Targeting Grade CUnit 2Algebra 2GCSE Mathematics

Top: Review 1 - How much do you know?Practice 1: Solving equations with the unknown on one side

Practice 2: Solving equations with the unknown on both sidesTAIL 1

Practice 3: Writing the expression in a different form using brackets

Practice 4: Forming equations

TAIL 2Can You ? Solving simple linear equations

Unknowns on both sides of the equation

Try a test

Factorising an expression

Form equations

Try a test

If not you need

TOPHow much do you know?Solve the following

(i)x + 5 = 16

(ii)3x + 4 = 19

(2)(b)6y + 9 = 45 (1)(c)2x 5 = -1 (2)

4(x + 3) = 20 (1) 29 = 9x - 7 (1) (Total 7 marks)

x = 11x = 5y = 6x = 2x = 4x = 2Are you ready for the answers ?

Practice 1:Solve:

(a)(i)4x + 2 = 18

(ii)8x 5 = 19

(iii)7 = 3y - 8

Multiply out the brackets first: 2(x + 3) = 16

(1)(c) 3(2x 3) = 9

(2)Lesson x = 3y = 5x = 5x = 3x = 4Are you ready for the answers ?

Practice 2:Solve:

(i)2x + 3 = x + 7

(2) (ii)8r + 3 = 5r + 12

(2) (iii)9x 14 = 4x + 11

(2)

(iv)20y 16 = 18y - 10

(2)

Lesson x = 43r = 9 r = 35x = 25 x = 52y = 6 y = 3Are you ready for the answers ?

5y + 6 = 212(x + 4) = 125(y - 3) = 48x + 12 = 204x + 5 = 2x + 93y 2 = 2y + 815x + 6 = 7x - 220y 16 = 18y - 10TAIL 13x 5 = 105t 8 = t + 16Are you ready for the answers ?Next

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5y + 6 = 212(x + 4) = 125(y 3) = 54x +5 = 2x + 93y 2 = 2y + 815x + 6 = 7x - 220y 16 = 18y -10x = 3y = 3 x = 2x = 1x = 2y = 10t = 6x = -1Are you ready for the answers ?TAIL AnswersLesson 3x 5 = 105t 8 = t + 168x + 12 = 20y = 3y = 4

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This is the exact reverse of multiplying out the brackets. Factorising means...Putting brackets inThis is what you have to do...Take out the biggest number that goes into all the termsTake out each letter that will go into every term the highest powerFactorise 3x + 6 3 divides into 3 and 6 = 3(x + 2)Multiply out the brackets to check...3(x + 2) = 3x + 6 For more click here

5x + 15x 5 divides into 5 and 15 x divides into x and x = 5x(x + 3)

Multiply out the brackets to check

5x(x + 3) = 5x + 15x

4x - 8xy 4 divides into 4 and 8 x divides into x and x = 4x(x 2y)

Multiply out the brackets to check

4x(x 2y) = 4x - 8xy Look at these examplesFor more practice click here

Can you factorise these? Write down your solutions to:

1.9x + 12

2.10x - 6 9 3x

3x + 5xy

x - 9x x + x

3x + 6xy

p + 6p

8x + 4x

ax + ax (10)

Lesson 3(3x + 4)2(x -3)3(3 x)x(3 + 5y)x(x 3)x(x + 1)3x(x + 2y)p(p + 6)4x(2x + x)ax(x + 1)Are you ready for the answers ?

1.Mr Smith owns minibuses and coaches.Each minibus has 12 seats.(a)Write an expression, in terms of m, for the number of seats in m minibuses.(1)Each coach has 48 seats(b)Write an expression, in terms of m and c, for the number of seats in m minibuses and ccoaches.(2)(Total 3 marks)Forming equationsHave a go at...12m12m + 48cMore practiceAre you ready for the answers ?

Lisa packs pencils in boxes.She packs 12 pencils in each box.Lisa packs x boxes of pencils.

Write an expression, in terms of x, for the number of pencils Lisa packs..................................(1)

Lisa also packs pens in boxes.She packs 10 pens into each box.Lisa packs y boxes of pens.(b)Write down an expression, in terms of x and y, for the total number of pens and pencils Lisa packs..................................(2)(Total 3 marks)

12x10y + 12xMore practiceAre you ready for the answers ?

The diagram represents a garden. All measurements are given in metres. The garden has a flowerbed in one corner. The flowerbed is a square of side x.

(a)Write down an expression, in terms of x, for the shortest side of the garden......................................(1)(b)Find an expression, in terms of x, for the perimeter of the garden. Give your answer in its simplest form......................................(2)The perimeter of the garden is 20 metres.(c)Find the value of x. (2)(Total 5 marks)x + 24x + 144x + 14 = 20 4x = 6 x = 6/4 = 1More practiceAre you ready for the answers ?

The cost, in pounds, of hiring a car can be worked out using this rule.

(a)Work out the cost of hiring a car for 4 days.9

(2)Bishen hired a car.The cost was 120(b)Work out the number of days for which Bishen hired the car.

..(2)The cost of hiring a car for n days is C pounds.(c)Write down a formula for C in terms of n.

..(3)(Total 7 marks)Add 3 to the number of days hireMultiply your answer by 10 More practice70910(n+3)Are you ready for the answers ?

The width of a rectangle is x centimetres. The length of the rectangle is (x + 4) centimetres.

Find an expression, in terms of x, for the perimeter of the rectangle. Give your expression in its simplest form

.(2)The perimeter of the rectangle is 54 centimetres.Work out the length of the rectangle.

cm(3)(Total 5 marks)4x + 84x + 8 = 54 4x = 46 x = 46/4 = 11 The length must be 11 + 4 = 15 cm.15Are you ready for the answers ?

TAIL 2Factorise 15x + 5

Factorise6y - 3y

Factorisea + a

Factorise18x + 12x

Simplifyxy - xy

5(3x +1)3y(2y 1)a(a + 1)6x(3x + 2)xy(y 1)Click for the next question1.Are you ready for the answers ?

Jennifer made x cakes. She put 4 sweets on top of each cake.(a)Write down an expression, in terms of x, for the number of sweets she used...(1)Paul made 3 more cakes than Jennifer.(b)Write down an expression, in terms of x, for the number of cakes Paul made...(1)Paul also put 4 sweets on each of his cakes.(c)Write down an expression, in terms of x, for the number of sweets Paul used...(1)(Total 3 marks)TAIL 22.4xx + 34(x + 3)Click for next questionAre you ready for the answers ?

Eggs are sold in boxes.A small box holds 6 eggs.A large box holds 12 eggs.Hina buys x small boxes of eggs.

Hina also buys 4 less of the large boxes of eggs than the small boxes.

(a)Find, in terms of x, the total number of eggs in the large boxes that Hina buys.

.......................... (1)(b)Find, in terms of x, the total number of eggs that Hina buys.Give your answer in its simplest form.

.......................... (2) (Total 3 marks)TAIL 2Click for the next question12(x 4)12(x 4) large eggs and 6x small eggs12x 48 + 6x = 18x - 4818x - 48Are you ready for the answers ?

4.The perimeter of this triangle is 19 cm.All lengths on the diagram are in centimetres.

Work out the value of t. t = (Total 3 marks)3t + 6 = 19 3t = 13 t = 13/3 = 44Lesson Are you ready for the answers ?