This Grade 9 Mathematics Algebra + Geometry Notebook is an essential tool for any student studying math! It includes detailed notes and examples on key topics, including algebra and geometry, to help students understand and master the subject. With its clear and concise format, it makes learning a...
, Key – core concepts
REAL NUMBERS NATURAL NUMBERS
NUMBERS “FAMILY”/SYSTEM
The number line consists of all the Rational
(Q) and Irrational (Q') numbers which
Even numbers : 2;4;6;8….
together form the set of Real (ℝ) numbers.
Odd numbers : 1;3;5;7…
UNREAL NUMBERS
Prime numbers : 2;3;5;7;11;13… (1 is not a prime
√−25 is an example of a non-real number. number)
There is no number that, when squared, will
Composite numbers : 4;6;8;9;10;12 (numbers with
equal -25.
more than 2 factors)
√−25 does not exist on the number line. Square numbers : 1;4;9;16;25…
The real and non-real numbers together
form the complex numbers. Cubic numbers : 1;8;27;64;125…
COUNTING NUMBERS
INTEGERS
RASIONAL NUMBER
any number that can be written as a fraction, i.e. a
𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝐴
or [where A & B ∈ Z ; B ≠ 0]
𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝐵
W All integers.
W All fractions.
W All terminating decimal fractions.
W All repeating decimal fractions.
IRRASIONAL NUMBERS
W All non-terminating, non-repeating decimal
Can only be written in a number form with infinite, numbers
non-repeating digits after the decimal point, the W Pi (π)
numbers can NOT be written as a FRACTION W √Positive non − square
3
W √Positive non − cubic
, Key – core concepts
BODMAS CALCULATIONS WITH BRACKETS ()
NB ! At minus - and brackets ()
Inside the bracket (-3)² = (-3)(-3) =+9
No bracket -3² =-(3)(3) = -9
Outside the bracket -(3)² =-(3)(3) = -9
CALCULATIONS WITH ROOTS √
+ or – under √ [first SIMPLIFY under the √]
W √16 + 9=√25
W √16 + 9≠√16 + √9
x or ÷ under the √ [divide √ and work out each
part's √ separately]
W √16 × 9=√144
SIGN RULES [X ÷] W √16 × 9=√16 × √9
, Key – core concepts
ADDITION + * SUBTRACTION - SCM * LCD
W Same signs (add together and KEEP the sign) SCM (Smallest Common Multiple )
W Different signs (subtract and keep the largest
(ALSO SCD = smallest common denominator)
number's sign)
MULTIPLY THAT WHICH APPEARS WITH THE BIGGEST ONE
Characters inside and outside brackets (multiply together to
AND THAT WHICH IS SHORT [FRACTIONAL] (largest
get a new character. Two signs next to each other must
number's factors and what remains with the other)
become one sign)
Determine the SCM of 9 and 12:
INVERSES
Multiples of 9 are: 9; 18; 27; 36; 45; 54; 63; …
addition inverse of -4 = 4
Multiples of 12 are: 12; 24; 36; 48; 60; 72; …
multiplicative inverse of -2 = -½ The SCM of 9 and 12 is: 36
MULTIPLES * FACTORS GCF / HCF (Greatest [HIGHEST] common denominator /
factor)
MULTIPLES MULTIPLY ONLY WHAT IS COMMON TO ALL
[count in the number] (numbers common to all)
E.G : 2, 4, 6, 8, 10 [MULTIPLES OF 2] Determine the SCM of 8 and 10.
FACTORS Step 1. What is the LCF of the 2 numbers: It is 2
Factors of 8: 1; 2; 4; 8 Factors of 10: 1; 2; 5; 10
[numbers that can divide exactly into the number]
Step 2. Determine the product of 8 and 10: 8 x 10 = 80
E.G : 1, 2, 3, 6, 9, 18 [FACTORS OF 18]
Step 3. Divide the product of the numbers by the LCF: 80 ÷ 2 = 40
PRIME NUMBERS
Step 4. The SCM of 8 and 10 is 40
[number with only 2 factors namely 1 and the number itself]
[2, 3, 5, 7, 11, 13, 17, 19]
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