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Pure Mathematics Algebra and Functions 1


Indices

1) am x an = am+n Or 52x 53 = 55 = 3125

2) am÷ an = am-n Or 54÷52 = 52 = 25

3
3) (am)n = amn Or (52) = 56 = 15625

4) a-n = a
1
n Consider 7-3…

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Polynomial expressions

A polynomial is and algebraic expression which is the sum of a number of terms. They have four
terms. The highest power of x is 3.

Adding and Subtracting

(x2 - 2x + 7) + (3x2 + 5x + 6) = 4x2 + 3x + 13

(x3 -…

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Quadratic Functions

The graph of y = ax2 + bx + c
.

i:a>0 ii : a < 0




All quadratic functions are symmetrical about a vertical axis.

The x-coordinates of the point(s) where the curve crosses the x-axis are determined by solving
ax2 + bx + c = 0…

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Completing the square

Consider the expression x2 + 6x + 11.

We can write x2 + 6x = (x + 3)2 - 9 and so we say that

x2 + 6x = (x + 3)2 - 9 + 11

= (x + 3)2 + 2 (NOTE: the `3' is obtained…

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And 3x + 7y = 44 (2)

From (1) we see that x = 13 - 2y

Substitute in (2), 3(13 - 2y) + 7y = 44

39 + y = 44

y = 5

Substitute this value in (1), x = 13 - 2(5)

x = 3

We also…

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Sketch the graph of y = x2 + x - 6



We are looking below the x-axis so we want one region, and hence one inequality.

So the solution is - 3 < x < 2

Example 2
1
Solve y = x2 + 1
2 x - 120


We…

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(x - 2)(x + 1) = 0

x = 2 or x =- 1


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