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100+ Free GTLE Mathematics Specialism Practice Questions

Pass your Ghana Teacher Licensure Examination (GTLE) Subject Specialism - Mathematics exam on the first try — instant access, no signup required.

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2026 Statistics

Key Facts: GTLE Mathematics Specialism Exam

100

Practice questions with step-by-step calculations in this test bank

OpenExamPrep database

50%

NTC Ghana official passing score threshold

NTC consultation guidelines

35%

Weight of Algebra and Functions in the GTLE Mathematics syllabus

NTC content blueprint

GH¢150

Re-sit registration fee for a single GTLE paper

NTC registration notice

2 hours

Time limit allocated for the Subject Specialism paper

exams.ntc.gov.gh details

Act 1023

The Education Regulatory Bodies Act establishing the licensing mandate

Ghana Parliament

The NTC GTLE Mathematics Subject Specialism is a 100-question computer-based paper assessing advanced algebra, geometry, calculus, statistics, and mathematics teaching pedagogy. Passing this along with the GPK and Pedagogy papers is required for professional licensing in Ghana.

Sample GTLE Mathematics Specialism Practice Questions

Try these sample questions to test your GTLE Mathematics Specialism exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Convert the binary number $11011_2$ to a base ten (decimal) number.
A.25
B.27
C.29
D.31
Explanation: To convert $11011_2$ to base ten, we sum the powers of 2 for each digit: $1\times 2^4 + 1\times 2^3 + 0\times 2^2 + 1\times 2^1 + 1\times 2^0$. This evaluates to $16 + 8 + 0 + 2 + 1 = 27$. Expressing numbers in powers of their base is the foundational method for any base conversion.
2A school textbook originally priced at GH¢ 120.00 is sold at a 15% discount during a promotional sales event. What is the sale price of the textbook?
A.GH¢ 102.00
B.GH¢ 105.00
C.GH¢ 108.00
D.GH¢ 110.00
Explanation: The discount amount is calculated as $15\% \text{ of } 120 = 0.15 \times 120 = 18$. The sale price is the original price minus the discount: $120 - 18 = 102$. Alternatively, the sale price can be computed as $85\% \text{ of } 120 = 0.85 \times 120 = 102$.
3Simplify the expression: $\frac{2}{3} - \frac{1}{4} + \frac{5}{6}$.
A.$\frac{3}{4}$
B.$\frac{5}{4}$
C.$\frac{7}{6}$
D.$\frac{13}{12}$
Explanation: To simplify $\frac{2}{3} - \frac{1}{4} + \frac{5}{6}$, we find the Least Common Multiple (LCM) of the denominators 3, 4, and 6, which is 12. Convert each fraction: $\frac{8}{12} - \frac{3}{12} + \frac{10}{12}$. Now perform the operations: $\frac{8 - 3 + 10}{12} = \frac{15}{12} = \frac{5}{4}$.
4Express the number $0.000456$ in standard form (scientific notation).
A.$4.56 \times 10^{-4}$
B.$4.56 \times 10^{-5}$
C.$45.6 \times 10^{-5}$
D.$4.56 \times 10^{-3}$
Explanation: To write $0.000456$ in standard form ($A \times 10^n$, where $1 \le A < 10$), we move the decimal point 4 places to the right to get $4.56$. Moving the decimal point to the right corresponds to a negative power of ten, yielding $4.56 \times 10^{-4}$.
5In a class of 40 students, 25 study Mathematics, 18 study Physics, and 8 study both subjects. How many students study neither Mathematics nor Physics?
A.3
B.5
C.7
D.9
Explanation: Let $M$ be the set of students studying Mathematics and $P$ be the set of students studying Physics. According to the principle of inclusion-exclusion: $|M \cup P| = |M| + |P| - |M \cap P| = 25 + 18 - 8 = 35$. The number of students studying neither is the total number of students minus those studying at least one: $40 - 35 = 5$.
6Simplify the surd expression: $\sqrt{75} - \sqrt{12}$.
A.$3\sqrt{3}$
B.$5\sqrt{3}$
C.$2\sqrt{3}$
D.$\sqrt{63}$
Explanation: Simplify each radical by finding perfect square factors: $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$ and $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$. Subtracting these yields: $5\sqrt{3} - 2\sqrt{3} = (5-2)\sqrt{3} = 3\sqrt{3}$.
7Solve the exponential equation for $x$: $3^{2x-1} = 27$.
A.$x = 1$
B.$x = 2$
C.$x = 3$
D.$x = 4$
Explanation: First, express 27 as a power of 3: $27 = 3^3$. The equation becomes $3^{2x-1} = 3^3$. Since the bases are equal, equate the exponents: $2x - 1 = 3$. Solve for $x$: $2x = 4 \implies x = 2$.
8During a decimal multiplication lesson, a student claims that $0.3 \times 0.2 = 0.6$. Which of the following best diagnoses the student's mathematical misconception?
A.The student multiplied the tenths digits but did not adjust the place value to hundredths.
B.The student added the decimal values instead of multiplying them.
C.The student believes that multiplying decimal numbers always yields a value larger than the inputs.
D.The student does not understand basic single-digit multiplication facts.
Explanation: The student multiplied the digits $3 \times 2 = 6$ but kept the place value as tenths, failing to recognize that $\frac{3}{10} \times \frac{2}{10} = \frac{6}{100} = 0.06$. Helping students convert decimals to fractions is a key pedagogical strategy to visualize and correct this place value error.
9Rationalize the denominator of the following expression: $\frac{3}{\sqrt{5} - \sqrt{2}}$.
A.$\sqrt{5} - \sqrt{2}$
B.$\sqrt{5} + \sqrt{2}$
C.$\frac{3(\sqrt{5} + \sqrt{2})}{7}$
D.$3(\sqrt{5} + \sqrt{2})$
Explanation: To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator, which is $\sqrt{5} + \sqrt{2}$: $\frac{3(\sqrt{5} + \sqrt{2})}{(\sqrt{5} - \sqrt{2})(\sqrt{5} + \sqrt{2})}$. The denominator expands as a difference of squares: $(\sqrt{5})^2 - (\sqrt{2})^2 = 5 - 2 = 3$. This simplifies to: $\frac{3(\sqrt{5} + \sqrt{2})}{3} = \sqrt{5} + \sqrt{2}$.
10Solve the equation for real values of $x$: $2^{2x} - 6(2^x) + 8 = 0$.
A.$x = 1 \text{ or } x = 2$
B.$x = 2 \text{ or } x = 4$
C.$x = 0 \text{ or } x = 1$
D.$x = 1 \text{ or } x = 3$
Explanation: Let $u = 2^x$. The equation becomes a quadratic equation: $u^2 - 6u + 8 = 0$. Factor the quadratic: $(u - 2)(u - 4) = 0$, which gives $u = 2$ or $u = 4$. Substitute back $u = 2^x$: $2^x = 2 \implies x = 1$, and $2^x = 4 \implies 2^x = 2^2 \implies x = 2$. Thus, the solutions are $x=1$ or $x=2$.

About the GTLE Mathematics Specialism Exam

The Mathematics Subject Specialism paper is the content-focused exam for JHS, SHS, and TVET mathematics teacher candidates in Ghana. It tests advanced high school content, foundational college algebra, geometry, trigonometry, calculus, probability, and statistics, as well as mathematics pedagogy. It aims to ensure that mathematics educators have a strong grasp of both subject matter and pedagogical methods, such as diagnostic assessment of student errors and the use of physical and visual representations.

Assessment

One core subject-specialization paper. Taken alongside the GTLE General Professional Knowledge (GPK) paper and the level-specific Pedagogy paper by JHS, SHS, and TVET mathematics teacher candidates.

Time Limit

2 hours (120 minutes)

Passing Score

A minimum passing score of 50% is required across the papers (subject to NTC regulation updates).

Exam Fee

GH¢450 fresh (3 papers); re-sit GH¢150/210/385; indexing GH¢50 fresh (National Teaching Council (NTC) Ghana)

GTLE Mathematics Specialism Exam Content Outline

25%

Number and Number Systems

Fractions, decimals, percentages, indices, surds, scientific notation, number bases, sets, and basic number theory.

35%

Algebra and Functions

Algebraic expressions, linear/quadratic equations, inequalities, systems of equations, sequences/series (APs and GPs), and function analysis (domain, range, composition, and inverses).

20%

Geometry and Trigonometry

Plane and solid geometry, coordinates, angles, polygons, circles, mensuration (area, perimeter, volume), bearings, and trigonometric ratios, identities, graphs, and equations.

10%

Calculus and Coordinate Geometry

Limits, derivatives, differentiation rules (power, product, quotient, chain rule), simple integration, equations of straight lines and circles, and rates of change.

10%

Probability and Statistics

Data representation, measures of central tendency and dispersion, simple and compound probability, permutations, combinations, and basic binomial distribution.

How to Pass the GTLE Mathematics Specialism Exam

What You Need to Know

  • Passing score: A minimum passing score of 50% is required across the papers (subject to NTC regulation updates).
  • Assessment: One core subject-specialization paper. Taken alongside the GTLE General Professional Knowledge (GPK) paper and the level-specific Pedagogy paper by JHS, SHS, and TVET mathematics teacher candidates.
  • Time limit: 2 hours (120 minutes)
  • Exam fee: GH¢450 fresh (3 papers); re-sit GH¢150/210/385; indexing GH¢50 fresh

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

GTLE Mathematics Specialism Study Tips from Top Performers

1Understand the NTC Table of Specifications: Prioritize Algebra and Functions (35%) and Number and Number Systems (25%) as they make up 60% of the exam.
2Work through calculations step-by-step: The exam tests not just final numerical answers but algebraic manipulation, theorem applications, and systematic integration/differentiation.
3Review student misconceptions: Be prepared for pedagogical questions detailing how to diagnose common student errors in decimals, fractions, or algebraic signs.
4Practice coordinate geometry and circle theorems: Ensure you know how to write equations of lines/circles and apply theorems for angles in alternate segments, tangents, and cyclic quadrilaterals.

Frequently Asked Questions

Who is required to write the GTLE Mathematics Subject Specialism paper?

This paper is mandatory for teacher candidates who wish to be licensed to teach mathematics at the Junior High School (JHS), Senior High School (SHS), or TVET levels in Ghana.

What is the passing mark for the GTLE Mathematics paper?

The National Teaching Council (NTC) typically sets the passing score at 50%. However, candidates must review the official guidelines on exams.ntc.gov.gh for potential updates during each examination cycle.

What content areas are tested in the Mathematics Specialism paper?

The exam is divided into five core domains: Number and Number Systems (25%), Algebra and Functions (35%), Geometry and Trigonometry (20%), Calculus and Coordinate Geometry (10%), and Probability and Statistics (10%). Pedagogical content knowledge is integrated across these areas.

Are calculators allowed in the examination?

Yes, standard non-programmable scientific calculators are generally allowed for the mathematics papers. Candidates must confirm the specific calculator models approved by the NTC before the exam date.

What happens if I fail the Mathematics Subject Specialism paper?

You will be registered as a re-sit candidate. You only need to register and pay for the specific paper you failed (GH¢150 for a single paper re-sit).