Form 4 Mathematics builds on three algebra skills: expanding, factorising and solving. A short test on each shows which gap to repair first.
This page sits under SPM Mathematics, and connects to the Form 4 Mathematics chapters.
Which three skills should I test?
Expanding turns 3(x − 4) into 3x − 12. Factorising reverses it: 6x + 9 becomes 3(2x + 3). Solving finds x in 2x − 7 = 11.
Chapters like quadratic functions and equations use all three in one question, so a gap in any one shows up there.
Worked example: two errors, two repairs
An original pair of questions: expand and simplify 2(x + 5) − 3(x − 2), then factorise 4x² − 12x.
Expansion error. A student writes 2x + 10 − 3x − 2 = −x + 8. The sign on −3 × −2 was missed: it should be +6, so the correct line is 2x + 10 − 3x + 6 = −x + 16.
Factorising error. A student writes 4x² − 12x = 4(x² − 3x). This is correct but incomplete, because x is also common, so the full factor is 4x(x − 3). Check by expanding: 4x × x = 4x² and 4x × −3 = −12x.
Both errors are small, and both are found by the same move: expand your answer back and compare.
What mistake causes the most damage later?
Sign errors when a bracket follows a minus. The error −3(x − 2) → −3x − 6 looks natural and passes unnoticed on a fast read.
The fix is to write the multiplier beside every term: −3 × x and −3 × −2. Two extra seconds prevent the error in every later chapter.
A two-week repair plan
Days 1 to 4: expanding, ten questions a day, checking each by substituting x = 2. Days 5 to 9: factorising, always expanding back to check. Days 10 to 14: solving, checking each answer in the original equation.
Record errors in the mistake log tool, and use the algebra step repair trainer for extra drills on the step that keeps failing.
A short self-check
Factorise 9x² − 6x and check your answer by expanding.
Answer
The common factor is 3x, so 9x² − 6x = 3x(3x − 2). Check: 3x × 3x = 9x² and 3x × −2 = −6x. A student who writes 3(3x² − 2x) has taken out only the number.
When might one-to-one tuition help?
If the test shows gaps in all three skills, or the plan stalls on the same step, a teacher can repair them in the order your Form 4 chapters need. That avoids spending two weeks on a skill you had already secured.
You can begin with the one-hour trial class (from RM50), a real taught lesson, using the algebra questions you find hardest. The fee is agreed before the trial, and the schedule is agreed with the teacher. More is on the SPM Mathematics tuition page.