Paper 1F June 2025 Foundation tier, Question 21, also on the Higher paper 4 marks
x5 × x7 = xm
Find the value of m
y8 ÷ y3 = yn
Find the value of n
Simplify fully (5a4r2)3
Reveal mark scheme
Edexcel IGCSE Maths
x5 × x7 = xm
Find the value of m
y8 ÷ y3 = yn
Find the value of n
Simplify fully (5a4r2)3
x5 x7 = xm
Find the value of m
y8 ÷ y3 = yn
Find the value of n
Simplify fully (5a4r2)3
Simplify a6 a10
Simplify c30 c12
Factorise y2 10y
21
Hence, solve y2 10y
21
0
Also involves Fractions
Show clear algebraic working.
Write down the value of 50
Find the value of k
Simplify fully 2d4e5
3
Simplify 8d 4d
7d
Simplify m 10 p
Solve x 5
19
Simplify a a
a
a
k 8 and n = 12
Work out the value of 9k 4n
Simplify p3
5
Expand and simplify 2n4n
3
n
n
4
Show clear algebraic working.
Simplify (2p)0 where p 0
y9y–3 = yn
Find the value of n
Simplify fully (5a4c2)3
A 25
5
72 B
23
53
74
Write down the highest common factor (HCF) of 5A and 2B Give your answer as a product of prime factors.
A 25
5
72 B
23
53
74
Work out the value of AB
2 Give your answer as a product of prime factors.
Also involves Simplifying and manipulating expressions
Find the value of n
Show your working clearly.
Find the value of 3.42
Find the cube root of 373 248
Write 7 7
7
7
7
7 as a single power of 7
Write one set of brackets in each calculation to make the answer correct.
5 + 3 × 2 = 16
10 − 8 − 10 − 6 ÷ 2 = 0
Find the value of n
Show clear algebraic working.
Simplify h15 h3
Simplify fully 2g3k5
4
work out the value of n
27 45
4x
Calculate the value of x
Simplify 6a × 2c
Simplify 4d + 3e + d – 5e
Solve 4x – 7 = 23
Write down the prime number that lies between 90 and 100
Find the cube root of 79 507
Work out the value of 42 × 53
Write 2250 as a product of powers of its prime factors. Show your working clearly.
Simplify (2c4d7)3
Find the value of 5y0 where y 0
Factorise fully 16a2b3 + 20a3b
Factorise x2 + 9x – 22
Hence solve x2 + 9x – 22 = 0
Simplify m10 ÷ m3
kn k4 = k12
Write down the value of n
Simplify (3x6y8)2
Work out the value of n Show your working clearly.
Find 4% of 4.5 10157 Give your answer in standard form.
Also involves Simplifying and manipulating expressions
Express in the form pxn where p and n are integers.
Show clear algebraic working.
Simplify w12 w3
Simplify 5m4p22m3p
12Solve 2–4x = 32
Work out the value of m
5–10 ÷ 5– 4 = 5n
Work out the value of n
Also involves Substitution into formulae
y = c4 when x = c2 where c is a positive constant.
Find a formula for y in terms of x and c Give your answer in its simplest form.
Simplify c × c × c c
c
Solve 5 + x = 12
Expand 5(2 + 3h)
Factorise g2 + 7g
Also involves Powers and roots
Work out the value of (4 + 3 + 6)2
64 = 4n
Write down the value of n
Write down all the figures on your calculator display.
Also involves Straight line graphs · Factors, multiples and primes
Write down the value of (m + 2)0 where m is a positive integer.
Simplify (3a2b4)3
Factorise fully 14x2y4 + 21x3y2
The diagram shows a straight line drawn on a grid.
Write down an equation of the line.
Write down the value of (m + 2)0 where m is a positive integer.
Simplify (3a2b4)3
Factorise fully 14x2y4 + 21x3y2
The diagram shows a straight line drawn on a grid.
Write down an equation of the line.
Expand and simplify 5x(3x + 4)(2x – 1)
Also involves Quadratic equations
Find the values of n such that
Show clear algebraic working.
Simplify 8 (4t)0
x6 ÷ x−5 = xp
Find the value of p
Simplify fully (2k2m4)3
P = 3352
7 Q = 32
5
72
Write down the highest common factor (HCF) of P and Q
P = 3352
7 Q = 32
5
72
Work out the value of P3Q Give your answer in the form 3x
5y
7z where x, y and z are positive integers.
Expand and simplify (3 x – 1)(x + 2)(3 x + 1)
Write 1200 as a product of powers of its prime factors. Show your working clearly.
Find an expression for x in terms of k and n
Show clear algebraic working.
Simplify a0where a 0
Factorise fully 10c3d2 + 15cd4
Find an expression for x in terms of k and n
Simplify a7 a4
Simplify w15 ÷ w3
Simplify (8x5y3)2
Make t the subject of c = t3 – 8v
Simplify a7 a4
Simplify w15 ÷ w3
Simplify (8x5y3)2
Make t the subject of c = t3 – 8v
Expand and simplify 5 x (x + 2)(3 x – 4)
(b) Simplify completely
Write down the value of x0
Given that 2–3 29 = 2n
find the value of n
find the value of m
Write down the value of x0
Given that 2–3 29 = 2n
find the value of n
find the value of m
a = 6 1040
Work out the value of a3 Give your answer in standard form.
Write 3.6 103 as a product of powers of its prime factors. Show your working clearly.
Write down the value of g0
Factorise x2 – 11x + 24
A = 2835
114 B = 26
3
118
Find the highest common factor (HCF) of A and B.
Find the lowest common multiple (LCM) of 2A and 3B. Give the LCM as a product of powers of its prime factors.
Write down the value of g0
Factorise x2 – 11x + 24
Also involves Solving exponential equations
Write
as a single fraction in its simplest form.
Given that 4k+ 3 = 162k
find the value of k. Show your working clearly.
Write down the value of y0
Give your answer in standard form.
Also involves Simplifying and manipulating expressions
Simplify (3k2)4
Simplify (21m4n) (3n–5)
find the value of n.
A = 2 343 B = 16
337
Find the highest common factor (HCF) of A and B.
Express the number A B as a product of powers of its prime factors. Give your answer in its simplest form.
A = 2 343 B = 16
337
Find the highest common factor (HCF) of A and B.
Express the number A B as a product of powers of its prime factors. Give your answer in its simplest form.
find the values of n for which M = 2
Here are the first five terms of a number sequence.
1 3 9 27 81
Find the next term of this sequence.
Explain how you found this term.
The 9th term of this number sequence is 6561
Find the 10th term of this sequence.
Write 880 as a product of powers of its prime factors. Show your working clearly.
23Given that 150x = 1
write down the value of x.
Given that 3–8 ÷ 3–6 = 3n
find the value of n.
Also involves Simplifying and manipulating expressions
Show clear algebraic working.
find the value of x. Show clear algebraic working.
Make a the subject of d = g + 2 ac
Factorise fully 9e f− 12f
Expand and simplify (x+ 2)(x− 5)
Expand and simplify (m − 8)(m + 5)
Factorise fully 5y+ 20y2
Simplify (p2+ 3)0
Show clear algebraic working.
Also involves Simplifying and manipulating expressions
Show each stage of your working.
Simplify k + k + k + k
Write f as a single power of 9
Write f as a single power of 3
Write 517 52 as a single power of 5
Write 800 as a product of its prime factors. Show your working clearly.
Write 517 52 as a single power of 5
Write 800 as a product of its prime factors. Show your working clearly.
Also involves Quadratic equations
Find an expression for n in terms of y. Show clear algebraic working and simplify your expression.
Find the highest common factor (HCF) of 40 and 64
A = 2n × 3 × 5m
Write 8 A as a product of powers of its prime factors.
Also involves Simplifying and manipulating expressions
Simplify t9 ÷ t3
Simplify w5 w7
Simplify (5xy2)3
Also involves Factors, multiples and primes
A = 2n 3
5m
Write 8 A as a product of powers of its prime factors.
a = 25 1014n where n is an integer. Find an expression, in terms of n, for
Give your answer in standard form.
Also involves Simplifying and manipulating expressions
find an expression for n in terms of x and y.
Simplify (2e2 f3)3
Expand and simplify (3xy)(x + 3y)
Find the value of k.
Also involves Surds
Write 7 7
7
7
7 as a power of 7
Show that 64 is both a square number and a cube number.
Find the value of 113
Find the value of n.
(13–6)4 135 = 13k
Find the value of k.
Find the value of n.
(13–6)4 135 = 13k
Find the value of k.
Also involves Linear equations
128 = 42x 2x
Work out the value of x.
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