Lesson 10 of 10
🎓 Course Complete!
1. Understanding the Exam Papers
Knowing the structure of each paper helps you plan your time and approach every question strategically.
Paper 1 — No Calculator
- Duration: 2 hours
- Marks: 80 marks
- Questions: Short-answer questions — typically 25–30 questions
- Style: Each question is worth 1–3 marks. Must show all working even on short questions.
- No calculator allowed — exact arithmetic required
- Tip: Do not spend more than 2–3 minutes on any single part
Paper 2 — Calculator Allowed
- Duration: 2 hours 30 minutes
- Marks: 100 marks
- Questions: Structured questions — typically 10–11 questions
- Style: Multi-part questions (a)(b)(c)(d). Later parts are harder.
- Scientific calculator required
- Tip: Roughly 1.5 minutes per mark. A 6-mark question = ~9 minutes.
Time Management Strategy:
Paper 1: 80 marks in 120 minutes = 1.5 minutes per mark.
Paper 2: 100 marks in 150 minutes = 1.5 minutes per mark.
If a question is taking much longer than its mark value suggests — move on and return to it. One hard question is never worth sacrificing multiple easy questions.
Paper 1: 80 marks in 120 minutes = 1.5 minutes per mark.
Paper 2: 100 marks in 150 minutes = 1.5 minutes per mark.
If a question is taking much longer than its mark value suggests — move on and return to it. One hard question is never worth sacrificing multiple easy questions.
2. Complete Formula Reference Card
These are all the formulae you must know for Cambridge 4024 / 0580. Some are given on the formula sheet — but knowing them all saves time and avoids errors.
Number and Algebra
| Topic | Formula |
|---|---|
| Compound Interest | A = P(1 + r/100)ⁿ |
| Percentage Change | % change = (change / original) × 100 |
| Reverse Percentage | Original = Final ÷ (1 ± r/100) |
| Standard Form | A × 10ⁿ where 1 ≤ A < 10 |
| nth term (arithmetic) | a + (n−1)d = dn + (a−d) |
| nth term (geometric) | arⁿ⁻¹ |
| Sum of geometric series | Sₙ = a(rⁿ−1)/(r−1) |
| Quadratic formula | x = [−b ± √(b²−4ac)] / 2a |
| Discriminant | Δ = b²−4ac. Δ>0: two roots; Δ=0: one root; Δ<0: no real roots |
| Completing the square | ax²+bx+c = a(x + b/2a)² + (c − b²/4a) |
| Direct proportion | y = kx |
| Inverse proportion | y = k/x (or xy = k) |
| Speed | Speed = Distance ÷ Time |
| Density | Density = Mass ÷ Volume |
| Pressure | Pressure = Force ÷ Area |
Coordinate Geometry
| Topic | Formula |
|---|---|
| Gradient | m = (y₂−y₁)/(x₂−x₁) |
| Length of segment | d = √[(x₂−x₁)²+(y₂−y₁)²] |
| Midpoint | M = ((x₁+x₂)/2, (y₁+y₂)/2) |
| Equation of line | y = mx + c | y−y₁ = m(x−x₁) |
| Parallel lines | m₁ = m₂ |
| Perpendicular lines | m₁ × m₂ = −1 → m₂ = −1/m₁ |
Geometry and Mensuration
| Shape | Perimeter / Area / Volume / SA |
|---|---|
| Circle | C = 2πr = πd | A = πr² |
| Arc length | l = (θ/360) × 2πr |
| Sector area | A = (θ/360) × πr² |
| Trapezium | A = ½(a+b)h |
| Triangle area | A = ½bh | A = ½ab sinC |
| Cylinder | V = πr²h | SA = 2πr²+2πrh |
| Cone | V = ⅓πr²h | SA = πr²+πrl | l = √(r²+h²) |
| Sphere | V = (4/3)πr³ | SA = 4πr² |
| Pyramid | V = ⅓ × base area × h |
| Interior angle sum | S = (n−2) × 180° |
| Exterior angle sum | Always 360° |
| Similar shapes | Lengths: k | Areas: k² | Volumes: k³ |
Trigonometry
| Topic | Formula |
|---|---|
| SOH CAH TOA | sin θ = O/H | cos θ = A/H | tan θ = O/A |
| Sine Rule | a/sin A = b/sin B = c/sin C |
| Cosine Rule (side) | a² = b²+c²−2bc cos A |
| Cosine Rule (angle) | cos A = (b²+c²−a²)/2bc |
| Area of triangle | Area = ½ab sin C |
| Trig solutions in 0°–360° | sin: θ and 180°−θ | cos: θ and 360°−θ | tan: θ and θ+180° |
Matrices and Vectors
| Topic | Formula |
|---|---|
| Determinant of 2×2 | det[[a,b],[c,d]] = ad−bc |
| Inverse of 2×2 | M⁻¹ = (1/det) × [[d,−b],[−c,a]] |
| Solve MX=B | X = M⁻¹B |
| Vector magnitude | |v| = √(x²+y²) for v = (x over y) |
| AB⃗ (position vectors) | AB⃗ = b − a |
| Midpoint (position vectors) | OM⃗ = ½(a+b) |
Statistics and Probability
| Topic | Formula |
|---|---|
| Mean (frequency table) | x̄ = Σ(fx) / Σf |
| Frequency density | FD = Frequency ÷ Class Width |
| Probability | P(A) = favourable / total |
| Complement | P(A') = 1 − P(A) |
| Independent events | P(A and B) = P(A) × P(B) |
| Mutually exclusive | P(A or B) = P(A) + P(B) |
| Conditional probability | P(A|B) = P(A and B) / P(B) |
| IQR | IQR = Q3 − Q1 |
3. The 30 Most Common Exam Mistakes
These are the errors that Cambridge examiners report year after year. Avoiding them can add 10–20 marks to your score.
Number and Algebra Mistakes
| # | Mistake | Correct Approach |
|---|---|---|
| 1 | Dividing by a negative without reversing the inequality sign. | −2x < 6 → x > −3 (sign reverses when dividing by −2). |
| 2 | Using simple interest formula instead of compound interest. | Always use A = P(1+r/100)ⁿ when interest is compounded. |
| 3 | Forgetting to square root the final answer in Pythagoras. | a²=b²+c² gives a², not a. Always take √ at the end. |
| 4 | Wrong order in fg(x): applying f first instead of g first. | fg(x) = f(g(x)) — g is applied FIRST, then f. |
| 5 | Losing negative signs when expanding brackets. | −2(x−3) = −2x + 6 (not −2x − 6). Multiply every term. |
| 6 | Rounding intermediate calculations too early. | Keep full calculator precision throughout. Round only the final answer. |
| 7 | Confusing significant figures with decimal places. | 0.00457 to 2 d.p. = 0.00. To 2 s.f. = 0.0046. Start from first non-zero digit for s.f. |
| 8 | Incorrect upper/lower bounds — using ± whole unit instead of ± half unit. | Rounded to nearest 0.1 → bounds are ±0.05, not ±0.1. |
| 9 | Forgetting both solutions when solving quadratics. | Quadratics have at most TWO solutions. Always check for both. |
| 10 | Getting standard form wrong — A value not between 1 and 10. | 12.4 × 10³ must be rewritten as 1.24 × 10⁴. Check A always. |
Geometry and Trigonometry Mistakes
| # | Mistake | Correct Approach |
|---|---|---|
| 11 | Using slant height instead of perpendicular height in volume formulas. | V = ⅓πr²h always needs perpendicular h. Use h=√(l²−r²) first. |
| 12 | Forgetting to add 2 radii when finding perimeter of a sector. | Perimeter = arc length + 2r. Never just arc length. |
| 13 | Using height as the slant side of a triangle in area calculations. | Area = ½ × base × perpendicular height — never the hypotenuse. |
| 14 | Not giving reasons in circle theorem questions. | Every angle found in circle theorem questions needs a written reason. |
| 15 | Only finding one solution to a trig equation in 0°–360°. | sin and cos equations always have TWO solutions in 0°–360°. Use the quadrant rules. |
| 16 | Confusing similar shape area and volume ratios. | If lengths ratio = k, area ratio = k² and volume ratio = k³. Never use k for area. |
| 17 | Bearings written without three digits. | Always write 045°, not 45°. Always three digits. |
| 18 | Using the sine rule when the cosine rule is needed (SSA vs SAS). | Two sides + included angle → cosine rule. Two angles + one side → sine rule. |
| 19 | Ignoring the ambiguous case in sine rule problems. | When finding an angle using the sine rule, always check if both acute and obtuse solutions are valid. |
| 20 | Calculating exterior angle sum incorrectly for irregular polygons. | Exterior angle sum is ALWAYS 360° for ANY convex polygon, regular or not. |
Matrices, Vectors and Transformation Mistakes
| # | Mistake | Correct Approach |
|---|---|---|
| 21 | Wrong order in combined transformation: applying the wrong matrix first. | For transformation A then B, matrix = BA (B written first but A applied first). |
| 22 | Forgetting to divide by the determinant when finding the inverse. | M⁻¹ = (1/det) × adjugate. The (1/det) factor is essential. |
| 23 | Confusing AB⃗ with BA⃗ in vector notation. | AB⃗ = b − a (finish − start). BA⃗ = a − b. Direction matters. |
| 24 | Forgetting to multiply by the scalar before finding an inverse. | If kM is the matrix, find det(kM) = k² det(M) for a 2×2 matrix. |
| 25 | Incomplete description of a transformation (missing one detail). | Rotation needs: angle, direction AND centre. Enlargement needs: scale factor AND centre. All four details always. |
Statistics and Probability Mistakes
| # | Mistake | Correct Approach |
|---|---|---|
| 26 | Plotting frequency (not frequency density) on a histogram y-axis. | Histogram y-axis = frequency density = frequency ÷ class width. |
| 27 | Reading the median from the wrong cumulative frequency value. | Median = n/2, not (n+1)/2, on a cumulative frequency graph. |
| 28 | Not stating that probabilities on each set of branches sum to 1. | Always check each branch set sums to 1 before writing final answers. |
| 29 | Using with-replacement probabilities for without-replacement problems. | Without replacement: second draw denominator decreases by 1. e.g. 5/10 then 4/9. |
| 30 | Only comparing averages when comparing distributions — forgetting spread. | Always compare BOTH the average (mean/median) AND the spread (range/IQR) in context. |
4. Exam Technique — Step by Step
Before the Exam
Equipment Check (bring all of these):
✓ Two working pens (blue or black ink)
✓ Two sharp pencils (for diagrams and graphs)
✓ Scientific calculator (Paper 2 only) — check battery beforehand
✓ Ruler (30 cm), compasses, protractor
✓ Eraser and pencil sharpener
✓ Clear geometry set — set square useful for parallel lines
✗ No correction fluid (Tipp-Ex) — cross out errors neatly with a single line
✓ Two working pens (blue or black ink)
✓ Two sharp pencils (for diagrams and graphs)
✓ Scientific calculator (Paper 2 only) — check battery beforehand
✓ Ruler (30 cm), compasses, protractor
✓ Eraser and pencil sharpener
✓ Clear geometry set — set square useful for parallel lines
✗ No correction fluid (Tipp-Ex) — cross out errors neatly with a single line
During the Exam — The Six Golden Rules
🥇 Rule 1 — Show ALL Working
Method marks are available even when the final answer is wrong. A correct method with an arithmetic slip still earns most marks. Never just write the answer — always show how you got there.
🥇 Rule 2 — Read Every Question Twice
Before writing anything, read the question completely. Identify: What is given? What is asked? What method is needed? Circle key words: "exact", "integer", "3 s.f.", "in terms of π".
🥇 Rule 3 — Use the Mark Allocation
The number of marks shown in brackets tells you how much work is expected. A [1 mark] question needs one line. A [4 mark] question needs multiple steps — show them all.
🥇 Rule 4 — Check Units and Accuracy
If the question asks for 3 significant figures — give 3 s.f. If it says "exact" — leave surds or π in the answer. If it says "nearest integer" — round. Always match the required accuracy.
🥇 Rule 5 — Sketch Diagrams
For geometry, trigonometry, and vectors — always draw a clear labelled diagram. Even a rough sketch prevents major errors by helping you see the structure of the problem.
🥇 Rule 6 — Check Your Answers
If time allows, verify answers by substituting back. For equations: check solution satisfies original equation. For probability: check all branches sum to 1. For geometry: check angle sums.
Specific Tips by Topic
| Topic | Key Exam Strategy |
|---|---|
| Number | In Paper 1 (no calculator), work in fractions where possible — exact. Estimate before calculating to check reasonableness. |
| Algebra | For rearranging formulae where the variable appears twice: expand → collect x terms → factorise → divide. |
| Quadratics | If the question says "give answers to 2 d.p." → use the formula. If it says "solve exactly" → factorise or complete the square. |
| Functions | fg(x) means apply g first then f. For f⁻¹(x): write y=f(x), swap x and y, solve for y. |
| Coordinate geometry | Always find gradient first. For perpendicular lines, flip and negate. Check with m₁×m₂=−1. |
| Circle theorems | Every angle needs a written reason. Identify all radii first (they are equal). Look for isosceles triangles. |
| Trigonometry | Label O, A, H before choosing formula. For non-right triangles: decide sine vs cosine rule using the decision table. |
| Mensuration | For composite shapes: split into standard shapes, calculate each, then add or subtract. List all components before calculating. |
| Vectors | To prove collinearity: show one vector is a scalar multiple of another AND they share a common point. |
| Matrices | Always verify M × M⁻¹ = I. For transformation matrices: columns are images of (1,0) and (0,1). |
| Statistics | Cumulative frequency: plot at UPPER boundary. Modal class = highest frequency density (not frequency). Compare BOTH average AND spread. |
| Probability | Draw tree diagrams first. Check all branches sum to 1. "At least one" → use complement method. |
5. Topic Self-Assessment Checklist
Use this checklist to identify which topics need more revision. Be honest — a topic is only ✅ if you can solve exam questions on it without notes.
| Topic | Key Skills to Master | Lesson |
|---|---|---|
| Number | HCF/LCM, standard form, percentage, reverse %, compound interest, surds, limits of accuracy, nth term | 1 |
| Algebra I | Expand, factorise (all methods), indices (all 7 laws), linear equations, simultaneous equations, change of subject (variable appears twice) | 2 |
| Algebra II | Quadratics (all 3 methods), completing the square, variation, composite/inverse functions, speed-time graphs | 3 |
| Coordinate Geometry | Gradient, midpoint, length, equation of line, parallel/perpendicular, perpendicular bisector, real-world linear graphs | 4 |
| Geometry | All angle facts, circle theorems (all 8 + reasons), similar triangles (k, k², k³), congruence conditions, constructions | 5 |
| Mensuration | All area/volume/SA formulae, arc/sector, composite shapes, similar solid ratios (k, k², k³) | 6 |
| Trigonometry | SOH CAH TOA, sine rule (incl. ambiguous case), cosine rule, ½ab sinC, bearings, 3D trig, trig equations in 0°–360° | 7 |
| Matrices | Addition, multiplication (AB≠BA), determinant, inverse, matrix equations | 8 |
| Vectors | Column vectors, magnitude, position vectors, AB⃗=b−a, midpoint, collinearity proof | 8 |
| Transformations | All 4 transformations (describe fully), transformation matrices, combined transformations | 8 |
| Statistics | Mean from grouped data, histograms (FD), cumulative frequency, box plots, comparing distributions | 9 |
| Probability | Basic probability, tree diagrams (with and without replacement), conditional probability, complementary method | 9 |
6. Grade Boundaries and Command Words
Typical Grade Boundaries (approximate)
O Level 4024 Grades (A* to E)
| Grade | Approx % needed |
|---|---|
| A* | ~80%+ |
| A | ~65–79% |
| B | ~50–64% |
| C | ~40–49% |
| D | ~30–39% |
| E | ~20–29% |
Boundaries vary by year — these are approximations.
What Gets You to A*
- Full marks on straightforward questions (never drop easy marks)
- Correct method even when arithmetic slips
- Full descriptions in geometry (all details)
- Both solutions in quadratic and trig problems
- Clear logical structure in multi-step problems
- Accurate graph drawing and reading
- Vector proofs with clear reasoning
Cambridge Mathematics Command Words
| Command Word | What It Means | Example |
|---|---|---|
| Write down / State | Give the answer with little or no working required. | "Write down the value of x." |
| Calculate / Find | Use calculation to obtain the answer. Show working. | "Calculate the area of the sector." |
| Show that | Prove the given result — every step must be shown clearly. You are given the answer; prove it. | "Show that angle ABC = 90°." |
| Prove | Give a formal mathematical argument — every step justified. | "Prove that triangles are congruent." |
| Sketch | Draw a rough diagram showing key features — not to scale but correct shape and labels. | "Sketch the graph of y = x²." |
| Draw | Draw accurately to scale using ruler, compasses, and/or protractor. | "Draw the perpendicular bisector of AB." |
| Describe fully | Give ALL necessary details of the transformation/relationship. | "Describe fully the transformation." |
| Explain | Give a reason or justification in words. | "Explain why the matrix is singular." |
| Hence | Use the result from the previous part to answer this part. | "Hence find the value of x." |
| Hence or otherwise | You may use the previous result OR any other valid method. | "Hence or otherwise solve..." |
| Estimate | Give an approximate answer — often by rounding values to 1 s.f. first. | "Estimate the value of 3.87 × 19.2." |
7. Mixed Revision — Exam-Style Questions
These questions span the whole syllabus — just like a real Cambridge paper. Work through them without notes first.
📝 Final Mixed Practice Questions
Q1 [3 marks] — Number
Without a calculator, find the exact value of (2.4 × 10⁵) × (5 × 10⁻³) ÷ (4 × 10⁴). Give your answer in standard form.
Step 1: Multiply first: (2.4 × 5) × 10^(5+(−3)) = 12 × 10² = 1.2 × 10³
Step 2: Divide: (1.2 × 10³) ÷ (4 × 10⁴) = (1.2/4) × 10^(3−4) = 0.3 × 10⁻¹
Rewrite: 0.3 × 10⁻¹ = 3 × 10⁻²
Step 2: Divide: (1.2 × 10³) ÷ (4 × 10⁴) = (1.2/4) × 10^(3−4) = 0.3 × 10⁻¹
Rewrite: 0.3 × 10⁻¹ = 3 × 10⁻²
Q2 [4 marks] — Algebra
Solve the equation (3x−1)/(x+2) − 2/(x−1) = 1. Show all working.
Multiply throughout by (x+2)(x−1):
(3x−1)(x−1) − 2(x+2) = (x+2)(x−1)
3x²−4x+1 − 2x−4 = x²+x−2
3x²−6x−3 = x²+x−2
2x²−7x−1 = 0
x = (7 ± √(49+8))/4 = (7 ± √57)/4
x = (7+√57)/4 ≈ 3.64 or x = (7−√57)/4 ≈ −0.14
(3x−1)(x−1) − 2(x+2) = (x+2)(x−1)
3x²−4x+1 − 2x−4 = x²+x−2
3x²−6x−3 = x²+x−2
2x²−7x−1 = 0
x = (7 ± √(49+8))/4 = (7 ± √57)/4
x = (7+√57)/4 ≈ 3.64 or x = (7−√57)/4 ≈ −0.14
Q3 [4 marks] — Geometry and Mensuration
A solid consists of a hemisphere of radius 5 cm on top of a cylinder of radius 5 cm and height 8 cm. Find (a) the total volume (b) the total surface area. Give answers to 3 s.f.
(a) Volume:
Cylinder: πr²h = π×25×8 = 200π
Hemisphere: (2/3)πr³ = (2/3)π×125 = (250/3)π
Total = 200π + 250π/3 = 850π/3 ≈ 890 cm³
(b) Surface Area:
Curved cylinder: 2πrh = 2π×5×8 = 80π
Circular base (bottom only): πr² = 25π
Hemisphere curved: 2πr² = 50π
(No circle between hemisphere and cylinder — they join)
Total SA = 80π + 25π + 50π = 155π ≈ 487 cm²
Cylinder: πr²h = π×25×8 = 200π
Hemisphere: (2/3)πr³ = (2/3)π×125 = (250/3)π
Total = 200π + 250π/3 = 850π/3 ≈ 890 cm³
(b) Surface Area:
Curved cylinder: 2πrh = 2π×5×8 = 80π
Circular base (bottom only): πr² = 25π
Hemisphere curved: 2πr² = 50π
(No circle between hemisphere and cylinder — they join)
Total SA = 80π + 25π + 50π = 155π ≈ 487 cm²
Q4 [5 marks] — Trigonometry
In triangle ABC: AB = 7 cm, BC = 9 cm, angle ACB = 42°. Find angle ABC. Hence find the area of triangle ABC.
Using sine rule to find angle ABC:
sin(ABC)/AC = sin(ACB)/AB → First find angle ABC:
sin(ABC)/9 = sin42°/7
sin(ABC) = 9×sin42°/7 = 9×0.6691/7 = 0.8601
Angle ABC = sin⁻¹(0.8601) = 59.4° (or obtuse: 120.6°)
Check obtuse: 42°+120.6°=162.6° <180° → both valid.
Taking acute: angle BAC = 180°−42°−59.4° = 78.6°
Area = ½×AB×BC×sin(ABC) = ½×7×9×sin(59.4°) = ½×63×0.8616 ≈ 27.1 cm²
(For obtuse: area = ½×7×9×sin(120.6°) = ½×63×0.8616 ≈ 27.1 cm² — same area!)
sin(ABC)/AC = sin(ACB)/AB → First find angle ABC:
sin(ABC)/9 = sin42°/7
sin(ABC) = 9×sin42°/7 = 9×0.6691/7 = 0.8601
Angle ABC = sin⁻¹(0.8601) = 59.4° (or obtuse: 120.6°)
Check obtuse: 42°+120.6°=162.6° <180° → both valid.
Taking acute: angle BAC = 180°−42°−59.4° = 78.6°
Area = ½×AB×BC×sin(ABC) = ½×7×9×sin(59.4°) = ½×63×0.8616 ≈ 27.1 cm²
(For obtuse: area = ½×7×9×sin(120.6°) = ½×63×0.8616 ≈ 27.1 cm² — same area!)
Exam Tip: In the ambiguous case (SSA), both triangles often give the same area since sin θ = sin(180°−θ). Always state both possibilities for the angle unless the context rules one out.
Q5 [4 marks] — Vectors
OABC is a parallelogram. OA⃗ = a, OC⃗ = c. M is the midpoint of AB and N is the point on OB such that ON:NB = 1:3. Find OM⃗ and MN⃗. Show that M, N, and a third relevant point are collinear.
OB⃗ = OA⃗ + AB⃗ = a + c (since OABC parallelogram: AB⃗ = OC⃗ = c)
OM⃗ = OA⃗ + AM⃗ = a + ½c
ON⃗ = ¼OB⃗ = ¼(a+c)
MN⃗ = ON⃗ − OM⃗ = ¼a+¼c − a−½c = −¾a − ¼c = −¼(3a+c)
Check collinearity with O: OM⃗ = a+½c = ½(2a+c).
MN⃗ = −¼(3a+c). These are not scalar multiples → M and N are not on a line through O.
MN⃗ = −¼(3a + c)
OM⃗ = OA⃗ + AM⃗ = a + ½c
ON⃗ = ¼OB⃗ = ¼(a+c)
MN⃗ = ON⃗ − OM⃗ = ¼a+¼c − a−½c = −¾a − ¼c = −¼(3a+c)
Check collinearity with O: OM⃗ = a+½c = ½(2a+c).
MN⃗ = −¼(3a+c). These are not scalar multiples → M and N are not on a line through O.
MN⃗ = −¼(3a + c)
Q6 [4 marks] — Statistics and Probability
The probability that it rains on any day is 0.3. Find the probability that (a) it rains on exactly 2 out of 3 consecutive days (b) it rains on at least one of the 3 days.
(a) Exactly 2 rainy days:
P(rain)=0.3, P(no rain)=0.7. Three ways: RRD, RDR, DRR where R=rain, D=dry.
Each has probability: 0.3×0.3×0.7 = 0.063
P(exactly 2) = 3 × 0.063 = 0.189
(b) At least one rainy day:
P(at least one) = 1 − P(none)
P(no rain all 3) = 0.7³ = 0.343
P(at least one) = 1 − 0.343 = 0.657
P(rain)=0.3, P(no rain)=0.7. Three ways: RRD, RDR, DRR where R=rain, D=dry.
Each has probability: 0.3×0.3×0.7 = 0.063
P(exactly 2) = 3 × 0.063 = 0.189
(b) At least one rainy day:
P(at least one) = 1 − P(none)
P(no rain all 3) = 0.7³ = 0.343
P(at least one) = 1 − 0.343 = 0.657
Exam Tip: "Exactly k successes" from n independent trials uses: P = C(n,k) × pᵏ × (1−p)^(n−k). Here C(3,2)=3. "At least one" always uses the complement method.
8. Final Words — You Are Ready!
🎓 Congratulations on completing the full O Level Mathematics course!
You have covered every topic in the Cambridge 4024 / 0580 syllabus:
Number · Algebra · Coordinate Geometry · Geometry · Mensuration · Trigonometry · Matrices · Vectors · Transformations · Statistics · Probability
The difference between a good grade and an excellent grade comes down to three things:
You have covered every topic in the Cambridge 4024 / 0580 syllabus:
Number · Algebra · Coordinate Geometry · Geometry · Mensuration · Trigonometry · Matrices · Vectors · Transformations · Statistics · Probability
The difference between a good grade and an excellent grade comes down to three things:
1. Consistent Practice
Mathematics is learned by doing, not reading. Attempt past papers under timed conditions. Identify weak topics and revisit those lessons.
2. Show Your Working
Method marks save grades. A correct method with a wrong final answer still earns 2–3 marks. Never sacrifice working for speed.
3. Read Questions Carefully
Many marks are lost not from lack of knowledge, but from misreading questions. Note: exact answers, significant figures, units, and what is actually being asked.
Recommended Final Revision Plan (4 weeks before exam):
Week 1 — Lessons 1–3: Number, Algebra I, Algebra II. Do 10 past paper questions per topic.
Week 2 — Lessons 4–6: Coordinate Geometry, Geometry, Mensuration. Focus on circle theorems and formulae.
Week 3 — Lessons 7–8: Trigonometry, Matrices, Vectors, Transformations. Practice all four transformation descriptions.
Week 4 — Lesson 9 + Full Papers: Statistics, Probability, then two full past papers under timed conditions. Review all mistakes carefully.
Week 1 — Lessons 1–3: Number, Algebra I, Algebra II. Do 10 past paper questions per topic.
Week 2 — Lessons 4–6: Coordinate Geometry, Geometry, Mensuration. Focus on circle theorems and formulae.
Week 3 — Lessons 7–8: Trigonometry, Matrices, Vectors, Transformations. Practice all four transformation descriptions.
Week 4 — Lesson 9 + Full Papers: Statistics, Probability, then two full past papers under timed conditions. Review all mistakes carefully.