National 5 Maths Essential Skills 2024 - Paper 1 Exam Technique
Overview
Paper 1: 40 marks, 1 hour, no calculator allowed.
Objective: Demonstrate live exam techniques; minimal editing to reflect genuine exam conditions.
Preparation: Familiarize with the formula sheet: quadratic formula, discriminant, sine and cosine rules, volume and area formulas, and standard deviation.
Exam Strategy
Initial Scan: Quickly go through the paper to gauge difficulty and manage time.
Timing: Aim for approximately 1 mark per minute.
Problem-Solving: If stuck, move on to the next question to manage time effectively.
Key Problems and Solutions
Question 1: Fractions
Convert mixed numbers to improper fractions.
Simplify by dividing top and bottom by common factors.
Question 2: Equation of a Line
Formula: Use y - b = m(x - a) or y = mx + c.
Gradient: Calculate using (y2 - y1) / (x2 - x1).
Find y-intercept and write equation.
Question 3: Change the Subject
Objective: Rearrange formula to make 'p' the subject.
Steps:
Multiply both sides by denominator.
Divide by coefficient of p squared.
Square root to solve for p.
Question 4: Circle Geometry
Concepts: Tangent-radius is 90 degrees; diameter makes right angle at circumference.
Use these properties to find missing angles.
Question 5: Nature of Roots
Use discriminant, b^2 - 4ac, to determine the nature of roots.
0: Two distinct roots
= 0: One real root
< 0: No real roots
Question 6: Sine Graph
Identify amplitude (A) and frequency (B).
Amplitude = maximum value; Frequency determined by number of waves in given interval.
Advanced Questions
Question 7: Reverse Percentages
Given: Price drop by 20% to a new value.
Calculation: If 80% = new value, reverse to find original price.
Question 8: Vectors
Use given relationships to express a vector in terms of others.
Question 9: Simplifying Indices
Rules: Power of a power; negative indices.
Express with positive indices by moving base to denominator.
Question 10: Area of Triangle
Formula: Area = 1/2 * ab * sin(C)
Use given sin value directly in non-calculator paper.
Question 11: Functions
Evaluate Function: Substitute given value into function.
Solve for unknowns using given function equality.
Question 12: Inequalities
Solve similar to equations, but remember to flip inequality when multiplying/dividing by negative.
Question 13: Volume and Scale Factor
Volume Scale Factor: Use to find linear dimensions by cube-rooting.
Question 14: Completing the Square
Form: x^2 - 4x - 1 = (x - h)^2 - k
Find roots using quadratic formula; express in radical form.
Conclusion
Demonstrated live problem-solving and exam strategies.