nth term of a arithmetic sequence

Answer 3

an = a + (n – 1)d

Question 4

Sum of arithmetic sequence

Answer 4

n/2(2a+(n-1)d)

Question 5

Sum of a finite geometric sequence

Answer 5

a(1-r^n)/ 1-r

Question 6

Sum of infinite geometric sequence

Answer 6

a/1-r

Question 7

n formula
r

Answer 7

n!/r!(n-r)!

Question 8

Cos(30)

Answer 8

Root 3 over 2

Question 9

Tan(30)

Answer 9

Root 3 over 3

Question 10

Sin(45)

Answer 10

Root 2 over 2

Question 11

Cos(45)

Answer 11

Root 2 over 2

Question 12

Tan(45)

Answer 12

1

Question 13

Sin(60)

Answer 13

Root 3 over 2

Question 14

Cos(60)

Answer 14

1/2

Question 15

Tan(60)

Answer 15

Root 3

Question 16

Arc length

Answer 16

ϴ × r

Question 17

Area of a sector

Answer 17

1/2 r^2 ϴ

Question 18

Nature of a stationary point

Answer 18

Second derivative is positive then minimum, if negative then maximum

Question 19

Trapezium rule

Answer 19

1/2h{(y0+yn)+2(y1+y2+…+yn-1)} where h=(b-a)/n

Question 20

How to solve dy/dx=f(x)

Answer 20

Multiply both sides by dx then integrate both sides. Don’t forget constant

Question 21

Effect of changing b value of a quadratic

Answer 21

changes the position of the minimum point

Question 22

Cubic with 3 real roots

Answer 22

y-coordinates of stationary points= 1 positive and 1 negative

Question 23

composite meaning

Answer 23

not prime

Question 24

1- sin^2x

Answer 24

(1-sin^2x)(1+sin^2x) or (-1-sinx)(-1+sinx)

Question 25

x^3 transformations

Answer 25

Must be in the form (x-a)^3-b

Question 26

solving ax^4-bx^2+c

Answer 26

Use quadratic formula to find x^2

Question 27

solving f(x)<g(x)<h(x)

Answer 27

find where f(x)<g(x) and where g(x) <h(x)