Everything Maths Grade 10

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 ...

34. 16 x 144 b 4 x 12 b 35. 52 y^324 y+4 10 ^5 y+5 36. 64  123  45 303  36 37. 93  202 4  52  35 38. 7 b+ 7b^2 4  7 b+ 3 ...

SOLUTION Step 1: Write as a fraction and simplify (0,008) (^13) ( 8 1000 ) (^13) = ( 1 125 ) (^13) = ( 1 53 )^13 = 1 (^13) 5 (^3 ...

2.4 Exponential equations EMAW Exponential equations have the unknown variable in the exponent. Here are some examples: 3 x+1= 9 ...

Worked example 10: Solving equations by taking out a common factor QUESTION Solve fort: 5 t+ 3: 5 t+1= 400. SOLUTION Step 1: Rew ...

Step 2: Solve forx 3 x= 81or 3 x= 1. However 3 x= 1 is undefined, so: 3 x= 81 3 x= 3^4 x= 4 Thereforex= 4 Worked example 12: Sol ...