CURRICULUM GRADE 10 -12 DIRECTORATE
NCS (CAPS) SUPPORT
JUST IN TIME LEARNER REVISION
DOCUMENT
MATHEMATICS
GRADE 10
2024
This document has been compiled by the FET Mathematics Subject Advisors together with
Top Teachers
,Mathematics KZN-GRADE 10 Revision 2024
TABLE OF CONTENTS
PAGE
TOPICS
NUMBERS
1. Algebra 3
2. Number Patterns 10
3. Functions 14
4. Finance 25
5. Probability 30
6. Statistics 34
7. Analytical Geometry 42
8. Trigonometry 56
9. Euclidean Geometry 66
10. Measurement 77
2
, Mathematics KZN-GRADE 10 Revision 2024
TOPIC 1. ALGEBRA
GUIDELINES, SUMMARY NOTES, & STRATEGIES
➢ Number system:
a
• We can write a rational number as a fraction, , where a and b and b 0 .
b
• We cannot express an irrational number as a fraction.
➢ Algebraic expressions:
Multiplying the sum of two or more numbers/variables is the same as multiplying the addends separately.
➢ Factorisation:
The golden rules of factorisation
Two terms Three terms Four terms
Step 1: Step 1: Step 1:
Apply the sign-change rule if Apply the sign-change Group in pairs and put brackets around each
necessary rule if necessary. pair separated by the + sign.
Step 2: Step 2: Step 2:
Take out the HCF if it exists. Take out the HCF if it Apply the sign-change rule if necessary.
Step 3: exists. Step 3:
Apply difference of two Step 3: Factorise the pairs.
squares or sum and difference Factorise the trinomial. Step 4:
of two cubes if possible. Take out the common bracket.
Step 5:
Factorise further if needs be.
3
, Mathematics KZN-GRADE 10 Revision 2024
➢ Simplification of algebraic fractions:
Addition and subtraction Multiplication and division
1. Factorise the denominator 1. When dividing remember to “invert and
2. Consider the sign-change rule multiply” when required.
3. Find the LCD and convert each fraction to an 2. Factorise the numerator and denominator
equivalent fraction with the same denominator 3. Consider the sign-change rule
(LCD) 4. Cancel and simplify
4. Write your answer as one fraction
➢ Laws of exponents:
am
a a = a
n m m+ n
n
= a m−n
a
m
a am
(a )
m n
= a mn (a b) n
= a n bn = m
b b
1
a0 = 1 x −n =
xn
➢ Equations:
Linear equations Quadratic equations
Remove the brackets. The equation will Remove any brackets and take all terms on one side of the
now be in a form of ax + q = 0 equals sign so that there is only a 0 on the side. The equation
now will be in a form of ax 2 + bx + c = 0 or ax 2 + q = 0 .
Add or subtract like terms, and terms Factorise the equation.
with variables one side and constant
terms on the other side.
Divide both sides by the coefficient of We find the solution to the equation by letting each factor
the variable. equal 0.
Simultaneous equations
When solving a pair of simultaneous linear equations, we are, in fact, finding a common point – the point
of intersection of two lines.
Elimination method Substitution method
• Make the coefficients of one of the • Use the simplest of the two given equations to express one
variables the same in both of the variables in terms of the other.
equations. • Substitute into the second equation. By doing this we
• Eliminate the variable by adding the reduce the number of equations and the number of
equations together or subtracting variables by one.
one equation from the other. • We now have one equation with one unknown variable
• Simplify and solve for one variable which can be solved.
• Substitute the variable back into • Use the solution to substitute back into the first equation
either original equation and solve to find the value of the other unknown variable.
for the other variable.
Literal equations
• We isolate the unknown variable by asking “what is it joined to?” and “how is it joined?” We then
perform the opposite operation to both sides as a whole.
• If the unknown variable is in two or more terms, then we take it out as a common factor.
• If we have to take the square root of both sides, remember that there will be a positive and a negative
answer.
4
NCS (CAPS) SUPPORT
JUST IN TIME LEARNER REVISION
DOCUMENT
MATHEMATICS
GRADE 10
2024
This document has been compiled by the FET Mathematics Subject Advisors together with
Top Teachers
,Mathematics KZN-GRADE 10 Revision 2024
TABLE OF CONTENTS
PAGE
TOPICS
NUMBERS
1. Algebra 3
2. Number Patterns 10
3. Functions 14
4. Finance 25
5. Probability 30
6. Statistics 34
7. Analytical Geometry 42
8. Trigonometry 56
9. Euclidean Geometry 66
10. Measurement 77
2
, Mathematics KZN-GRADE 10 Revision 2024
TOPIC 1. ALGEBRA
GUIDELINES, SUMMARY NOTES, & STRATEGIES
➢ Number system:
a
• We can write a rational number as a fraction, , where a and b and b 0 .
b
• We cannot express an irrational number as a fraction.
➢ Algebraic expressions:
Multiplying the sum of two or more numbers/variables is the same as multiplying the addends separately.
➢ Factorisation:
The golden rules of factorisation
Two terms Three terms Four terms
Step 1: Step 1: Step 1:
Apply the sign-change rule if Apply the sign-change Group in pairs and put brackets around each
necessary rule if necessary. pair separated by the + sign.
Step 2: Step 2: Step 2:
Take out the HCF if it exists. Take out the HCF if it Apply the sign-change rule if necessary.
Step 3: exists. Step 3:
Apply difference of two Step 3: Factorise the pairs.
squares or sum and difference Factorise the trinomial. Step 4:
of two cubes if possible. Take out the common bracket.
Step 5:
Factorise further if needs be.
3
, Mathematics KZN-GRADE 10 Revision 2024
➢ Simplification of algebraic fractions:
Addition and subtraction Multiplication and division
1. Factorise the denominator 1. When dividing remember to “invert and
2. Consider the sign-change rule multiply” when required.
3. Find the LCD and convert each fraction to an 2. Factorise the numerator and denominator
equivalent fraction with the same denominator 3. Consider the sign-change rule
(LCD) 4. Cancel and simplify
4. Write your answer as one fraction
➢ Laws of exponents:
am
a a = a
n m m+ n
n
= a m−n
a
m
a am
(a )
m n
= a mn (a b) n
= a n bn = m
b b
1
a0 = 1 x −n =
xn
➢ Equations:
Linear equations Quadratic equations
Remove the brackets. The equation will Remove any brackets and take all terms on one side of the
now be in a form of ax + q = 0 equals sign so that there is only a 0 on the side. The equation
now will be in a form of ax 2 + bx + c = 0 or ax 2 + q = 0 .
Add or subtract like terms, and terms Factorise the equation.
with variables one side and constant
terms on the other side.
Divide both sides by the coefficient of We find the solution to the equation by letting each factor
the variable. equal 0.
Simultaneous equations
When solving a pair of simultaneous linear equations, we are, in fact, finding a common point – the point
of intersection of two lines.
Elimination method Substitution method
• Make the coefficients of one of the • Use the simplest of the two given equations to express one
variables the same in both of the variables in terms of the other.
equations. • Substitute into the second equation. By doing this we
• Eliminate the variable by adding the reduce the number of equations and the number of
equations together or subtracting variables by one.
one equation from the other. • We now have one equation with one unknown variable
• Simplify and solve for one variable which can be solved.
• Substitute the variable back into • Use the solution to substitute back into the first equation
either original equation and solve to find the value of the other unknown variable.
for the other variable.
Literal equations
• We isolate the unknown variable by asking “what is it joined to?” and “how is it joined?” We then
perform the opposite operation to both sides as a whole.
• If the unknown variable is in two or more terms, then we take it out as a common factor.
• If we have to take the square root of both sides, remember that there will be a positive and a negative
answer.
4
