🌙 • Module 13 : Refreshen Your Brain — Exam Essentials Flashcards
A final power-up before your IGCSE! This deck covers key formulas, common exam traps, fast-solving tricks, graph hacks, algebra shortcuts, and smart ways to tackle word problems. Master these last-minute strategies and walk into your exam feeling ever so prepared!
What is the formula for the area of a triangle?
Area = 1/2 x base x height
What is Pythagoras’ Theorem?
a²+b²=c²
Where c is the hypotenuse of a right-angled triangle.
What is the quadratic formula?
𝑥 = (-b ± √b²-4ac)/2a
What is the formula for simple interest?
I = P x r x t
Where P is the principal, r is the rate, and t is the time.
What is the formula for compound interest?
A = P(1+ (r/100))ᵗ,
Where A is the amount, P is the principal, r is the rate, and t is the time.
What is the formula for the area of a circle, and the circumference?
Area = πr², where r is the radius
Circumference = 2πr
What’s a trap when solving quadratic equations by factoring?
Don’t forget to check the greatest common factor (GCF) first.
Always factor it out before proceeding.
How should you approach a word problems involving percentages?
Convert the percentage to a decimal, then use it to calculate part of the whole or increase/decrease the value.
How do you solve word problems involving two variables?
Set up two equations from the problem, and use substitution or elimination methods to solve.
How can you quickly check if a quadratic equation is factorable?
Calculate b² - 4ac (the discriminant). If it’s a perfect square, the quadratic is factorable.
What’s a trick to simplify algebraic fractions?
Factor both the numerator and denominator, then cancel out any common factors.
What should you focus on when sketching quadratic graphs?
Find the vertex (turning point), and x-intercepts (roots). Use these key points to sketch the shape.
How do you interpret the gradient of a line on a graph?
The gradient is the slope of the line, calculated as
change in y/change in x.
What’s a key tip for solving word problems under pressure?
Underline key information in the problem and break it down into smaller, manageable steps.
How should you handle questions that involve units?
Always check and convert units before performing calculations to avoid mistakes.
How do you test for solutions in word problems involving probability?
List all outcomes in a sample space, then determine the likelihood of the event by counting favorable outcomes and dividing by the total outcomes.
What’s the best approach when you’re asked to find the cost after a percentage increase?
Multiply the original price by 1 + percentage increase/100
What’s the trick when completing the square for a quadratic?
Half the coefficient of x, square it, and add it to both sides of the equation.
How do you add vectors geometrically?
Use the tip-to-tail method: place the tail of the second vector at the tip of the first, then draw the vector from the origin to the tip of the second vector.
What’s a smart approach to unit conversions during exams?
Memorize key conversion factors.
Distance —
1km=1000m
1m =100cm
1cm=10mm
Volume —
1m³=1000L
1L=1000cm³
1cm³=1mL
Mass/Weight —
1kg =1000g
1 tonne =1000kg
Time —
1hr =60 mins
1min =60 secs
1 day=24hrs
1 week=7 days
Speed —
1m/s=3.6km/h
What to do when you’re stuck on a problem?
Tip : Move on to the next question. Come back to the tricky one with fresh eyes after solving some easier ones. Don’t waste too much time on a single problem.
Best method to check your work quickly?
Use the reverse method to verify your answer.
For example, if you’ve solved for x, substitute your solution back into the original equation to see if it holds true.
How do you remember orders in equations?
Remember BODMAS!
Brackets,
Orders (powers/indices or roots),
Division,
Multiplication,
Addition,
Subtraction.
How to approach trigonometric problems?
Tip : Remember the basic identities:
SOHCAHTOA for sine, cosine, and tangent.
Sine = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent
“Some Old Hippie Caught Another Hippie Tripping On Apples”
Use the unit circle for quick reference and remember the angles 0°, 30°, 45°, 60°, and 90°.
Tip : Quick trick for finding the sum of an arithmetic sequence…
Sum = n/2 x (first term + last term)
Where n is the number of terms.
It’s like averaging the first and last term, then multiplying by how many terms you have.
Tip : Trick to remember how to solve inequities…
If you multiply or divide by a negative number, flip the inequality sign!
Example: -2x > 6 becomes x < -3 when you divide by -2.
Tip : Remembering the sine rule…
The sine rule is (a/sinA) = (b/sinB) = (c/sinC).
Think : “Opposite over sine of the angle”.
Use this when you have non-right-angled triangles.
