Edexcel AS And A Level Mathematics Pure Mathematics Year 1/AS 1st Edition Greg Attwood - Solutions

Expand and simplify if possible:a. 5(x + 1)(x − 4) b. 7(x − 2)(2x + 5) c. 3(x − 3)(x − 3)d. x(x − y)(x + y) e. x(2x + y)(3x + 4) f. y(x − 5)(x + 1)g. y(3x − 2y)(4x + 2) h. y(7 − x)(2x − 5) i. x(2x + y)(5x − 2)j. x(x + 2)(x + 3y − 4) k. y(2x +
Simplify √75 − √12 giving your answer in the form a√3, where a is an integer.
Factorise completely:a. x3 + 2x b. x3 − x2 + x c. x3 − 5xd. x3 − 9x e. x3 − x2 − 12x f. x3 + 11x2 + 30xg. x3 − 7x2 + 6x h. x3 − 64x i. 2x3 − 5x2 − 3xj. 2x3 + 13x2 + 15x k. x3 − 4x l. 3x3 + 27x2 + 60x
Expand and simplify if possible:a. x(x + 4)(x − 1) b. (x + 2)(x − 3)(x + 7) c. (2x + 3)(x − 2)(3x − 1)
Factorise completely x4 − y4.
Expand the brackets:a. 3(5y + 4) b. 5x2(3 − 5x + 2x2) c. 5x(2x + 3) − 2x(1 − 3x) d. 3x2(1 + 3x) − 2x(3x −2)
a. Find the value of 811/4.b. Simplify x(2x−1/3)4.
A cuboid has dimensions x + 2 cm, 2x − 1 cm and 2x + 3 cm. Show that the volume of the cuboid is 4x3 + 12x2 + 5x – 6 cm3.
Given that (2x + 5y)(3x − y)(2x + y) = ax3 + bx2y + cxy2 + dy3, where a, b, c and d are constants, find the values of a, b, c and d.
Factorise completely 6x3 + 7x2 − 5x.
Factorise these expressions completely:a. 3x2 + 4x b. 4y2 + 10y c. x2 + xy + xy2 d. 8xy2 + 10x2y
Given that y = 1/8x3 express each of the following in the form kxn, where k and n are constants.a. y1/3b. 1/2y−2
Factorise:a. x2 + 3x + 2 b. 3x2 + 6x c. x2 − 2x − 35 d. 2x2 − x − 3e. 5x2 − 13x − 6 f. 6 − 5x − x2
Factorise:a. 2x3 + 6x b. x3 − 36x c. 2x3 + 7x2 − 15x
Solve the equationGive your answer in the form a√b where a and b are integers. 8 + x√12 = 8.x √√3
Factorise completely x − 64x3.
Express 272x + 1 in the form 3y, stating y in terms of x.
A rectangle has a length of (1 + √3) cm and area of √12 cm2. Calculate the width of the rectangle in cm. Express your answer in the form a + b√3 , where a and b are integers to be found.
a. Calculate the value of the discriminant for each of these five functions:i. f(x) = x2 + 8x + 3 ii. g(x) = 2x2 − 3x + 4 iii. h(x) = −x2 + 7x − 3iv. j(x) = x2 − 8x + 16 v. k(x) = 2x − 3x2 − 4b. Using your answers to part a, match the same five functions to these sketch
Rationalise the denominator and simplify: A d √√3 b 23-√37 23+√37 1 √2-1 e с 1 (2+√3)² 3 √3-2 f 1 (4-√7)²
Show thatcan be written in the form √a + √b, where a and b are integers. 5 √75-√50
Show thatcan be written as 4x−1/2 − 4 +  x1/2. (2-√x) √x 2
Simplify:a. 9x3 ÷ 3x−3 b. (43/2)1/3 c. 3x−2 × 2x4 d. 3x1/3 ÷ 6x2/3
Evaluate:a. (8/27)2/3b. (225/289)3/2
Simplify:a. 3/√63b. √20 + 2√45 − √80
a. Find the value of 35x2 + 2x − 48 when x = 25.b. By factorising the expression, show that your answer to part a can be written as the product of two prime factors.
Given thatcan be written in the form 4xa +  xb, write down the value of a and the value of b. 5 4x3 + x² X
The diagram shows a section of a suspension bridge carrying a road over water.The height of the cables above water level in metres can be modelled by the function h(x) = 0.000 12x2 + 200, where x is the displacement in metres from the centre of the bridge.a. Interpret the meaning of the constant
Expand and simplify if possible:a. √2 (3 + √5) b. (2 − √5 )(5 + √3) c. (6 − √2 )(4 − √7)
a. Given that x3 − x2 − 17x − 15 = (x + 3)(x2 + bx + c), where b and c are constants, work out the values of b and c.b. Hence, fully factorise x3 − x2 − 17x − 15.
Given that y =  1/64x3 express each of the following in the form kxn, where k and n are constants.a. y1/3 b. 4y−1
Expand and simplify (√11− 5)(5 − √11).
Given that 243√3  =  3a, find the value of a.
Sketch the graphs of the following equations. For each graph, show the coordinates of the point(s) where the graph crosses the coordinate axes, and write down the coordinate of the turning point and the equation of the line of symmetry.a. y = x2 − 6x + 8 b. y = x2 + 2x − 15 c. y = 25
Using the functions f(x) = 5x + 3, g(x) = x2 − 2 and h(x) = √x + 1 , find the values of:a. f(1) b. g(3) c. h(8) d. f(1.5) e. g (√2)f. h (−1) g f(4) + g(2) h. f(0) + g(0) + h(0)i. g(4)/h(3)
Solve the following equations without a calculator. Leave your answers in surd form where necessary.a. y2 + 3y + 2 = 0 b. 3x2 + 13x − 10 = 0 c. 5x2 − 10x = 4x + 3 d. (2x − 5)2 = 7

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