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Targeting Grade C Unit 2 Algebra 2 GCSE Mathematics

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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 sides Test 1 Practice 3: Writing the expression in a different form using brackets Practice 4: Forming equations Test 2 Can 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

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TOP How 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) (d)4(x + 3) = 20 (1) (e)29 = 9x - 7 (1) (Total 7 marks) Lesson x = 11 x = 5 y = 6 x = 2 x = 4 x = 2 Are you ready for the answers ?

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Practice 1: Solve : (a)(i)4x + 2 = 18 (ii)8x – 5 = 19 (iii)7 = 3y - 8 Multiply out the brackets first: (a) 2(x + 3) = 16 (1) (c) 3(2x – 3) = 9 (2) Lesson x = 3 y = 5 x = 5 x = 3 x = 4 Are you ready for the answers ?

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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 = 4 3r = 9 r = 3 5x = 25 x = 5 2y = 6 y = 3 Are you ready for the answers ?

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1 2 3 4 5 6 7 8 9 10 5y + 6 = 21 2(x + 4) = 12 5(y - 3) = 4 8x + 12 = 20 4x + 5 = 2x + 9 3y – 2 = 2y + 8 15x + 6 = 7x - 2 20y – 16 = 18y - 10 Test 1 3x – 5 = 10 5t – 8 = t + 16 Are you ready for the answers ? Next

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1 2 3 4 5 6 7 8 9 10 5y + 6 = 21 2(x + 4) = 12 5(y – 3) = 5 4x +5 = 2x + 9 3y – 2 = 2y + 8 15x + 6 = 7x - 2 20y – 16 = 18y -10 x = 3 y = 3 x = 2 x = 1 x = 2 y = 10 t = 6 x = -1 Are you ready for the answers ? Test Answers Lesson 3x – 5 = 10 5t – 8 = t + 16 8x + 12 = 20 y = 3 y = 4

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This is the exact reverse of multiplying out the brackets. Factorising means... Putting brackets in This is what you have to do... Take out the biggest number that goes into all the terms Take out each letter that will go into every term – the highest power Factorise 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

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5x² + 15x 5 divides into 5 and 15 x divides into x² and x = 5x(x + 3) Multiply out the brackets to check … 5x(x + 3) = 5x² + 15x 4x² - 8xy 4 divides into 4 and 8 x divides into x² and x = 4x(x – 2y) Multiply out the brackets to check… 4x(x – 2y) = 4x² - 8xy Look at these examples For more practice click here

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Lesson Can you factorise these? Write down your solutions to: 1.9x + 12 2.10x - 6 3.9 – 3x 4.3x + 5xy 5.x² - 9x 6.x² + x 7.3x² + 6xy 8.p² + 6p 9.8x² + 4x 10.ax² + ax (10) 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 ?

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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 c coaches. ……………………………… (2) (Total 3 marks) Forming equations Have a go at... 12m 12m + 48c More practice Are you ready for the answers ?

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Lisa packs pencils in boxes. She packs 12 pencils in each box. Lisa packs x boxes of pencils. (a)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) 12x 10y + 12x More practice Are you ready for the answers ?

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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 + 2 4x + 14 4x + 14 = 20 4x = 6 x = 6/4 = 1½ More practice Are you ready for the answers ?

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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’ hire Multiply your answer by 10 More practice 70 9 10(n+3) Are you ready for the answers ?

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The width of a rectangle is x centimetres. The length of the rectangle is (x + 4) centimetres. (a)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. (b)Work out the length of the rectangle. …………………cm (3) (Total 5 marks) 4x + 8 4x + 8 = 54 4x = 46 x = 46/4 = 11½ The length must be 11½ + 4 = 15½ cm. 15½ Are you ready for the answers ? Lesson

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Test 2 (a)Factorise 15x + 5 (b)Factorise6y² - 3y (c)Factorisea² + a (d)Factorise18x² + 12x (e)Simplifyxy² - xy 5(3x +1) 3y(2y – 1) a(a + 1) 6x(3x + 2) xy(y – 1) Click for the next question 1. Are you ready for the answers ?

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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) Test 2 2. 4x x + 3 4(x + 3) Click for next question Are you ready for the answers ?

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3.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) Test 2 Click for the next question 12(x – 4) 12(x – 4) large eggs and 6x small eggs 12x – 48 + 6x = 18x - 48 18x - 48 Are you ready for the answers ?

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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 = 4⅓ 4⅓4⅓ Lesson Are you ready for the answers ?

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