Grade 11 Maths Papers Sinhala Medium: Term Test Practice Set

When grade 11 maths starts feeling heavy, it is usually not because you “cannot do maths”. It is because the paper asks for many different skills in one sitting: algebra, functions, geometry, trigonometry style reasoning, probability or statistics depending on the syllabus, and careful calculation. A good term test practice set helps you train that mix, not just one chapter.

This practice set is written for Sinhala medium learners who want to build confidence for term tests, using the same kind of thinking you would use in real past papers. I also included worked examples, because grade 11 maths rewards students who can show the steps clearly, not only get the final answer.

If you already use resources like e kalvi and eKalvi style collections, you will recognize the pattern: term tests are where weak topics show up fast. So let’s turn that pressure into practice, with a set that feels like an actual exam.

How to use this practice set (so it actually improves your score)

A lot of students try one question at a time, check answers, then move on. That can work for easy topics, but grade 11 maths is different. The exam tests speed, accuracy, and method choice under time limits.

The approach I recommend is simple. Start by attempting each group with a timer. If you get stuck for more than a few minutes, switch to a targeted technique instead of staring. Then, after you finish, you review your mistakes by category: algebra slips, sign mistakes, missing conditions, or careless arithmetic.

Here is a short rule that saves time during revision:

Practice like you sit the paper. Do not treat every question like a homework question. Mark the points where you took too long. Those are the exact places where your term test score is leaking.

Before you begin, prepare two things: a clean page for working, and a correction page titled “mistakes to avoid”. You will thank yourself later.

A quick session plan (use this exact flow)

Do questions without looking at solutions for the first attempt
Mark anything you solved incorrectly and anything you did not reach
Redo only the missed parts, but this time write the method neatly
Note the mistake type on your correction page
Do a short mixed set on the next day (even 20 to 30 minutes)

This “redo only the missed parts” method is where most improvement comes from.

What grade 11 term tests usually try to measure

Without pretending every school follows the same paper style, grade 11 maths term tests usually reward these habits:

clear algebra manipulation (especially where signs and fractions appear)
choosing the correct identity or formula rather than guessing
showing reasoning in geometry and trigonometry style questions
careful reading of “find”, “prove”, “determine”, and “if” conditions
checking the answer makes sense in the given range or constraint

A small personal note: the students I have seen jump from average to strong usually stop “computing blindly”. They start pausing for one second to ask, “What form should this end in?” That one second reduces wrong turns a lot.

Practice set A: algebra and functions (exam-style mixed questions)

Try these in order. If you want, stop after each subtopic group and review your steps.

Question A1: Solve and simplify

Solve for (x): [ \frac2x-3x-1 - \fracx+1x+2 = 1 ] Guidance: First note the restrictions (x \neq 1) and (x \neq -2). Then combine fractions.

Solution (worked):

[ \frac2x-3x-1 - \fracx+1x+2 = 1 ] Bring to common denominator ((x-1)(x+2)): [ \frac(2x-3)(x+2) - (x+1)(x-1)(x-1)(x+2) = 1 ] So [ (2x-3)(x+2) - (x+1)(x-1) = (x-1)(x+2) ] Expand the left: [ (2x-3)(x+2)=2x(x+2)-3(x+2)=2x^2+4x-3x-6=2x^2+x-6 ] [ (x+1)(x-1)=x^2-1 ] Thus left side: [ (2x^2+x-6) - (x^2-1) = x^2+x-5 ] Right side: [ (x-1)(x+2)=x^2+x-2 ] Set equal: [ X^2+x-5 = x^2+x-2 ] So (-5=-2), which is impossible. Answer: No solution.

What this question trains: It trains fraction handling and also “recognizing inconsistency” instead of forcing an answer.

Question A2: Quadratic factor check

Factorize fully: [ X^2 - 5x + 6 ] Solution:

We need two numbers that multiply to (6) and add to (-5): (-2) and (-3). So [ X^2-5x+6=(x-2)(x-3) ] Answer: ((x-2)(x-3)).

Question A3: Solve a rational inequality (keep signs controlled)

Solve: [ \fracx-2x+1 \ge 0 ] Solution:

Critical points: (x=2) (zero) and (x=-1) (undefined). Build sign intervals:

(x<-1)
(-1
(x\ge 2)

Test one value per interval, for example (x=-2), (x=0), (x=3):

If (x=-2): (\frac-4-1 >0) so inequality holds
If (x=0): (\frac-21<0) so it does not hold
If (x=3): (\frac14>0) so it holds

Also include (x=2) because expression equals zero and zero is allowed in “(\ge 0)”. Exclude (x=-1).

Answer: (x\in (-\infty,-1)\cup [2,\infty)).

Question A4: Function reasoning

If (f(x)=2x^2-3x), find (f(3)) and solve (f(x)=0).

Solution:

[ F(3)=2(9)-3(3)=18-9=9 ] For (f(x)=0): [ 2x^2-3x=0 ] Factor: [ X(2x-3)=0 ] So (x=0) or (x=\frac32).

Answer: (f(3)=9), zeros are (x=0) and (x=\frac32).

Practice set B: equations, identities, and “show the method” questions

These are the questions where marks are won or lost by how neatly you manage algebra.

Question B1: Simplify using algebraic steps

Simplify: [ \frac(x^2-9)(x-3) ] For (x \neq 3).

Solution:

Use difference of squares: [ X^2-9=(x-3)(x+3) ] So [ \frac(x-3)(x+3)(x-3) = x+3 ] Restriction (x \neq 3) is already noted.

Answer: (x+3).

Question B2: Solve a linear equation inside a fraction

Solve: [ \frac3x-12 = \fracx+53 ]

Solution:

Cross multiply: [ 3(3x-1)=2(x+5) ] [ 9x-3=2x+10 ] [ 7x=13 ] [ X=\frac137 ]

Answer: (x=\frac137).

Question B3: Expand and collect terms carefully

Expand: [ (2x-1)(x+4) ]

Solution:

Distribute: [ (2x-1)(x+4)=2x(x+4)-1(x+4)=2x^2+8x-x-4=2x^2+7x-4 ]

Answer: (2x^2+7x-4).

Practice set C: geometry and reasoned steps (build exam confidence)

Geometry questions can feel intimidating until you practice the same “shape thinking” every time. The goal is not only to reach a number, but to connect angles, triangles, and relationships logically.

Question C1: Angles in a triangle (work method, not guessing)

In triangle (ABC), angle (A = 40^\circ) and angle (B = 70^\circ). Find angle (C).

Solution:

Angles in a triangle sum to (180^\circ): [ C=180^\circ-(40^\circ+70^\circ)=180^\circ-110^\circ=70^\circ ] Answer: (70^\circ).

Question C2: Perimeter and algebra link

A rectangle has length (x+5) and width (2x-1). If the perimeter is (42), find (x).

Solution:

Perimeter of rectangle: [ 2[(x+5)+(2x-1)]=42 ] Inside bracket: [ (x+5)+(2x-1)=3x+4 ] So: [ 2(3x+4)=42 ] [ 6x+8=42 ] [ 6x=34 ] [ X=\frac346=\frac173 ]

Answer: (x=\frac173).

Question C3: Similar triangles (if your term test includes this)

Triangles (PQR) and (STU) are similar. If (PQ=6) corresponds to (ST=9), and (QR=8) corresponds to (TU), find (TU).

Solution:

Similarity ratio: [ \fracSTPQ=\frac96=\frac32 ] Corresponding side (TU) matches (QR): [ TU = QR \times \frac32 = 8 \times \frac32=12 ] Answer: (TU=12).

Practice set D: trigonometry style questions (common in grade 11)

Trigonometry questions can be solved faster once you recognize which relationship you need, especially if the paper includes right triangle problems or angle values.

Question D1: Find an angle using sine

In a right triangle, the side opposite angle (\theta) is 3 and the hypotenuse is 5. Find (\sin\theta) and (\theta).

Solution:

[ \sin\theta=\frac\textopposite\texthypotenuse=\frac35 ] For (\theta), you would use a calculator or trig table, because (\sin^-1(3/5)) is not a “nice” exact angle in all syllabi. So: [ \theta \approx \sin^-1(0.6) ] [ \theta \approx 36.9^\circ ]

Answer: (\sin\theta=\frac35), (\theta \approx 36.9^\circ).

Question D2: Basic identity to simplify

Simplify: [ \sin^2 x + \cos^2 x ]

Solution:

Use identity: [ \sin^2 x + \cos^2 x = 1 ]

Answer: (1).

Practice set E: probability and data thinking (keep it practical)

Many term tests include probability or a data interpretation part. The trick is to translate the language into a clear method.

Question E1: Simple probability with equally likely outcomes

A bag contains 3 red balls and 2 blue balls. One ball is chosen at random. Find probability of choosing a red ball.

Solution:

Total balls (=3+2=5) Probability of red: [ \frac35 ] Answer: (\frac35).

Question E2: Mean and interpretation (no overthinking)

The marks of five students are: 28, 35, 30, 32, 25. Find the mean.

Solution:

Sum: [ 28+35+30+32+25=150 ] Mean: [ \frac1505=30 ] Answer: 30.

The mistakes that cost marks (and how to prevent them)

If you want a high score, it helps to know exactly where students lose points. Based on what I see in correction sessions, most errors fall into a few patterns.

Here is the most common set to watch for:

Mixing up signs in expansions like ((x-3)(x+2))
Forgetting restrictions in rational expressions, like (x \neq 1)
Solving an equation and not checking it against the restriction
Doing correct algebra but writing steps too messy to earn method marks
Stopping after the calculator answer without writing a sensible unit or final form when needed

You can fight these mistakes with two habits: write restrictions clearly, and circle your final answer before you move on, then do a quick reason check (does it match the form the question asked for?).

A short “mock term test” mixed drill (timed, like the real thing)

Set a timer for 45 minutes. Attempt all questions below. If you cannot finish, that is normal. The point is to learn which parts you need to practice again.

Question M1 (Algebra): Solve for (x)

[ \fracx+2x-1 = 3 ] Show steps and state any restrictions.

Question M2 (Quadratic): Factorize

[ 2x^2 - 7x + 3 ] Factor fully.

Question M3 (Equation): Solve

[ 5(2x-1)=3x+7 ]

Question M4 (Trigonometry): Identity

[ 1-\cos^2\theta ] Rewrite in terms of (\sin^2\theta).

Question M5 (Probability): Counting method

A test paper has 8 questions. A student chooses 2 questions at random. Find the probability that the student grade 11 english term test papers chooses exactly 1 “hard” question, if there are 3 hard questions and 5 easy questions.

If you do not want to compute the probability in one go, you can list outcomes using combinations. Just keep the method clean.

Answer check (so you can grade yourself honestly)

I will give solutions in a compact form here, but try to do them first without looking.

M1:

[ \fracx+2x-1=3 \Rightarrow x+2=3(x-1)=3x-3 ] [ 2=2x-3 \Rightarrow 2x=5 \Rightarrow x=\frac52 ] Restriction (x \neq 1), so it is valid.

M2:

Try factors for (2x^2 -7x +3): [ 2x^2-7x+3=(2x-1)(x-3) ] Check: (2x^2-6x-x+3=2x^2-7x+3).

M3:

[ 5(2x-1)=10x-5=3x+7 \Rightarrow 7x=12 \Rightarrow x=\frac127 ]

M4:

Identity: [ \sin^2\theta = 1-\cos^2\theta ] So the expression equals (\sin^2\theta).

M5:

Total ways choose 2 questions: [ \binom82=28 ] Ways to choose exactly 1 hard and 1 easy: [ \binom31\binom51=3 \times 5=15 ] Probability: [ \frac1528 ]

Where to find extra Sinhala medium practice without losing time

If you are searching online for grade 11 maths papers sinhala medium or grade 11 maths past papers sinhala medium with answers, it helps to choose sources that provide both questions and correction-style answers. Many pages show only question copies, and without method steps, you end up repeating mistakes.

Also, if you use study materials like grade 10 maths term test papers sinhala medium or grade 9 maths past papers sinhala medium with answers, treat them as warm-ups. The skills are related, and you will notice which concepts are still shaky, before the grade 11 paper reveals them.

You may also come across materials labeled in ways like grade 11 english papers pdf download or grade 11 science term test papers sinhala medium. Even if those are not maths, they can still help with paper habits, like how to manage time and how answers are expected to be presented. That part matters a lot in term tests.

For additional Sinhala term test practice sets, students often rely on e kalvi, eKalvi style pages. If you are using such platforms, focus on matching your current term syllabus. A good practice question is the one that uses the same skills you are learning now, not the one that looks “hard”.

Final study push: make tomorrow’s revision easy

If you have 30 to 40 minutes before your next class test or term exam, do not start a new chapter. Instead:

Write out the 5 topics or question types you struggled with during this practice set. Then redo only those, using the solutions here as a guide. Keep the working neat. If your working is readable, you will remember it later. If it is messy, you will have to relearn from zero.

That is the quiet reason strong students score higher. Not because they study longer, but because they revise smarter.

If you want, tell me which subtopics your current grade 11 maths syllabus is focusing on for your school term, and I can generate another Sinhala medium term test practice set tailored to that exact mix of algebra, geometry, trigonometry, and probability.