Secondary 3 G2 Mathematics Tutor Bukit Timah | Solving Quadratics by Completing the Square. Did you know? A quadratic can be rewritten as a perfect square plus a number.
This Secondary 3 G2 Mathematics tutor guide for Bukit Timah families explains solving quadratics by completing the square with worked examples, quick checks and independent practice. Use the student’s school chapter list to match the current learning sequence.
The basic identity
x²+6x+9=(x+3)². Half of the x coefficient is 3; its square is 9.
A helpful tutoring exercise changes the given values and asks the student to explain the method without copying the original worked solution. Identify the first incorrect decision before correcting arithmetic.
Complete a square
x²+6x+5=(x+3)²−4, because expanding the square gives x²+6x+9.
A helpful tutoring exercise changes the given values and asks the student to explain the method without copying the original worked solution. Identify the first incorrect decision before correcting arithmetic.
Solve an equation
For x²+6x+5=0, write (x+3)²=4, so x+3=±2 and x=−1 or −5.
A helpful tutoring exercise changes the given values and asks the student to explain the method without copying the original worked solution. Identify the first incorrect decision before correcting arithmetic.
Turning point
The graph y=(x+3)²−4 has minimum value −4 at x=−3 and turning point (−3,−4).
A helpful tutoring exercise changes the given values and asks the student to explain the method without copying the original worked solution. Identify the first incorrect decision before correcting arithmetic.
Non-unit coefficient
2x²+8x+3=2(x+2)²−5. Factor out 2 from the quadratic and linear terms before completing the square.
A helpful tutoring exercise changes the given values and asks the student to explain the method without copying the original worked solution. Identify the first incorrect decision before correcting arithmetic.
Check roots
For x²+6x+5=0, substituting −1 gives 1−6+5=0, and substituting −5 gives 25−30+5=0.
A helpful tutoring exercise changes the given values and asks the student to explain the method without copying the original worked solution. Identify the first incorrect decision before correcting arithmetic.
Common error
Remember both positive and negative square roots when solving z²=k for positive k.
A helpful tutoring exercise changes the given values and asks the student to explain the method without copying the original worked solution. Identify the first incorrect decision before correcting arithmetic.
Seven-day revision plan
Day 1: identify the definitions. Day 2: work through the first example. Day 3: change the numbers. Day 4: attempt a mixed problem. Day 5: explain and correct mistakes. Day 6: connect the skill to another chapter. Day 7: retest independently after a delay.
Frequently asked questions
How do I start? Name the known quantities and what must be found. How can I check? Substitute the result into the original relationship, compare the units and test whether the magnitude makes sense. What should a tutor diagnose? The first mistaken step, not only the final answer.
Official syllabus and small-group tutorial context
Consult the 2027 SEC G2 Mathematics K210 syllabus for exact assessment requirements. The unchanged eduKateSG Mathematics reference describes three-pupil tutorials near Sixth Avenue. Confirm current Secondary 3 G2 class fit, tutor, fees, venue and timetable directly.
Related Secondary 3 G2 Mathematics guides
See Reverse Percentages, Quadratic Graphs and Estimated Mean.