Paper 1 June 2025 Higher tier, Question 7 6 marks
Reveal mark scheme
Reveal mark scheme
Solve 9 < 2y + 4 < 12
Reveal mark scheme
Edexcel GCSE Maths
Topic questions Pure mathematics Simplifying and manipulating expressions
113 questions · 435 marks · about 8 hours
Solve 9 < 2y + 4 < 12
17g(x) = 1 โ 3xh(x) = 2x2 โ 1 Show that 3gh(x) + hg(x) = 0 has just one solution for x.
9 3xโ1(4x โ x3) = a + bxn for all the values of x that are not zero. Find the value of a, the value of b and the value of n.
Show that (2 x + 3)(x โ 1)(x + 2) can be written in the form ax3 + bx2 + cx + d where a, b, c and d are integers.
Simplify y10 รท y2
Simplify (e3)2
Expand x(3x2 + 5)
Expand and simplify (n + 5)(n โ 2)
23Ben is trying to make m the subject of p = + 5 Here is his working.
m = 3 p โ 5 Benโs answer is wrong.
What mistake has Ben made?
Factorise fully 2x3y + 4xy2
Ben is trying to make m the subject of p = + 5 Here is his working.
m = 3 p โ 5 Benโs answer is wrong.
What mistake has Ben made?
Factorise fully 2x3y + 4xy2
Find the value of n.
Write 64m12 in the form amb where a and b are integers.
Factorise 6 a + 15
Solve 4(3y + 1) = 28
Kate was asked to factorise x2 + 5x + 6 in the form (x + a)(x + b) Kate says, โThe sum of a and b must be 6 and the product of a and b must be 5โ
Explain what is wrong with Kateโs statement.
Factorise fully 2m2 โ 2
Factorise fully ax + bx โ ay โ by
Here are two cuboids.
All lengths are measured in centimetres. The volume of cuboid A is 142 cm3 greater than the volume of cuboid B. Work out the value of x.
Simplify 2x ร 3y
Simplify 3d โ 4e + 2d + e
Factorise fully 15w2 โ 5w
On the number line below, show the set of values of x for which โ2 x โค 4
Also involves Indices
Simplify fully 2x3y5 ร 7x2y
Simplify (m2)โ3
Also involves Indices
Simplify fully 2x3y5 ร 7x2y
Simplify (m2)โ3
Expand and simplify (3 x โ 1)(2 x + 3)(x โ 5)
Given that x + y = 8 work out the value of n.
Simplify 7a + a โ 5a
Factorise 6 x โ 15
Factorise m2 + 5m
Also involves Factors, multiples and primes
Factorise 3k2 + 11k โ 4
Expand and simplify (3 x + 2)(2 x โ 5)
Factorise x2 โ 16
Factorise 6x2 โ 5x โ 4
Hence, or otherwise, solve 6x2 โ 5x โ 4 < 0
Expand and simplify 3 (2 y โ 5) + 7 (y + 2)
Factorise fully 6x2 + 15x
Make g the subject of the formula f = 3g + 11
Expand and simplify 3(2y โ 5) + 7(y + 2)
Factorise fully 6x2 + 15x
Make g the subject of the formula f = 3g + 11
Expand and simplify (x + 7)(x โ 2)(x + 3)
Write
Simplify 8h3 + 14h3 โ 2h3
Simplify (9y + 12y) รท 3
find, in its simplest form, the ratio x:y
Simplify 19 + 5 b + 4 c โ 7 b + c
Factorise 8d โ 6
24The diagram shows 8 identical regular octagons joined to enclose a shaded shape.
Each octagon has sides of length a. Find, in terms of a, an expression for the area of the shaded shape.
Simplify (m2)3
Simplify x5รx8
Expand 4p(p2 + 3p)
Simplify (m2)3
Simplify x5x8
Expand 4p(p2 + 3p)
12Show that (x โ 1)(x + 3)(x โ 5) can be written in the form ax3 + bx2 + cx + d where a, b, c and d are integers.
Factorise a2 โ b2
Show that 240 โ 1 is the product of two consecutive odd numbers.
There is a total of y counters in a box. There are x pink counters and 5 blue counters in the box. The rest of the counters are green. x:y = 1: 3 Freda takes at random two counters from the box. Find, in terms of x, an expression for the probability that Freda takes two counters of the same colour.
Solve m โ 3 = 4
Solve 3n + n = 24
Factorise x2 + 10x + 9
Prove that (2m + 1)2 โ (2n โ 1)2 = 4(m + n)(m โ n + 1)
Sophia says that the result in part (a) shows that the difference of the squares of any two odd numbers must be a multiple of 4
Is Sophia correct? You must give reasons for your answer.
Simplify 4 c + 7 d + 3 c โ d
Solve 5(2m โ 6) = 40
There are x sweets in a box. There are y sweets in a packet.
Write an expression, in terms of x and y, for the total number of sweets in 3 boxes and 2 packets.
10Peter has to subtract (x2 โ 2x โ 4) from (x2 + 3x + 5) Here is his working
= x + 1 Explain what is wrong with Peterโs working.
Simplify fully (3x5y6)4
Expand and simplify (x + 2)(x โ 3)(x + 4)
Simplify (x3)5
Expand and simplify 4(x + 3) + 7(4 โ 2x)
Factorise fully 15x3 + 3x2y
Also involves Indices
Simplify (x3)5
Expand and simplify 4(x + 3) + 7(4 โ 2x)
Factorise fully 15x3 + 3x2y
Expand 3(4 โ 2 x)
Factorise 4p + 6
The diagram shows rectangle STUV. TQU and SRV are straight lines. All measurements are in cm.
The area of trapezium QUVR is Acm2 Show that A = 2x2 + 20x
The diagram shows rectangle STUV. TQU and SRV are straight lines. All measurements are in cm.
The area of trapezium QUVR is Acm2 Show that A = 2x2 + 20x
Factorise fully 4p2 โ 36
Show that (m + 4)(2m โ 5)(3m + 1) can be written in the form am3 + bm2 + cm + d where a, b, c and d are integers.
Expand 2(a + d)
Factorise 6y2 โ 5y
Solve 4x โ 7 = 37
Here is a shape with all its measurements in centimetres.
The area of the shape is Acm2 Show that A = 2x2 + 24x + 46
Simplify c5 รท c2
Simplify (d4)3
Expand and simplify (x โ 2)(3 x + 2)(2 x + 3)
Simplify ab
4
Simplify 4x + 3 โ x + 5
Expand y (y + 5)
Factorise 4a โ 6
Solve 2(5x โ 4) = 21
Simplify 4e2f 5ef3
Work out the value of a and the value of n.
an integer.
Expand x (x โ 4)
Factorise 15y โ 10
Solve 7(f โ 5) = 28
Make q the subject of p = 6 q + 7
Simplify (mโ2)โ3
Simplify 3e โ e + 4e
Also involves Indices
Simplify (3n4w2)3
Here are two squares, A and B.
The length of each side of square B is 4 cm greater than the length of each side of square A. The area of square B is 70 cm2 greater than the area of square A. Find the area of square B. Give your answer correct to 3 significant figures. You must show all your working.
Simplify 3 x + 5 y + 2 x โ 4 y
Solve 5p + 7 = 22
Simplify n3 ร n5
Simplify n3 ร n5
Express
as a single fraction in its simplest form.
Expand and simplify (x โ 3)(2x + 3)(4x + 5)
5 c + d = c + 4 d
Find the ratio c: d
6xยฒ = 7xy + 20yยฒ where x ห 0 and y ห 0
Find the ratio x: y
Also involves Indices
Simplify (p2)5
Simplify 12x7y3 รท 6x3y
Also involves Indices
Simplify (p2)5
Simplify 12x7y3 รท 6x3y
Factorise (x + y)2 + 3(x + y)
Expand and simplify (x + 5)(x โ 9)
Factorise fully 9x2 + 6x
Expand and simplify (x + 5)(x โ 9)
Factorise fully 9x2 + 6x
Prove algebraically that the sum of the squares of any two consecutive even numbers is always a multiple of 4
Expand 5(2 m โ 3)
Factorise 3 n + 12
The functions f and g are such that
Find fโ1(x)
Given that fg(x) = 2gf(x),
show that 15x2 โ 12x โ 1 = 0
Simplify 4e + 6f + 7e f
Show that (2x + 1)(x 3)(3x + 7) can be written in the form ax3 + bx2 + cx
d where a, b, c and d are integers.
Simplify 3mm
m + 3m
Simplify 2 n
p
4
Solve 3(x โ 4) = 12
Factorise fully 9b โ 3b2
Expand and simplify (5 x + 2)(2 x โ 3)
Factorise x2 + 4x + 3
Write
in the form
where a, b, c and d are integers.
Express +
โ
as a single fraction in its simplest form.
Also involves Symmetry
The diagram shows a pentagon. The pentagon has one line of symmetry.
AE = 4 x AB = 2 x + 1 BC = x + 2
All these measurements are given in centimetres.
The perimeter of the pentagon is 18 cm.
Show that 10 x + 6 = 18
Find the value of x.
Expand and simplify (x โ 2)(2 x + 3)(x + 1)
Find the value of n.
Solve 5x2 โ 4x โ 3 = 0 Give your solutions correct to 3 significant figures.
Simplify 3 4t
Simplify 8a โ 3a + 2a
P = 4 x + 3 y
x y = โ 2
Work out the value of P.
Expand 4 e (e + 2)
Solve 3(m โ 4) = 21
Factorise a2 โ b2
Hence, or otherwise, simplify fully (x2 + 4)2 โ (x2 โ 2)2
Also involves Rational expressions
Simplify m3 m4
Simplify (5np3)3
Simplify m3 m4
Simplify (5np3)3
Expand and simplify 5(p + 3) โ 2(1 โ 2 p)
Expand and simplify 5(p + 3) โ 2(1 โ 2 p)
Here are five straight rods.
All measurements are in centimetres.
The total length of the five rods is L cm.
Find a formula for L in terms of a. Write your formula as simply as possible.
Here is a rectangle and a right-angled triangle.
All measurements are in centimetres. The area of the rectangle is greater than the area of the triangle.
Find the set of possible values of x.
Simplify 3 fg
Simplify t ร t
Find the value of x.
(72)y10
Find the value of y.
100a ร 1000b can be written in the form 10w
Show that wa + 3b
Solve 2x2
Expand and simplify (2 x + 1)(3 x โ 2)
Factorise x2 + 6x + 9
Simplify y + 3 y โ 2 y
Factorise 4 m + 12
expression equation formula identity
inequality term factor multiple
Choose two words from the box above to make this statement correct.
5y is a........ in the........ 3x + 5y
The area of square ABCD is 10 cm2.
Show that x2 + 6x = 1
Work out the exact value of x.
2 โ โ
can be written as a single fraction in the form
where a and b are integers.
Work out the value of a and the value of b.
Memes
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