page 1 of 24 pages
MATHEMATICS:
Algebra, Exponents, Inequalities and Nature of Roots
Name: _______________ Surname: __________________
Class: ______
Issued: ________________________
Compiled by Kaleb
, page 2 of 24 pages
Content:
1) Equations a) Solve for 𝑥 by factorizing. page 3
b) Solve for 𝑥 using the quadratic formula. page 3
c) Equations containing a surd sign. page 5
d) Solve by substitution (𝑘-method). page 6 - 7
e) Solve for 𝑥 by completing the square. page 8
2) Quadratic Inequalities page 3 - 4
3) Exponents a) Exponential Equations. page 8
b) Working with exponential laws. page 9 - 11
4) Logarithmic Equations. page 12
5) Literal Equations. page 12
6) Equations with 2 unknown values. page 13
7) Cubic Expression Factorisation. page 13
8) Nature of Roots. page 15 - 18
9) Simultaneous Equations. page 19 - 24
Compiled by Kaleb
, page 3 of 24 pages
Basic Quadratic Equations:
Solve for 𝑥:
1.1.1 𝑥 2 − 4𝑥 + 5 = 0 (3) 1.1.1 𝑥 2 − 2𝑥 − 24 = 0 (3)
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Equations when you are FORCED to use the quadratic formula:
Solve for 𝑥:
1.1.2 𝑥(7𝑥 + 2) = 1 1.1.2 2𝑥 2 − 3𝑥 − 3 = 0
(correct to TWO decimal places) (4) (correct to TWO decimal places) (3)
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Quadratic Inequalities:
1.1.5 (𝑥 − 5)(𝑥 − 6) ≤ 56 (5) 1.1.3 2𝑥 (3𝑥 + 1) < 0 (3)
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_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
Compiled by Kaleb
MATHEMATICS:
Algebra, Exponents, Inequalities and Nature of Roots
Name: _______________ Surname: __________________
Class: ______
Issued: ________________________
Compiled by Kaleb
, page 2 of 24 pages
Content:
1) Equations a) Solve for 𝑥 by factorizing. page 3
b) Solve for 𝑥 using the quadratic formula. page 3
c) Equations containing a surd sign. page 5
d) Solve by substitution (𝑘-method). page 6 - 7
e) Solve for 𝑥 by completing the square. page 8
2) Quadratic Inequalities page 3 - 4
3) Exponents a) Exponential Equations. page 8
b) Working with exponential laws. page 9 - 11
4) Logarithmic Equations. page 12
5) Literal Equations. page 12
6) Equations with 2 unknown values. page 13
7) Cubic Expression Factorisation. page 13
8) Nature of Roots. page 15 - 18
9) Simultaneous Equations. page 19 - 24
Compiled by Kaleb
, page 3 of 24 pages
Basic Quadratic Equations:
Solve for 𝑥:
1.1.1 𝑥 2 − 4𝑥 + 5 = 0 (3) 1.1.1 𝑥 2 − 2𝑥 − 24 = 0 (3)
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
Equations when you are FORCED to use the quadratic formula:
Solve for 𝑥:
1.1.2 𝑥(7𝑥 + 2) = 1 1.1.2 2𝑥 2 − 3𝑥 − 3 = 0
(correct to TWO decimal places) (4) (correct to TWO decimal places) (3)
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
Quadratic Inequalities:
1.1.5 (𝑥 − 5)(𝑥 − 6) ≤ 56 (5) 1.1.3 2𝑥 (3𝑥 + 1) < 0 (3)
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
_________________________ _____________________________
Compiled by Kaleb
