One question at a time. Build your BGCSE understanding.
First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.
Continue in the practice tool above to load more questions, 50 at a time.
A 15% reduction removes 0.15 × 80 = 12 dollars from the original price, leaving 80 − 12 = 68 dollars. Equivalently, the sale price is 85% of the original, that is 0.85 × 80 = 68 dollars.
Rewrite both fractions over the common denominator 12: 2/3 = 8/12 and 1/4 = 3/12. Adding the numerators gives 8 + 3 = 11, so the sum is 11/12, and no common factor remains.
The interior angles of any triangle add up to 180°. Subtracting the two known angles gives 180 − 48 − 67 = 65°, which is positive and less than 180°, so it is a valid third angle.
Collect the x terms on one side and the constants on the other: 5x − 3x = 9 + 7, so 2x = 16 and x = 8. Substituting 8 back gives 33 on both sides, which confirms the solution.
The ratio 3 : 5 contains 3 + 5 = 8 equal parts, so each part is worth 240 ÷ 8 = 30 dollars. The larger share is 5 parts, that is 5 × 30 = 150 dollars, while the smaller share is 90 dollars.
Standard form requires A × 10ⁿ where 1 ≤ A < 10. Moving the decimal point in 0.00046 four places to the right gives 4.6, and because the original number is less than 1 the index is negative, so the answer is 4.6 × 10⁻⁴.
The mean of five numbers is 12, so their total must be 5 × 12 = 60. The four given numbers add to 9 + 14 + 10 + 15 = 48, so the missing number is 60 − 48 = 12.
There are 5 + 3 + 2 = 10 counters in total, and 3 + 2 = 5 of them are not red. The probability is therefore 5/10, which simplifies to 1/2; this also follows from P(not red) = 1 − P(red).
The wall, the ground and the ladder form a right-angled triangle with the ladder as the hypotenuse. The height up the wall is the side opposite the 65° angle, so height = 8 × sin 65° ≈ 8 × 0.9063 ≈ 7.25 m, which rounds to 7.3 m.
Rearranging the second equation gives x = y + 1. Substituting into the first gives 2(y + 1) + 3y = 12, so 5y + 2 = 12, giving y = 2 and then x = 3. Checking: 2(3) + 3(2) = 12 and 3 − 2 = 1.
To round to 3 decimal places, look at the fourth decimal digit. In 0.04728 that digit is 2, and since 2 is less than 5 the third decimal digit stays unchanged, so the value is 0.047.
The factor 4 multiplies every term inside the bracket, not just the first one. So 4 × 2x = 8x and 4 × 5 = 20, and because the second term inside the bracket is negative the result is 8x − 20.
The area of a rectangle is found by multiplying its length by its width. Here 7.5 × 4 = 30, and because area is measured in square units the answer is 30 cm².
We need two numbers whose product is 12 and whose sum is 7, namely 3 and 4. Since the product and the sum are both positive, both brackets take a plus sign, giving (x + 3)(x + 4).
Compound interest applies the rate to the new amount each year. After one year the value is 500 × 1.04 = 520, and after two years it is 520 × 1.04 = 540.80 dollars.
The exterior angles of any convex polygon add up to 360°. In a regular polygon all the exterior angles are equal, so the number of sides is 360 ÷ 24 = 15.
The probability that the first counter is red is 4/10, and then only 3 reds remain among the 9 counters left, giving 3/9. Multiplying these gives 12/90, which simplifies to 2/15.
First multiply both sides by 5 to obtain 5y = x + 2, then subtract 2 from both sides. This gives x = 5y − 2, with x now standing alone as the subject.
We look for two numbers whose product is −14 and whose sum is −5; these are −7 and 2. The equation therefore factorises as (x − 7)(x + 2) = 0, giving x = 7 or x = −2.
The cosine rule states that a² = b² + c² − 2bc cos A. Substituting gives BC² = 49 + 81 − 126 cos 120°, and since cos 120° = −0.5 this becomes 130 + 63 = 193, so BC = √193 ≈ 13.9 cm.
Multiply before adding. 3 × (−4) = −12, so the expression becomes −7 + (−12), which equals −19.
Divide the numerator by the denominator. 3 ÷ 8 = 0.375, so the fraction is written as 0.375.
Collect like terms separately. The a terms give 3a − a = 2a, and the b terms give 4b + 2b = 6b, so the result is 2a + 6b.
Use Pythagoras’ theorem: square the two legs and add them. 9² + 12² = 81 + 144 = 225, and √225 = 15 cm.
Profit is selling price minus cost price: $5,400 − $4,500 = $900. Percentage profit = 900 ÷ 4,500 × 100 = 20%.
Add 5 to both sides to get 3x < 12. Divide by positive 3, so the inequality sign stays the same: x < 4.
The area of a circle is πr². Since r = 6, r² = 36, so the area is 36π cm².
Convert 2 hours 30 minutes to 2.5 hours. Average speed = distance ÷ time = 240 ÷ 2.5 = 96 km/h.
Cube each factor in the bracket. The coefficient becomes 2³ = 8, and the exponents are multiplied by 3: x³ becomes x⁹ and y² becomes y⁶.
Exactly one rainy day can happen in two orders: rain then dry, or dry then rain. The probability is 0.3 × 0.7 + 0.7 × 0.3 = 0.21 + 0.21 = 0.42.
Standard form is written as A × 10^n, where 1 ≤ A < 10. For 0.00036, the decimal point moves four places to the right to give 3.6, so the exponent is −4. Therefore 0.00036 = 3.6 × 10^−4.
For two events, P(French or Spanish) = P(French) + P(Spanish) − P(both). Substituting gives 0.4 + 0.3 − 0.1 = 0.6. The subtraction avoids counting students who study both languages twice.
The volume of a cylinder is V = πr²h. Substitute r = 5 and h = 12: V = π × 5² × 12 = π × 25 × 12 = 300π. The units are cm³.
Complete the square: x² + 8x + 3 = (x + 4)² − 16 + 3 = (x + 4)² − 13. Since (x + 4)² ≥ 0, the smallest value is −13, occurring when x = −4. Thus the minimum value is −13.
'Their' is the possessive form of 'they' and shows that the books belong to the students. 'There' refers to a place, and 'they're' is a contraction of 'they are', neither of which fits before a noun in this sentence.
'It's' is the contraction of 'it is', which the sentence needs, and the possessive determiner 'your' takes no apostrophe at all. Putting an apostrophe after 'its' or writing 'you're' (you are) breaks the meaning of the sentence.
An adverb modifies a verb and answers the question 'how?'. 'Quickly' tells us how the children ran, so it is the adverb, while 'children' is a noun, 'ran' is a verb and 'towards' is a preposition.
With 'neither ... nor', the verb agrees with the nearer subject, which here is the plural 'students'. That makes 'were' correct, while the singular forms 'was', 'is' and 'has been' would agree with 'teacher' instead.
A passive sentence puts the receiver of the action first and uses a form of 'be' with a past participle, as in 'was repaired'. The other sentences are active because the doer, 'the mechanic', is the subject performing the action.
When the reporting verb is in the past, the present continuous 'am going' shifts to 'was going' and the time word 'now' becomes 'then'. The pronoun 'I' also changes to 'she' because the speaker is reporting someone else's words.
A complex sentence contains one main clause and at least one subordinate clause. 'Although the rain stopped' cannot stand alone and depends on the main clause 'the air stayed cold', so the whole sentence is complex.
'Reluctant' describes someone who hesitates or does not want to do something, so 'unwilling' is the closest match. 'Uncertain' suggests doubt about facts rather than a lack of willingness to act.
Formal writing avoids slang and contractions and states the purpose politely and directly. 'I am writing to express my strong interest in the advertised position' does this, while the other options use informal words such as 'reckon', 'give it a go' and 'dead good'.
The sudden silence and the hurry to look busy imply that the teachers do not want Mr Banda to see them relaxing, which suggests he makes them uneasy. Nothing in the sentence shows affection, eagerness or cleanliness, so those readings are unsupported by the evidence given.
The article 'an' is used before a word that begins with a vowel sound. The 'h' in 'hour' is silent, so the word starts with a vowel sound and requires 'an'. 'A' would be used before a consonant sound, and 'the' would wrongly suggest a specific hour already known to the reader.
'Since' marks the starting point of a situation that continues up to the present, and it is the correct partner for the present perfect 'has been'. 'For' would need a length of time such as 'three days', while 'during' would need the name of a period rather than a single day.
When three or more things are compared, English uses the superlative form. 'Short' is a one-syllable adjective, so its superlative is formed by adding '-est', giving 'shortest'. The comparative 'shorter' is used only when two things are compared.
'Affect' is a verb meaning to influence or have an impact on something, which is exactly what the rule does to the candidates. 'Effect' is usually a noun meaning a result, so it cannot fill a slot that requires a verb.
A metaphor states that one thing is another thing without using 'like' or 'as'. By calling the moon 'a silver coin', the writer makes a direct comparison, which is the defining feature of a metaphor. A simile would need wording such as 'like a silver coin'.
The past perfect 'had stopped' shows that the rain finished before another past action, 'arrived'. This tense makes the order of events clear. The simple past 'stopped' would leave the sequence unclear, and the present perfect 'has stopped' clashes with the past-time clause.