Huh Lab Maths › IGCSE Maths › Number
Topic 1 of the Cambridge IGCSE Mathematics (0580) syllabus: from types of number and sets to standard form, percentages and surds. Here is what each part asks, a practice question for each, and the mistakes that cost the most marks.
Each part with one practice question, made by the same engine your child plays. Parts marked Extended are for the Extended paper only.
Which of these is an INTEGER that is NOT a natural number?
−12. Natural numbers are the counting numbers 1, 2, 3, ... Integers also include zero and the negative whole numbers.
n(A) = 9, n(B) = 16 and n(A ∩ B) = 5.
Find n(A ∪ B).
20. Adding 9 and 16 counts the overlap twice. Take it off once: 9 + 16 − 5 = 20.
Evaluate 5⁰.
1. Anything (except 0) to the power 0 is 1.
Write 0.1111… as a fraction in its simplest form.
(The digit 1 repeats for ever.)
1/9. Call it x. 10x = 1.111…, and 10x − x = 1, so x = 1/9 = 1/9.
Which statement is true?
0.92 > 0.73. Write both the same way: 0.92 = 0.92 and 0.73 = 0.73. So 0.92 > 0.73.
5/6 ÷ 1/7 = ?
35/6. Flip the second fraction and multiply: 5/6 × 7/1 = 35/6.
Evaluate 2⁻².
1/4. A negative power means "one over": 2⁻² = 1/2² = 1/4.
Write 0.00065 in standard form.
6.5 × 10⁻⁴. Move the point 4 places so the number is between 1 and 10: 6.5 × 10⁻⁴.
Round each number to 1 significant figure to estimate
(27.7 × 3.9) ÷ 2.1
60. 27.7 ≈ 30, 3.9 ≈ 4 and 2.1 ≈ 2. 30 × 4 = 120, and 120 ÷ 2 = 60.
A length is 33 cm, to the nearest cm.
What is the upper bound?
33.5 cm. Half a unit either way: 33 + 0.5 = 33.5 cm.
$48 is shared in the ratio 5 : 7.
How much is the larger share?
$28. 5 + 7 = 12 parts. One part is 48 ÷ 12 = 4. The larger share is 7 × 4 = 28.
density = mass ÷ volume
A liquid has a density of 11 g/cm³. Find the mass of 100 cm³ of it.
1100 g. mass = density × volume = 11 × 100 = 1100 g.
$2,000 is invested at 10% simple interest per year.
How much interest after 5 years?
$1,000. One year: 10% of 2,000 = 200. Times 5 years = 1,000.
Write 1:15 pm in the 24-hour clock.
13:15. Afternoon and evening: add 12 to the hour. 13:15.
€1 = $1.2
Change €120 into dollars.
$144. Each euro is worth $1.2, so multiply: 120 × 1.2 = 144.
A population of 1,000 grows by 20% each year.
What is it after 2 years?
1,440. Each year it is multiplied by 1.2. After 2 years: 1,000 × 1.2² = 1,440. The 20% is taken of a NEW amount each year, so it is not 1,400.
Rationalise the denominator and simplify.
5/√5
√5. Multiply top and bottom by √5: 5√5 / 5 = √5.
Huh Lab checks every wrong answer against known mistakes like these, and goes back to the step behind the one your child keeps making.
√36 is 6, so the 36 comes out of the root as 6, not as 36.
10³ × 10⁴ is seven tens multiplied together: add the powers, 10⁷.
A percentage compares with the whole: divide by the whole, then times 100.
The percentage was of the ORIGINAL. Divide by the multiplier to go back.
In compound interest, year two earns interest on year one's interest as well.
Try dividing by 3 and 7: 21, 27 and 49 are odd but not prime.
Quarters plus quarters are still quarters. Only the tops are added.
Ask which currency has the bigger numbers. Going to it, multiply. Coming back, divide.
Short rounds on any topic, a new question every time, the exact mistake found, and a report to you after every session.
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