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Order of operations requires multiplication and division before addition and subtraction. So 4 × 2 = 8 and 6 ÷ 3 = 2, giving 3 + 8 − 2 = 9. Working strictly left to right is a common error that produces a different value.
Profit = 30 000 − 25 000 = 5 000 FCFA. Percentage profit is always calculated on the cost price, so (5 000 ÷ 25 000) × 100 = 20%. Dividing by the selling price instead gives the wrong figure.
Expand each bracket: 6x − 8 − 3x + 15. Note that −3 × −5 = +15. Collecting like terms gives 6x − 3x = 3x and −8 + 15 = 7, so the answer is 3x + 7.
Subtract 2x from both sides to get 3x − 7 = 8, then add 7 to get 3x = 15, so x = 5. Always perform the same operation on both sides to keep the equation balanced.
The angles of a triangle sum to 180°. The ratio has 2 + 3 + 4 = 9 parts, so one part is 180° ÷ 9 = 20°. The largest share is 4 parts = 4 × 20° = 80°.
For a regular polygon with n sides, each interior angle is (n − 2) × 180° ÷ n. For a hexagon, n = 6, giving 4 × 180° ÷ 6 = 720° ÷ 6 = 120°.
Standard form is A × 10ⁿ where 1 ≤ A < 10. Moving the decimal point four places right gives 4.5, so the exponent is −4, producing 4.5 × 10⁻⁴.
The prime outcomes on a die are 2, 3 and 5, so there are 3 favourable outcomes out of 6. The probability is 3/6 = 1/2. Note that 1 is not prime.
The total of all five numbers is mean × count = 12 × 5 = 60. The four known numbers sum to 9 + 10 + 14 + 15 = 48, so the fifth is 60 − 48 = 12.
This is a difference of two squares, since x² − 9 = x² − 3². The rule a² − b² = (a − b)(a + b) gives (x − 3)(x + 3).
By Pythagoras' theorem, the hypotenuse squared equals 6² + 8² = 36 + 64 = 100. The hypotenuse is the positive square root, √100 = 10 cm.
Adding the two equations eliminates y: 2x = 12, so x = 6. Substituting into x + y = 9 gives y = 3. Checking in the second equation, 6 − 3 = 3, which is correct.
Simple interest is I = PRT/100 = (40 000 × 5 × 3) ÷ 100 = 6 000 FCFA. Simple interest is calculated on the original principal only, not on accumulated interest.
Using index laws, 2³ × 2⁴ = 2⁷ and 2⁷ ÷ 2⁵ = 2² = 4. When multiplying powers of the same base you add the indices; when dividing you subtract them.
A scale of 1 : 50 000 means 1 cm on the map represents 50 000 cm in reality. Thus 4 cm represents 200 000 cm. Since 100 000 cm = 1 km, this equals 2 km.
The formula is C = 2πr, so r = C ÷ (2π) = 44 ÷ (2 × 22/7) = 44 × 7 ÷ 44 = 7 cm. Substituting the value back confirms 2 × 22/7 × 7 = 44.
Using FOIL: x·x = x², x·(−2) = −2x, 4·x = 4x, and 4·(−2) = −8. Combining −2x + 4x gives +2x, so the result is x² + 2x − 8.
The probability the first is red is 5/8. Given that, 4 reds remain among 7 balls, so the second is red with probability 4/7. Multiplying gives 20/56 = 5/14.
Multiply both sides by 3: 3V = πr²h. Divide by πh: r² = 3V/(πh). Taking the positive square root gives r = √(3V/(πh)).
Substitute n = 12 into the formula: 4 × 12 − 3 = 48 − 3 = 45. This is an arithmetic sequence with common difference 4.
We need two numbers that multiply to +6 and add to −5, namely −2 and −3. So the equation factorises as (x − 2)(x − 3) = 0, giving x = 2 or x = 3.
The volume of a cone is (1/3)πr²h = (1/3) × (22/7) × 49 × 24. Since (22/7) × 49 = 154, this becomes (1/3) × 154 × 24 = 154 × 8 = 1 232 cm³.
With tan θ = 3/4, take the opposite side as 3 and adjacent as 4, so the hypotenuse is √(9+16) = 5. Then sin θ = 3/5 and cos θ = 4/5, giving a sum of 7/5.
The gradient is (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3. Using y − 2 = 3(x − 1) gives y = 3x − 3 + 2 = 3x − 1. Checking (3, 8): 3(3) − 1 = 8, which is correct.
Cylinder volume = πr²h = (22/7) × 49 × 10 = 1 540 cm³. Each sphere has volume (4/3)πr³ = (4/3) × (22/7) × 42.875 = 179.67 cm³ approximately. Dividing gives 1 540 ÷ 179.67 ≈ 8.57, so 8 complete spheres can be made.
Profit = 15 000 − 12 000 = 3 000 FCFA, and percentage profit is always calculated on the cost price: (3 000 ÷ 12 000) × 100 = 25%.
Standard form requires a single non-zero digit before the decimal point, so 0.000 000 72 = 7.2 × 10⁻⁷ because the decimal point moves seven places to the right.
Expanding gives 6x − 15 − 2x + 8. Collecting like terms gives 4x − 7, taking care that −2 × −4 = +8.
2 hours 30 minutes is 2.5 hours, and average speed = distance ÷ time = 150 ÷ 2.5 = 60 km/h. The time must be converted to hours before dividing.
The angles of a quadrilateral sum to 360°, so 3x + 4x + 5x + 6x = 18x = 360, giving x = 20.
An irrational number cannot be written as a fraction of two integers. √2 has a non-terminating, non-repeating decimal expansion, whereas √49 = 7, 0.75 = 3/4 and 22/7 are all rational.
For an acute angle, sin 30° = 0.5, so θ = 30°. The sine of an acute angle increases from 0 to 1 as the angle grows from 0° to 90°.
The sample space is HH, HT, TH, TT, and three of these four outcomes contain at least one head, so the probability is 3/4. Equivalently, 1 − P(no head) = 1 − 1/4 = 3/4.
The exterior angles of any convex polygon add up to 360°, so the number of sides is 360 ÷ 24 = 15.
Subtracting 5 gives −2x < 6, and dividing both sides by −2 reverses the inequality sign, so x > −3.
The 10th term equals S₁₀ − S₉ = (100 + 30) − (81 + 27) = 130 − 108 = 22. Alternatively the sequence has first term 4 and common difference 2, giving 4 + 9(2) = 22.
A 90° anticlockwise rotation about the origin maps (x, y) to (−y, x), so (2, −1) becomes (1, 2).
Since 12 = 2² × 3, log₁₀ 12 = 2 log₁₀ 2 + log₁₀ 3 = 2(0.3010) + 0.4771 = 1.0791.
Total surface area = πr² + πrl = πr(r + l) = 3.14 × 6 × 16 = 301.44 cm². Both the circular base and the curved surface must be included.
The back bearing is found by adding 180° when the bearing is less than 180°, so 70° + 180° = 250°. Bearings are measured clockwise from north.
For any invertible matrix, det(M⁻¹) = 1 ÷ det(M), so the determinant of the inverse is 1/10. The determinant of the inverse is never negative when the original determinant is positive.
Dividing by 2 gives y = 3x − 2.5, so the gradient is 3, and a perpendicular line has gradient −1/3 because the product of the two gradients must be −1.
tan 35° = opposite ÷ adjacent, so opposite = 8 tan 35° = 8 × 0.7002 = 5.60 cm. The tangent ratio links the opposite and adjacent sides.
P(different) = P(WB) + P(BW) = (4/10 × 6/9) + (6/10 × 4/9) = 24/90 + 24/90 = 48/90 = 8/15. Drawing without replacement changes the denominator to 9 on the second draw.
Since 32 = 2⁵, the equation becomes 2^(x+1) = 2⁵, so x + 1 = 5 and x = 4.
Converting 80 cm to 0.8 m gives a volume of 2 × 1.5 × 0.8 = 2.4 m³. Since 1 m³ = 1 000 litres, the tank holds 2 400 litres.
For similar solids, volumes are in the ratio of the cubes of corresponding lengths, so V₁ : V₂ = 2³ : 3³ = 8 : 27. Hence V₂ = 40 × 27/8 = 135 cm³.
Equal roots occur when the discriminant b² − 4ac equals zero, so k² − 4(1)(9) = 0, giving k² = 36 and k = ±6. Both values must be stated.
Factorising gives (x − 2)(x + 2) divided by (x + 3)(x − 2), so the factor (x − 2) cancels to leave (x + 2)/(x + 3). The cancelled factor means x ≠ 2, and the denominator means x ≠ −3.
Velocity is the derivative ds/dt = 6t − 12, and the particle is at rest when velocity is zero, so 6t − 12 = 0 and t = 2 seconds.