A LEVEL MATHEMATICS TRANSITION BOOKLET PDF

Solving equations: linear quadratic

simultaneous linear

Corbettmaths

(d) y = 2x² + 9x + 1. (e) y = 2x² + x + 1. (f) y = ?x² + 5x + 2 y = 3x + 9 y = x² ? 5x ? 7 y = 3x² ? x ? 2. Question 2: Solve the following

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A LEVEL MATHEMATICS TRANSITION BOOKLET

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A LEVEL MATHEMATICS

TRANSITION BOOKLET

͞MATHEMATICIANS AREN'T PEOPLE WHO FIND MATHS EASY.

THEY'RE PEOPLE WHO ENJOY HOW HARD IT IS."

To prepare yourselves for the rigour of the A Level course you will need to complete this Transition Booklet Mark this yourself with red pen and highlight any areas of difficulty below

This will be checked in the first week back

Your understanding of these key concepts and skills will be assessed using our Mathematics Induction Test, due to take place within the first fortnight in

September.

Skills check RAG rating

Expanding and simplifying

Surds

Rules of indices

Factorising

Completing the square

Solving quadratics

Sketching quadratics

Linear simultaneous equations

Linear and quadratics simultaneous equations

Solving simultaneous equations graphically

Linear inequalities

Quadratic inequalities

Rearranging equations

͞ANYONE WHO HAS NEVER MADE A MISTAKE HAS NEVER TRIED

ANYTHING NEW."

Albert Einstein

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A LEVEL LINKS

Scheme of work: 1a. Algebraic expressions - basic algebraic manipulation, indices and surds

Key points

When you expand one set of brackets you must multiply everything inside the bracket by what is outside.

When you expand two linear expressions, each with two terms of the form ax + b, where a 0 and b 0, you

create four terms. Two of these can usually be simplified by collecting like terms.

Examples

Example 1 Expand 4(3x 2)

4(3x 2) = 12x 8 Multiply everything inside the bracket

by the 4 outside the bracket

Example 2 Expand and simplify 3(x + 5) 4(2x + 3)

3(x + 5) 4(2x + 3)

= 3x + 15 8x 12 = 3 5x

1 Expand each set of brackets

separately by multiplying (x + 5) by

3 and (2x + 3) by 4

2 Simplify by collecting like terms:

3x 8x = 5x and 15 12 = 3

Example 3 Expand and simplify (x + 3)(x + 2)

(x + 3)(x + 2) = x(x + 2) + 3(x + 2) = x2 + 2x + 3x + 6 = x2 + 5x + 6

1 Expand the brackets by multiplying

(x + 2) by x and (x + 2) by 3

2 Simplify by collecting like terms:

2x + 3x = 5x

Example 4 Expand and simplify (x 5)(2x + 3)

(x 5)(2x + 3) = x(2x + 3) 5(2x + 3) = 2x2 + 3x 10x 15 = 2x2 7x 15

1 Expand the brackets by multiplying

(2x + 3) by x and (2x + 3) by 5

2 Simplify by collecting like terms:

3x 10x = 7x

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Practice

1 Expand.

a 3(2x 1) b 2(5pq + 4q2) c (3xy 2y2)

2 Expand and simplify.

a 7(3x + 5) + 6(2x 8) b 8(5p 2) 3(4p + 9) c 9(3s + 1) 5(6s 10) d 2(4x 3) (3x + 5)

3 Expand.

a 3x(4x + 8) b 4k(5k2 12) c 2h(6h2 + 11h 5) d 3s(4s2 7s + 2)

4 Expand and simplify.

a 3(y2 8) 4(y2 5) b 2x(x + 5) + 3x(x 7) c 4p(2p 1) 3p(5p 2) d 3b(4b 3) b(6b 9)

5 Expand

1 2 (2y 8)

6 Expand and simplify.

a 13 2(m + 7) b 5p(p2 + 6p) 9p(2p 3)

7 The diagram shows a rectangle.

Write down an expression, in terms of x, for the area of the rectangle. Show that the area of the rectangle can be written as 21x2 35x

8 Expand and simplify.

a (x + 4)(x + 5) b (x + 7)(x + 3) c (x + 7)(x 2) d (x + 5)(x 5) e (2x + 3)(x 1) f (3x 2)(2x + 1) g (5x 3)(2x 5) h (3x 2)(7 + 4x) i (3x + 4y)(5y + 6x) j (x + 5)2 k (2x 7)2 l (4x 3y)2

Extend

9 Expand and simplify (x + 3)² + (x 4)²

10 Expand and simplify.

12xxxxquotesdbs_dbs17.pdfusesText_23

[PDF] A LEVEL MATHEMATICS TRANSITION BOOKLET

1 | P a g e

A LEVEL MATHEMATICS

TRANSITION BOOKLET

THEY'RE PEOPLE WHO ENJOY HOW HARD IT IS."

This will be checked in the first week back

September.

Skills check RAG rating

Expanding and simplifying

Rules of indices

Factorising

Completing the square

Solving quadratics

Sketching quadratics

Linear simultaneous equations

Linear and quadratics simultaneous equations

Solving simultaneous equations graphically

Linear inequalities

Quadratic inequalities

Rearranging equations

ANYTHING NEW."

Albert Einstein

2 | P a g e

A LEVEL LINKS

Key points

Examples

Example 1 Expand 4(3x 2)

4(3x 2) = 12x 8 Multiply everything inside the bracket

Example 2 Expand and simplify 3(x + 5) 4(2x + 3)

3(x + 5) 4(2x + 3)

1 Expand each set of brackets

3 and (2x + 3) by 4

2 Simplify by collecting like terms:

3x 8x = 5x and 15 12 = 3

Example 3 Expand and simplify (x + 3)(x + 2)

1 Expand the brackets by multiplying

2 Simplify by collecting like terms:

2x + 3x = 5x

Example 4 Expand and simplify (x 5)(2x + 3)

1 Expand the brackets by multiplying

2 Simplify by collecting like terms:

3x 10x = 7x

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Practice

1 Expand.

2 Expand and simplify.

3 Expand.

4 Expand and simplify.

5 Expand

6 Expand and simplify.

7 The diagram shows a rectangle.

8 Expand and simplify.

Extend

9 Expand and simplify (x + 3)² + (x 4)²

10 Expand and simplify.

12xxxxquotesdbs_dbs17.pdfusesText_23