Summary Grade 11 Mathematics Paper 1 Notes

Mathematics Paper 1 Notes
Exponents & surds
The number system

Exponents
1. a n = a.a.a.a (n times)
2. a 0 = 1 (a =/ 0)
3. a −n = a
1
n (a =/ 0)
1
4. a n = √n a a ≥ 0, n ≥ 2
1
5. a − n = n
1
√a
a > 0, n ≥ 2
m
= √a m = (√n a ) m mεz, n ≥ 2, a > 0
n
6. a n


Laws
- x n .y m = y n+m
- y n ÷ y m = y n−m
- (xy) m = x m y m
m
- ( yx ) m = x
y
m


- (y n ) m = y nm




Surds
Laws
n n
- √a x √b = √ab
n

n
√a
- n
√
a
b = n
√b


√
p q
- p pq
√a = √√a = √a
q


q
= (√p a) q
p
- √a

, n n
- √a ± b =/ √n a ± √b
Examples
1. √a 2 + b 2
Cannot be simplified
2. √6 2 + 8 2
= √100
= 10
3. √12
= √4.3
= 2√3
4. √3 24
3
√8.3
3
2√3
5. 1
2−√3
2+√3
= 2−1√3 × 2+√3
= 2+1√3
= 2 + √3
Equations & Inequalities
Solving Quadratic Equations
- Trinomials
- Common factor
- K-method
- Squaring both sides ​(CHECK)
- Square root both sides (+/-)
- Complete the square
- Quadratic formula
Inequalities
Quadratic Inequalities
- CV
- Number line
- Plus or minus
NB: if there is a fraction the denominator is undefined therefore do not include it