Equations and Inequalities (1) 1. Simplify:
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1 Equations and Inequalities (1) 1. Simplify: a. 4a + b + 3a - 2b b. 3y x 2y c. 5x2 20x 2. Find the value of each expression when a = 3, b = -5 and c = 2 a. 10a + 10b b. a + c 2 c. 10a c 3. Find the speed of a car when it travels 75 miles in 3 hours 4. Expand and simplify: a. 3(x + 1) + 2(x + 4) b. 4(d + 2) -2(3 + d) c. (x + 2)(x + 3) 5. Factorise: a. x 2 + 5x b. 7x 2-21x c. 9x + 12y 6.
2 1. Simplify: Equations and Inequalities ANSWERS a. 4a + b + 3a - 2b b. 3y x 2y c. 5x2 20x x 7a b 6y Find the value of each expression when a = 3, b = -5 and c = 2 a. 10a + 10b b. a + c 2 c. 10a c = -20 =7 =15 3. Find the speed of a car when it travels 75 miles in 3 hours Speed = distance time 75 miles Speed = 3 hours = 25 miles per hour 4. Expand and simplify: a. 3(x + 1) + 2(x + 4) b. 4(d + 2) -2(3 + d) c. (x + 2)(x + 3) 3x x + 8 4d d x 2 + 3x + 2x + 6 = 5x + 11 = 2d + 2 = x 2 + 5x Factorise: a. x 2 + 5x b. 7x 2-21x c. 9x + 12y = x(x + 5) = 7x(x 3) = 3(3x + 4y)
3 Equations and Inequalities (2) 1. Simplify: a. x 2 + x 2 + x b. c d 2c c. 16x3 20x 2. Find the value of each expression when a = 4, b = -2 and c = -5 a. 10a + 10b b. a + c 2 c. 10a c 3. Find the speed of a car when it travels 126 miles in 3 hours 4. Expand and simplify: a. 3(2x + 1) + 2(x - 4) b. 4(2-g) -2(2 + g) c. 3(2 j) -4(j 3) 5. Factorise: a. 5x 3 + 2x 2 b. 12x 2 y - 4x c. 9x 3 y + 12xy 6.
4 Equations and Inequalities (2) ANSWERS 1. Simplify: b. x 2 + x 2 + x b. c d 2c c. 16x3 20x 2x 2 + x 2c 2 d 4x Find the value of each expression when a = 4, b = -2 and c = -5 b. 10a + 10b b. a + c 2 c. 10a c = 20 = 29 = Find the speed of a car when it travels 126 miles in 3 hours speed = distance time speed = speed = 42 mph 4. Expand and simplify: b. 3(2x + 1) + 2(x - 4) b. 4(2-g) -2(2 + g) c. 3(2 j) -4(j 3) 6x x g -4-2g 6 3j -4j x 5 4-6g 18 7j 5. Factorise: b. 5x 3 + 2x 2 b. 12x 2 y - 4x c. 9x 3 y + 12xy x 2 (5x + 2) 4x(3xy 1) 3xy(3x 2 + 4) 6.
5 Equations and Inequalities (3) 1. Simplify: a. 2g 2a + g + a b. s t s 2 c. 12x3 2x 2. Find the value of each expression when a = 7, b = -3 and c = -4 a. 10a + bc b. b + c 2 c. 3a b 3. Find the speed of a toy car when it travels 12 metres in 3 seconds 4. Expand and simplify: a. 3(2x - 1) b. 4(2 x) + 3(x 5) c. x(x 2 3) + x(5 y) 5. Factorise: a. 3x + 2x 2 b. 12x 3-4x 2 c. 3ab 12a 6.
6 1. Simplify: Equations and Inequalities (3) ANSWERS b. 2g 2a + g + a b. s t s 2 c. 12x3 2x 3g a b. s 3 t c. 6x 2 2. Find the value of each expression when a = 7, b = -3 and c = -4 b. 10a + bc b. b + c 2 c. 3a b = 82 = 13 = Find the speed of a toy car when it travels 12 metres in 3 seconds speed = distance time 12 metres speed = 3 seconds speed = 4 metres per second speed = 4 m/s 4. Expand and simplify: b. 3(2x - 1) b. 4(2 x) + 3(x 5) c. x(x 2 3) + x(5 y) 6x x + 3x 15 x 3 3x + 5x xy 7 x x 3 + 2x xy 5. Factorise: b. 3x + 2x 2 b. 12x 3-4x 2 c. 3ab 12a x(3 + 2x) 4x 2 (3x 1) 3a(b 4) 6. a) 15 boxes x 8 pens = 120 pens = 89 pens left b) (rs) t = number of pens left
7 Equations and Inequalities (4) 1. Simplify: a. d f + 2d + 2f b. r 2 r 2 b c. 10x4 2x 2. Find the value of each expression when a = 2.5, b = -4 and c = 7 a. 10a + bc b. a + b 2 c. 5b 2a 3. A toy car travels at 8 m/s for 6 seconds. How far did it travel? 4. Expand and simplify: a. 2(2x - 1) b. 2(2 x) 3(x 5) c. x(x 2) + x(5 x) 5. Factorise: a. 2x + x 2 b. 12st 2s c. x 3-2x 2 6.
8 7. Simplify: Equations and Inequalities (4) ANSWERS b. d f + 2d + 2f b. r 2 r 2 b c. 10x4 3d + f br 4 5x 3 8. Find the value of each expression when a = 2.5, b = -4 and c = 7 b. 10a + bc b. a + b 2 c. 5b 2a = -3 = 18.5 = A toy car travels at 8 m/s for 6 seconds. How far did it travel? 8 = distance 6 8 x 6 = distance 48 metres = distance 10. Expand and simplify: b. 2(2x - 1) b. 2(2 x) 3(x 5) c. x(x 2) + x(5 x) 4x 2 4 2x 3x + 15 x 2 2x + 5x x 2 = 19 5x = 3x 11. Factorise: b. 2x + x 2 b. 12st 2s c. x 3-2x 2 x(2 + x) 2s(6t 1) x 2 (x 2) 2x 12.
9 Equations and Inequalities (5) 1. Simplify/expand and simplify: a. 8x + 2x y 3x b. 3(x + 2) 5 c. 4(2 x) + x(3 + y) 2. If F = ma, what's the value of F when m = 5 and a = 3? 3. A taxi firm charges 0.50 per mile plus a fixed charge of Write down a formula for the cost C of hiring this taxi to travel n miles. 4. Solve: a) x 3 = 8 b) 2x + 3 = 8 c) 2 = 4x + 14 d) 3x = x a) Write an expression for the perimeter of this shape: x + 2 cm x + 3 cm x + 3 cm 2x + 5 cm c) The perimeter of the shape is 43 cm. Work out the value of x
10 Equations and Inequalities (5) ANSWERS 6. Simplify/expand and simplify: b. 8x + 2x y 3x b. 3(x + 2) 5 c. 4(2 x) + x(3 + y) 7x y 3x x + 3x + xy 8 x + xy 7. If F = ma, what's the value of F when m = 5 and a = 3? F = ma F = 5 x 3 F = A taxi firm charges 0.50 per mile plus a fixed charge of Write down a formula for the cost C of hiring this taxi to travel n miles x number of miles C = n 9. Solve: d) x 3 = 8 e) 2x + 3 = x = x = 11 2x = 8 3 2x = x = 5 2 x = 2.5 e) 2 = 4x + 14 f) 3x = x x x 2 14 = 4x 12 = 4x 3x x = 1 2x = = x 3 = x x = 1 2 x = a) Write an expression for the perimeter of this shape: x x x x + 3 5x + 13 x + 3 cm x + 2 cm x + 3 cm f) The perimeter of the shape is 43 cm. Work out the value of x 5x + 13 = x = x = x = 30 5 x = 6 2x + 5 cm
11 Equations and Inequalities (6) 1. Simplify/expand and simplify: a. b + a c + 2b a + 3 b. 4(x + 8) 3x c. 3(5 x) + 2(3 + 2x) A plumber charges a 50 call-out fee, plus 20 per hour (h). Write an expression for the total cost the plumber will charge. a) Solve: b) x 13 = 5 c) 3x + 2 = 14 c) 4x + 2 = 2x + 7 d) 5x = 2(x + 1) 4. a) Write an expression for the perimeter of this shape: 5x + 2 cm 2x + 3 cm x cm 3x cm The perimeter of the shape is 52 cm. Work out the value of x
12 Equations and Inequalities (6) ANSWERS 5. Simplify/expand and simplify: b. b + a c + 2b a + 3 b. 4(x + 8) 3x c. 3(5 x) + 2(3 + 2x) 3b c + 3 4x x 15 3x x x x 6. F = ma F = 10 2 F = A plumber charges a 50 call-out fee, plus 20 per hour (h). Write an expression for the total cost the plumber will charge h Cost ( ) = h d) Solve: e) x 13 = x = x = 8 f) 3x + 2 = x = x = x = 12 3 x = 4 e) 4x + 2 = 2x + 7 f) 5x = 2(x + 1) 2 2 5x = 2x + 2 4x = 2x x 2x 4x = 2x + 5 5x 2x = 2 2x 2x 3x = 2 2x = x = 2.5 x = 2 3 x = a) Write an expression for the perimeter of this shape: 2x x x + 2x x x cm 14x + 10 cm The perimeter of the shape is 52 cm. Work out the value of x 14x + 10 cm = x = x = x = x = 3 2x + 3 cm 5x + 2 cm 3x cm x + 3 cm x cm 2x + 2 cm
13 Equations and Inequalities (7) 1. Simplify/expand and simplify: a. b a + c + 2b a + 5 b. 4(5 x) + 8x c. 3(4 2x) + 2(3 + x) 2. A garage charges 60 per mot service, plus 20 per hour (h) for the time taken to fix the car. Write an expression for the total cost the garage will charge 3. Write the inequality shown on the number lines a. b. c Show the inequality on the number line a. 1 < x < 6 b. -1 < x 1 c. 0 x Solve: a) 2x 5 = 9 b) 3x + 2 = x a) Write an expression for the perimeter of this shape: 5x + 3 cm 2x + 4 cm 4 cm 3x cm The perimeter of the shape is 56 cm. Work out the value of x
14 Equations and Inequalities (7) ANSWERS 7. Simplify/expand and simplify: b. b a + c + 2b a + 5 b. 4(5 x) + 8x c. 3(4 2x) + 2(3 + x) 3b 2a + c x + 8x 12 6x x x 18 4x 8. A garage charges 60 per mot service, plus 20 per hour (h) for the time taken to fix the car. Write an expression for the total cost the garage will charge = h 9. Write the inequality shown on the number lines a. x < 4 b. x > 2 c. x Show the inequality on the number line a. 1 < x < 6 b. -1 < x 1 c. 0 x Solve: c) 2x 5 = 9 d) 3x + 2 = x a) Write an expression for the perimeter of this shape: 5x + 3 cm 2x + 4 cm 3x cm 2x x x x + 3x = 14x x cm 4 cm 2x + 3 cm The perimeter of the shape is 56 cm. Work out the value of x = x = 3
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