Everything Maths Grade 10

Step 2: Find the three terms in the second bracket We can replacexandyin the factorised form of the expression for the differenc ...

1.8 Simplification of fractions EMAQ We have studied procedures for working with fractions in earlier grades. 1. a b  c d = ac ...

Step 3: Cancel the common factor in the numerator and the denominator to give the final answer = a+ 1 ax Worked example 19: Simp ...

Step 2: Make all denominators the same so that we can add or subtract the fractions The lowest common denominator is(x2) (x+ 2). ...

Exercise 1 – 10: 1.Simplify (assume all denominators are non-zero): a) 3 a 15 b) 2 a+ 10 4 c) 5 a+ 20 a+ 4 d) a^2 4 a a 4 e) 3 ...

g) 2 xy + 4 xz + 3 yz h) 5 t 2 1 t 3 i) k+ 2 k^2 + 2 1 k+ 2 j) t+ 2 3 q + t+ 1 2 q k) 3 p^2 4 + 2 (p2)^2 l) x x+y + x^2 y^2 x ...

Irrational numbers are numbers that cannot be written as a fraction with the numerator and denominator as integers. If thenthro ...

3.State whether each of the following numbers are rational or irrational. a)^3 p 4 b) 45  c) p 9 d)^3 p 8 4.Ifais an integer,bi ...

19.Write the following irrational numbers to 3 decimal places and then write each one as a rational number to get an approximati ...

27.Solve by factorising: a) 172 152 b) 132 122 c) 1200452 1200352 d) 262 242 28.Represent the following as a product of its ...

e) m^2 + 11m+ 18 4(m^2 4)  3 m^2 + 27m 24 m^2 48 m f) t^2 + 9t+ 18 5(t^2 9)  4 t^2 + 24t 100 t^2 300 t g) 4 b^2 3 b 6 h) x^2 ...

27a.2DVZ 27b.2DW2 27c.2DW3 27d.2DW4 28a.2DW5 28b.2DW6 28c.2DW7 28d.2DW8 28e.2DW9 29a.2DWB 29b.2DWC 29c.2DWD 29d.2DWF 29e.2DWG 29 ...

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CHAPTER^2 Exponents 2.1 Introduction 44 2.2 Revision of exponent laws 45 2.3 Rational exponents 50 2.4 Exponential equations 52 ...

2 Exponents 2.1 Introduction EMAS Exponential notation is a short way of writing the same number multiplied by itself many times ...

VISIT: Interested in finding out why raising a real number to the power of zero is one? Try work it out for yourself. If you get ...

Worked example 1: Applying the exponential laws QUESTION Simplify: 23 x 24 x 2. 4 x^3 2 x^5 3. 12 p^2 t^5 3 pt^3 4.(3x)^2 5. ...

Step 2: Simplify the exponents = 22 n 22 n 21 24 n = 22 n+2n+1 24 n = 24 n+1 24 n = 2^4 n+1(4n) = 2 Worked example 3: Exponent ...

NOTE: When working with exponents, all the laws of operation for algebra apply. Worked example 4: Simplifying by taking out a co ...

SOLUTION Step 1: Change the bases to prime numbers 9 x 1 3 x+ 1 = ( 32 )x 1 3 x+ 1 = 32 x 1 3 x+ 1 Recognise that 32 x= (3x)^2 ...