Teacher License Math 2 Study Plan: 8 Weeks or 4 Weeks by Standard Weights

Last verified: 30 October 2026. Our sources are the Professional License Test for Educational Professions page on the Education and Training Evaluation Commission (ETEC) website and the candidate guide for the Mathematics (Level 2) test. This guide is independent: it is not affiliated with ETEC, Qiyas (the National Center for Assessment), the Ministry of Education or any government body.

In short: the specialized test in mathematics (Level 2) covers twelve standards, and five of them (algebra and functions, geometry, numbers, statistics, and calculus) make up 74% of the questions. Calculators are not allowed, so arithmetic by hand and estimation are part of your preparation from day one. Below you will find an 8-week plan, a 4-week plan, a list of formulas to memorise and a plan for the last week.

Know what you are facing

• Questions: 88 multiple-choice questions with four options, and our mock exams have the same number.
• Time: 120 minutes, about 80 seconds a question.
• No penalty for wrong answers: so never leave a question blank. A score of 50 means 44 correct answers, 70 means 62 and 80 means 71.
• No calculator: ETEC bans it in both the General Educational Test and the specialized test.
• Your date: the latest specialized test window was 18 to 31 October 2026, and the next one is expected in late January 2027. The two plans below are in weeks, so pick the one closest to the weeks you have left (registration steps).
• Your target: the license level is set by the lower of your specialized and General Educational scores, together with your qualification and experience, so do not neglect either one. Aim for 50, 70 or 80 in both.

Where the questions go

These are the weights of the twelve standards from the specification table in the candidate guide (p. 7). The questions column is each standard's share of 88 questions, and it is the same split our mock exams use. Both plans below follow these weights.

The 8-week plan

Five days for new standards, one day for redoing wrong answers and one day of rest or light review. The first six weeks cover the heaviest standards, the seventh covers the rest and the eighth is for mock exams.

The 4-week plan

For when you have a month left. It concentrates on the heaviest standards and groups the small ones into a single week. The pace is faster (about 40 to 50 questions a day), so start with the free questions on day 1 to find your weakest standards and give them more time.

With either plan, read the guide to the standards and indicators to see what sits under each standard, and open the practice area: it has 10 free questions, while the full question bank and the full mock exams come with 7-day or lifetime access (prices).

Practise arithmetic without a calculator

You do not need a special gift, only small habits repeated. From week one, spend 10 minutes a day on the following, and try each one on paper, not only in your head.

• Memorise ready tables: squares up to 20, cubes up to 10, powers of 2 up to 2^{10}=1024, the roots of perfect squares, and common fractions as decimals (such as \frac{1}{8}=0.125 and \frac{3}{8}=0.375).
• Split the multiplication: 48\times25=48\times100\div4=1200, and 17\times 6=10\times6+7\times6.
• Percentages from 10%: 10% is a shift of the decimal point, 5% is half of that, 15% is the two added together and 25% is a quarter.
• Roots and constants by approximation: \sqrt2\approx1.41, \sqrt3\approx1.73 and \pi\approx3.14 or \frac{22}{7}; for a quick comparison, \pi\approx3 is enough.
• Estimate before you solve: round numbers to the nearest ten or hundred, work out the approximate result, then eliminate options far from it. The units digit is often enough to tell two options apart.
• Check by substitution: in equations, put your answer back into the original equation; with four options, substituting the options themselves can be faster than solving.
• Leave long arithmetic until last: write the formula in symbols first, and cancel before you multiply. For example, \dfrac{36\times25}{15}=\dfrac{12\times25}{5}=60.

Formulas to memorise

Write them on a card and review it every morning from week one, and try writing them from memory before you look. If you cannot recall a formula, derive it from a simple case: for example, the sum of an arithmetic sequence comes from pairing the first term with the last.

Numbers and algebra

• x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} and the discriminant \Delta=b^2-4ac
• Sum of roots -\dfrac{b}{a}, product of roots \dfrac{c}{a}
• (a\pm b)^2=a^2\pm 2ab+b^2, a^2-b^2=(a-b)(a+b), a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)
• \(|x|a\iff x>a\) or \(x<-a\)
• a^m\cdot a^n=a^{m+n}, (a^m)^n=a^{mn}, a^{-n}=\dfrac{1}{a^n}, a^{1/n}=\sqrt[n]{a}
• \log_a(xy)=\log_a x+\log_a y, \log_a x^k=k\log_a x, \log_a x=\dfrac{\ln x}{\ln a}
• |z|=\sqrt{a^2+b^2}, z\bar z=|z|^2, z=r(\cos\theta+i\sin\theta) for z=a+bi
• Arithmetic sequence: a_n=a_1+(n-1)d and S_n=\dfrac{n}{2}(a_1+a_n)
• Geometric sequence: a_n=a_1r^{n-1} and S_n=\dfrac{a_1(1-r^n)}{1-r}; for the infinite series S=\dfrac{a_1}{1-r} when \(|r|<1\)
• A 2\times2 matrix: \det=ad-bc, inverse \dfrac{1}{ad-bc}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}

Geometry and measurement

• Distance between two points \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, midpoint \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)
• Slope m=\dfrac{y_2-y_1}{x_2-x_1}, line y-y_1=m(x-x_1), distance from a point to a line \dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}
• Circle: (x-h)^2+(y-k)^2=r^2, circumference 2\pi r, area \pi r^2, sector area \dfrac{1}{2}r^2\theta
• Triangle area \dfrac{1}{2}bh, trapezoid \dfrac{1}{2}(a+b)h, sum of a polygon's angles (n-2)\times180^\circ
• Cylinder V=\pi r^2h, cone V=\dfrac{1}{3}\pi r^2h, sphere V=\dfrac{4}{3}\pi r^3 with surface area 4\pi r^2, pyramid V=\dfrac{1}{3}Bh
• \sin^2\theta+\cos^2\theta=1, \sin2\theta=2\sin\theta\cos\theta, \cos2\theta=\cos^2\theta-\sin^2\theta
• Law of sines \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}, law of cosines c^2=a^2+b^2-2ab\cos C
• Ellipse \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1, hyperbola \dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1, parabola y^2=4px
• Vectors: \vec a\cdot\vec b=|\vec a||\vec b|\cos\theta, length |\vec v|=\sqrt{x^2+y^2}

Calculus

• \dfrac{d}{dx}x^n=nx^{n-1}, (uv)'=u'v+uv', \left(\dfrac{u}{v}\right)'=\dfrac{u'v-uv'}{v^2}, \dfrac{d}{dx}f(g(x))=f'(g(x))\,g'(x)
• \dfrac{d}{dx}\sin x=\cos x, \dfrac{d}{dx}\cos x=-\sin x, \dfrac{d}{dx}e^x=e^x, \dfrac{d}{dx}\ln x=\dfrac{1}{x}
• \displaystyle\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C where n\neq-1, and \displaystyle\int_a^b f(x)\,dx=F(b)-F(a)
• \displaystyle\lim_{x\to0}\dfrac{\sin x}{x}=1

Statistics, probability and logic

• \bar x=\dfrac{\sum x}{n}, variance \sigma^2=\dfrac{\sum(x-\bar x)^2}{n}, standard deviation \sigma=\sqrt{\sigma^2}
• P(A\cup B)=P(A)+P(B)-P(A\cap B), P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}
• {}_nP_r=\dfrac{n!}{(n-r)!}, {}_nC_r=\dfrac{n!}{r!\,(n-r)!}, (a+b)^n=\sum_{k=0}^{n}{}_nC_k\,a^{n-k}b^k
• De Morgan's laws: \neg(p\wedge q)\equiv\neg p\vee\neg q and \neg(p\vee q)\equiv\neg p\wedge\neg q; contrapositive p\to q\equiv\neg q\to\neg p

The last week

1. Day 1: a full mock exam of 88 questions in 120 minutes, on paper with only a pen, no phone and no calculator. Record your score and the time you spent on each standard.
2. Day 2: redo every question you got wrong and write down the reason for each: a formula you forgot, an arithmetic slip or a question you did not understand. Then answer ten new questions from your weakest standard.
3. Days 3 and 4: your three weakest standards from the mock exam, with weak-spots questions, redoing wrong answers and 10 minutes of mental arithmetic.
4. Day 5: a second timed full mock exam. Compare its score with the first, standard by standard; errors of the same kind that remain are your real weaknesses.
5. Day 6: only the wrong answers from both mock exams and your formula card. Do not start a new topic.
6. The day before the test: light review of no more than an hour, and enough sleep. Confirm your date and centre in your profile and that your ID is valid.

Common traps in maths questions

• The square root sign: \sqrt{x^2}=|x|, not x, and solving x^2=9 gives x=\pm3.
• Dividing an inequality by a negative number: the inequality sign flips: \(-2x>6\Rightarrow x<-3\).
• Squaring a sum: (a+b)^2\neq a^2+b^2; the correct form is a^2+2ab+b^2.
• The domain of a function: exclude values that make a denominator zero, put a negative under an even root, or make the argument of a logarithm non-positive.
• Differentiation: do not forget the chain rule; the derivative of \sin(3x) is 3\cos(3x).
• Probability: permutations when order matters and combinations when it does not; ask yourself whether changing the order changes the outcome.

This plan is our suggestion for organising your time and does not guarantee any score, and your mock exam score is an estimate of readiness, not an official result. Start unit practice with algebra, functions and geometry (38% together), and keep the full mock exam for the end of the plan.