Edexcel GCSE Maths · N1–N9

Structure and calculation

50 maths questions with worked answers with answers for N1–N9 Structure and calculation in Edexcel GCSE Maths (spec 1MA1). Practise with flashcards, a topic quiz, a random quiz across the course, 5 crosswords, or read every question and answer below. Not official Pearson material.

All 50 questions and answers

Question 1 · Ordering · N1
Write these in order from smallest: 0.6, 58, 0.59, 23.
Answer:
Convert to decimals: 58 = 0.625 and 23 = 0.666…
Order: 0.59, 0.6, 58, 23.
Question 2 · Inequality symbols · N1
Insert < or > between −7 and −4.
Answer:
−7 is further below zero than −4.
−7 < −4.
Question 3 · Ordering · N1
Order from smallest: −3.2, −3.02, −3.5, −3.25.
Answer:
The most negative number is smallest.
−3.5, −3.25, −3.2, −3.02.
Question 4 · Inequality symbols · N1
What does the symbol ≠ mean?
Answer:
It means "is not equal to".
For example, 3 + 4 ≠ 8.
Question 5 · Negative numbers · N2
Calculate −8 × −6.
Answer:
A negative multiplied by a negative is positive.
−8 × −6 = 48.
Question 6 · Negative numbers · N2
Calculate −15 ÷ 3 + 7.
Answer:
Divide first: −15 ÷ 3 = −5.
−5 + 7 = 2.
Question 7 · Written methods · N2
Calculate 3.6 × 0.4.
Answer:
36 × 4 = 144.
There are two decimal places in total, so 3.6 × 0.4 = 1.44.
Question 8 · Written methods · N2
Calculate 7.2 ÷ 0.08.
Answer:
Multiply both numbers by 100: 720 ÷ 8.
720 ÷ 8 = 90.
Question 9 · Mixed numbers · N2
Calculate 213 + 134.
Answer:
Whole numbers: 2 + 1 = 3. Fractions: 13 + 34 = 412 + 912 = 1312 = 1112.
Total = 4112.
Question 10 · Mixed numbers · N2
Calculate 112 × 223.
Answer:
Convert to improper fractions: 32 × 83.
246 = 4.
Question 11 · Fractions · N2
Calculate 56 ÷ 23.
Answer:
Multiply by the reciprocal: 56 × 32 = 1512.
Simplify: 54 = 114.
Question 12 · Place value · N2
Given 23 × 47 = 1081, find 2.3 × 0.47.
Answer:
2.3 is 23 ÷ 10 and 0.47 is 47 ÷ 100.
1081 ÷ 1000 = 1.081.
Question 13 · Order of operations · N3
Calculate 4 + 6 × 3².
Answer:
Index first: 3² = 9. Then multiply: 6 × 9 = 54.
4 + 54 = 58.
Question 14 · Order of operations · N3
Calculate (12 − 4)² ÷ 4.
Answer:
Brackets first: 12 − 4 = 8. Then 8² = 64.
64 ÷ 4 = 16.
Question 15 · Inverse operations · N3
A number is multiplied by 6 and then 11 is subtracted. The result is 37. Find the number.
Answer:
Work backwards: 37 + 11 = 48.
48 ÷ 6 = 8.
Question 16 · Reciprocals · N3
What is the reciprocal of 0.25?
Answer:
0.25 = 14.
The reciprocal is 41 = 4.
Question 17 · Primes · N4
List the prime numbers between 20 and 40.
Answer:
A prime has exactly two factors.
23, 29, 31, 37.
Question 18 · Prime factorisation · N4
Write 180 as a product of prime factors in index form.
Answer:
180 = 2 × 90 = 2 × 2 × 45 = 2 × 2 × 3 × 15 = 2 × 2 × 3 × 3 × 5.
180 = 2² × 3² × 5.
Question 19 · HCF · N4
Find the highest common factor of 84 and 120.
Answer:
84 = 2² × 3 × 7 and 120 = 2³ × 3 × 5.
HCF = 2² × 3 = 12.
Question 20 · LCM · N4
Find the lowest common multiple of 18 and 24.
Answer:
18 = 2 × 3² and 24 = 2³ × 3.
LCM = 2³ × 3² = 72.
Question 21 · HCF and LCM · N4
Buses leave every 12 minutes and trams every 20 minutes. Both leave at 9:00. When do they next leave together?
Answer:
LCM of 12 and 20: 12 = 2² × 3, 20 = 2² × 5, so LCM = 60.
They next leave together at 10:00.
Question 22 · Prime factorisation · N4
A = 2³ × 3 × 5² and B = 2 × 3² × 5. Find the HCF of A and B.
Answer:
Take the lowest power of each common prime.
HCF = 2 × 3 × 5 = 30.
Question 23 · Listing · N5
How many two-digit codes can be made using the digits 1, 2, 3 and 4 if digits can repeat?
Answer:
There are 4 choices for each digit.
4 × 4 = 16 codes.
Question 24 · Product rule · N5 · Higher only
A menu has 3 starters, 5 mains and 4 desserts. How many three-course meals are possible?
Answer:
Use the product rule for counting.
3 × 5 × 4 = 60 meals.
Question 25 · Product rule · N5 · Higher only
How many ways can 4 different books be arranged on a shelf?
Answer:
4 choices for the first place, then 3, 2 and 1.
4 × 3 × 2 × 1 = 24.
Question 26 · Powers · N6
Calculate 2⁵.
Answer:
2 × 2 × 2 × 2 × 2.
2⁵ = 32.
Question 27 · Roots · N6
Find the cube root of 125.
Answer:
5 × 5 × 5 = 125.
∛125 = 5.
Question 28 · Powers · N6
Which is larger, 3⁴ or 4³?
Answer:
3⁴ = 81 and 4³ = 64.
3⁴ is larger.
Question 29 · Index laws · N7
Simplify 5⁷ × 5³.
Answer:
Add the indices when multiplying.
5⁷ × 5³ = 5¹⁰.
Question 30 · Index laws · N7
Simplify (2⁴)³.
Answer:
Multiply the indices for a power of a power.
(2⁴)³ = 2¹².
Question 31 · Index laws · N7
What is 7⁰?
Answer:
Any non-zero number to the power 0 is 1.
7⁰ = 1.
Question 32 · Negative indices · N7 · Higher only
Evaluate 4⁻².
Answer:
A negative index means the reciprocal.
4⁻² = 14² = 116.
Question 33 · Fractional indices · N7 · Higher only
Evaluate 27 to the power 23.
Answer:
Take the cube root first: ∛27 = 3.
Then square: 3² = 9.
Question 34 · Fractional indices · N7 · Higher only
Evaluate 16 to the power −12.
Answer:
16 to the power 12 is √16 = 4.
The negative index gives the reciprocal: 14.
Question 35 · Surds · N7 · Higher only
Simplify √72.
Answer:
72 = 36 × 2.
√72 = √36 × √2 = 6√2.
Question 36 · Surds · N7 · Higher only
Simplify √12 + √27.
Answer:
√12 = 2√3 and √27 = 3√3.
2√3 + 3√3 = 5√3.
Question 37 · Surds · N7 · Higher only
Rationalise the denominator of 6√3.
Answer:
Multiply top and bottom by √3: 6√33.
Simplify: 2√3.
Question 38 · Surds · N7 · Higher only
Expand and simplify (3 + √2)(3 − √2).
Answer:
Difference of two squares: 3² − (√2)².
9 − 2 = 7.
Question 39 · Exact answers · N8
Give the exact circumference of a circle with diameter 9 cm.
Answer:
Circumference = πd.
π × 9 = 9π cm.
Question 40 · Exact answers · N8
Calculate 34 of 225 exactly.
Answer:
225 = 125.
34 × 125 = 3620 = 95 = 145.
Question 41 · Exact answers · N8 · Higher only
A circle has area 49π cm². Find its exact circumference.
Answer:
πr² = 49π, so r = 7 cm.
Circumference = 2πr = 14π cm.
Question 42 · Standard form · N9
Write 340 000 in standard form.
Answer:
Move the decimal point 5 places.
340 000 = 3.4 × 10⁵.
Question 43 · Standard form · N9
Write 0.00072 in standard form.
Answer:
Move the decimal point 4 places right.
0.00072 = 7.2 × 10⁻⁴.
Question 44 · Standard form · N9
Write 5.06 × 10³ as an ordinary number.
Answer:
Multiply 5.06 by 1000.
5060.
Question 45 · Standard form · N9
Calculate (3 × 10⁴) × (5 × 10⁶). Give your answer in standard form.
Answer:
3 × 5 = 15 and 10⁴ × 10⁶ = 10¹⁰.
15 × 10¹⁰ = 1.5 × 10¹¹.
Question 46 · Standard form · N9
Calculate (8 × 10⁹) ÷ (2 × 10³).
Answer:
8 ÷ 2 = 4 and 10⁹ ÷ 10³ = 10⁶.
4 × 10⁶.
Question 47 · Standard form · N9 · Higher only
Calculate (6 × 10⁵) + (4 × 10⁴). Give your answer in standard form.
Answer:
Convert: 600 000 + 40 000 = 640 000.
6.4 × 10⁵.
Question 48 · Standard form · N9 · Higher only
Light travels 3 × 10⁸ m per second. How far does it travel in 2 × 10³ seconds?
Answer:
Distance = speed × time.
3 × 10⁸ × 2 × 10³ = 6 × 10¹¹ m.
Question 49 · Calculator use · N3
Use a calculator to work out √(5.2² + 3.9²). Give your answer to 1 decimal place.
Answer:
5.2² + 3.9² = 27.04 + 15.21 = 42.25.
√42.25 = 6.5.
Question 50 · Negative numbers · N2
The temperature is −6 °C. It rises by 11 °C. What is the new temperature?
Answer:
−6 + 11.
5 °C.

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