International A LevelMaths: Pure 1EdexcelExam Questions1. Algebra & Functions1.5 Polynomials

Polynomials (Edexcel International A Level Maths: Pure 1)

Exam Questions

2 hours22 questions
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1
Sme Calculator5 marks

Expand

(i)
3 left parenthesis x squared plus 4 right parenthesis

(ii)
5 y squared left parenthesis y minus 6 right parenthesis

(iii)
x y left parenthesis 2 x plus 7 y right parenthesis

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2
Sme Calculator5 marks

Expand and simplify

(i)
left parenthesis 2 x plus 3 right parenthesis left parenthesis x minus 4 right parenthesis

(ii)
2 p left parenthesis p plus 3 right parenthesis left parenthesis p minus 2 right parenthesis

(iii)
left parenthesis y minus 1 right parenthesis left parenthesis y minus 2 right parenthesis squared

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3
Sme Calculator4 marks

(i) A triangle has base left parenthesis 6 x plus 8 right parenthesis and height 2 x units. Find an expression for the area of the triangle.

(ii) A cube has side length of open parentheses 3 x space minus space 5 close parentheses units. Find an expression for the volume of the cube.

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4
Sme Calculator5 marks

Factorise

(i)
5 x minus 20

(ii)
2 y squared minus 4 y

(iii)
8 x y squared plus 6 x y

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5
Sme Calculator7 marks

Factorise

(i)
x squared plus 5 x plus 4

(ii)
x squared minus 7 x plus 12

(iii)
x squared plus 5 x minus 14

(iv)
x squared minus 81

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6
Sme Calculator4 marks

Factorise

(i)
4 x squared minus 4 x minus 15

(ii)
3 x cubed plus 11 x squared minus 4 x

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1
Sme Calculator5 marks

Expand and simplify

(i)
5 left parenthesis x squared minus 3 right parenthesis plus 3 x left parenthesis x plus 8 right parenthesis

(ii)
4 y squared minus 2 y squared left parenthesis y minus 8 right parenthesis

(iii)
2 x squared left parenthesis 2 x plus 4 right parenthesis minus 3 x left parenthesis 2 x minus 7 right parenthesis

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2a
Sme Calculator1 mark

Expand and simplify y left parenthesis 2 x plus 2 right parenthesis left parenthesis 7 minus x right parenthesis.

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2b
Sme Calculator2 marks

A rectangle has side lengths of left parenthesis 3 x minus 2 y plus 5 right parenthesis units and left parenthesis x plus 3 y minus 1 right parenthesis units. Find an expression for the area of the rectangle in terms of x and y.

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3
Sme Calculator5 marks

Expand and simplify

(i)
left parenthesis 3 x plus 2 right parenthesis left parenthesis 2 x plus 6 right parenthesis

(ii)
left parenthesis 3 minus p right parenthesis left parenthesis p minus 2 right parenthesis

(iii)
left parenthesis y plus 5 right parenthesis squared left parenthesis y minus 8 right parenthesis

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4
Sme Calculator2 marks

Given that left parenthesis 3 x plus y right parenthesis left parenthesis 2 x minus 3 y right parenthesis left parenthesis x minus 2 y right parenthesis equals a x cubed plus b x squared y plus c x y squared plus d y cubedwhere  a,b,c and d are constants, find the values of a,b,c and d.

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5
Sme Calculator7 marks

Factorise

(i)
5 x squared minus 7 x minus 6

(ii)
2 x squared plus 2 x minus 12

(iii)
15 x squared plus 13 x plus 2

(iv)
9 x squared minus 16

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6
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Factorise completely 3 x cubed minus 51 x squared plus 126 x.

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1a
Sme Calculator1 mark

Expand and simplify left parenthesis 2 minus x right parenthesis left parenthesis 3 x plus 1 right parenthesis left parenthesis x plus 1 right parenthesis.

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1b
Sme Calculator2 marks

A square has side lengths of left parenthesis 5 x minus 2 y plus 3 right parenthesis units. Find an expression for the length of the diagonal of the square in terms of xand y .

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2
Sme Calculator5 marks

Expand and simplify

(i)
left parenthesis x minus 2 right parenthesis left parenthesis 3 x plus 2 right parenthesis left parenthesis 2 x plus 6 right parenthesis

(ii)
left parenthesis 2 minus p right parenthesis squared left parenthesis p plus 3 right parenthesis

(iii)
left parenthesis y plus 6 right parenthesis cubed

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3
Sme Calculator2 marks

Given that left parenthesis 2 x minus 3 y right parenthesis squared left parenthesis y minus 2 x right parenthesis equals a x cubed plus b x squared y plus c x y squared plus d y cubed, where a,b,c and d are constants, find the values of a,b,c and d.

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4
Sme Calculator7 marks

Factorise

(i)
negative x squared plus 26 x – 169

(ii)
10 x squared minus 11 x plus 3

(iii)
4 x squared minus 25 y squared

(iv)
18 x cubed minus 6 x squared minus 12 x

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5
Sme Calculator2 marks

Factorise completely 15 x cubed plus 19 x squared minus 10 x.

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1
Sme Calculator5 marks

Expand and simplify

(i)
left parenthesis x plus 3 right parenthesis squared plus left parenthesis x minus 2 right parenthesis left parenthesis 2 x plus 4 right parenthesis

(ii)
3 x left parenthesis 8 minus x right parenthesis left parenthesis 3 x minus 3 right parenthesis

(iii)
left parenthesis p plus 6 right parenthesis to the power of 4

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2a
Sme Calculator2 marks

Expand and simplify left parenthesis x plus y right parenthesis left parenthesis x minus y right parenthesis left parenthesis y minus x right parenthesis left parenthesis negative x minus y right parenthesis.

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2b
Sme Calculator2 marks

A cuboid has a length of left parenthesis 2 x minus 3 y plus 3 right parenthesis spaceunits , a width of left parenthesis 2 x plus 3 y minus 3 right parenthesis spaceunits, and a height of left parenthesis x minus y right parenthesisunits. Find an expression for the volume of the cuboid in terms of x and y.

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3
Sme Calculator3 marks

Given that left parenthesis a x plus b y right parenthesis left parenthesis 2 x plus y right parenthesis left parenthesis x minus 3 y right parenthesis equals 8 x cubed plus c x squared y plus d x y squared minus 9 y cubed , where a,b,c and d are constants, find the values of a,b,c and d.

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4
Sme Calculator7 marks

Factorise

(i)
12 x squared minus 17 x minus 5

(ii)
10 x cubed plus 55 x squared plus 60 x

(iii)
15 x cubed minus 6 x squared minus 9 x

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5
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Factorise completely x to the power of 5 y minus x y to the power of 5.

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