You might know a formula but not know when to use it. In maths, that’s often where it all comes down to: recognising the situation, choosing the right tool and showing the steps. To make progress in the third year of secondary school in Morocco, practise these three skills together. [1] The topics listed below are taken from the Year 9 resources consulted. The examples have been created specifically for this article. This guide highlights key topics; it is not intended to replace your full course or your examination syllabus.
Literal calculation: secures the first few lines
Expanding and factoring are then used in equations and problems. If you get a sign wrong at the start, the whole rest of the calculation may turn out to be incorrect, even though you chose the right method.
Example: 3(x + 2) – 2x = 3x + 6 – 2x = x + 6. To factorise 5x + 15, identify the common factor 5: you get 5(x + 3). Check by working it out again. This quick check helps you work without relying on the answer key.
Powers and square roots: avoid misleading habits
In a product of powers with the same base, the exponents are added together: 2³ × 2² = 2⁵ = 32. For a root, look for a perfect square: √50 = √(25 × 2) = 5√2. Be careful not to make up a rule for addition: √(9 + 16) equals 5, whereas √9 + √16 equals 7. Write this example on your worksheet if you often confuse the two situations.
Equations, inequalities and systems: explain each step
To solve 3x + 5 = 20, subtract 5 from both sides: 3x = 15. Then divide by 3: x = 5. Check: 3 × 5 + 5 = 20.
In an inequality, the direction changes when you multiply or divide by a negative number. For example, -2x > 6 gives x < -3. For a system such as x + y = 7 and x – y = 1, add the two equations together: 2x = 8, so x = 4 and y = 3.
Pythagoras and Thales: start with the conditions
Pythagoras’ theorem applies to a right-angled triangle. If the two sides adjacent to the right angle measure 3 cm and 4 cm, the square of the hypotenuse is 3² + 4² = 25. Its length is therefore 5 cm.
According to Thales, suppose that M lies on the line segment [AB], that N lies on [AC] and that (MN) is parallel to (BC). If AM = 2, AB = 6 and AC = 9, then AM/AB = AN/AC. Therefore, AN = 9 × 2/6 = 3, in the same unit. Without the conditions of alignment and parallelism, this equality cannot be deduced in this way.
Trigonometry: label the sides in relation to the angle
In a right-angled triangle, if the side opposite an acute angle measures 3 cm and the hypotenuse measures 5 cm, the sine of that angle is 3/5 = 0.6. The word «opposite» depends on which angle you choose. Mark that angle before selecting a formula.
The cosine uses the adjacent side and the hypotenuse; the tangent uses the opposite side and the adjacent side. A small, annotated diagram helps to avoid a great deal of confusion.
Plotting, straight lines and functions: linking calculations to drawings
Given that A(1; 2) and B(5; 6), the midpoint of [AB] has coordinates ((1 + 5)/2; (2 + 6)/2), which is (3; 4). The coordinates of the vector AB are (4; 4). For the linear function f(x) = 2x + 1, the image of 3 is 7. Finding the preimage of 9 amounts to solving 2x + 1 = 9, so x = 4. The point (3; 7) lies on the line with equation y = 2x + 1. The image, preimage and point on a line are thus related.
Statistics and space: don’t forget either the numbers or the units
For the values 8, 10, 10 and 12, the mean is (8 + 10 + 10 + 12)/4 = 10. The number 10 appears twice: it must be counted twice. The median is also 10 in this example, but it is not always equal to the mean.
A cone with a radius of 3 cm and a height of 4 cm has a volume of π × 3² × 4/3 = 12π cm³. A length is expressed in cm, an area in cm² and a volume in cm³.
Which chapters are worth the most points?
There is no single marking scheme that applies to all topics. Read the relevant guidelines and the marking scheme for your past papers. Calculus, equations and geometry deserve particular attention because they feature in several types of question, not because a fixed number of marks is guaranteed for them.
Work through an example, hide the answer, then change the numbers. If you keep getting stuck at the same point, show this step to your teacher or contact Elite Academy to find out about the courses available.
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→ See also: Standardised exam for Year 3 of secondary school: the complete guide to passing it · The perfect revision sheet: the template that really works
