EJU Mathematics Course 1: Algebra, Quadratic Functions, Measurement, and Probability
Scope of the domain
EJU Mathematics Course 1 tests algebraic manipulation, quadratic functions, plane and solid measurement with trigonometry, and elementary probability. Course 1 does not require calculus, vectors, complex numbers, or matrices; those belong to Course 2. Questions are calculation-heavy and often combine two syllabus areas, so identify the standard form, ratio, or counting model before computing.
Core rules
- For radicals, enforce a≥0: √(a²)=|a|, and rationalise denominators by multiplying by the conjugate. Linear inequalities keep interval solutions; |x−a|<r means a−r<x<a+r.
- A quadratic ax²+bx+c has axis x=−b/(2a); vertex form a(x−p)²+q gives the maximum or minimum directly. The discriminant D=b²−4ac determines the number of real roots; roots sum −b/a and product c/a.
- Solve quadratic inequalities by finding roots and testing sign intervals; reverse the inequality when multiplying or dividing by a negative number.
- In triangle measurement, use a/sin A=b/sin B=c/sin C and a²=b²+c²−2bc cos A; the area is ½bc sin A. Check whether the given angle is included between the two known sides before choosing the cosine rule.
- Probability uses P(A)=n(A)/n(U); use permutations when order matters and combinations when it does not. For independent events, multiply probabilities; the complement P(A′)=1−P(A) is often faster.
Worked example
Solve x²−5x+6≤0. Factor: (x−2)(x−3)≤0. The roots are 2 and 3, and the parabola opens upward, so the expression is negative between the roots. Hence 2≤x≤3. Check x=2.5: 6.25−12.5+6=−0.25≤0.
Function and counting checks
For y=ax²+bx+c, the sign of a gives opening direction; the vertex is the only turning point. For counting, distinguish arrangements of distinct objects from selections from groups; with replacement, each stage multiplies choices. When events overlap, use P(A∪B)=P(A)+P(B)−P(A∩B).
Traps
Do not drop the absolute value in √(a²); do not use the sine rule ambiguously without checking the angle sum; do not count ordered and unordered selections interchangeably; and do not forget that a quadratic inequality's solution may be a single point or empty when D<0. Also check whether a measurement answer needs degrees or radians.