Level 100 First-Semester Mathematics: 30 Objective Questions and Answers for Colleges of Education

Are you a Level 100 student at a College of Education in Ghana preparing for your first-semester mathematics examinations? This practice test contains 30 objective questions covering number systems, fractions, percentages, ratios, algebraic expressions, linear equations, inequalities, and sequences.

The questions are designed to help student-teachers practise mathematical concepts and assess their understanding before examinations.

Course area: Number and Algebra
Level: 100
Semester: First Semester
Total questions: 30
Total marks: 30

Instructions: Answer all questions. Select the correct option from A, B, C, and D. Each question carries one mark. Check your answers using the answer key at the end.

SECTION A: Number Systems and Basic Arithmetic

Question 1

Which of the following is an irrational number?

A. \( \frac{3}{4} \)

B. \( 0.25 \)

C. \( \sqrt{2} \)

D. \( 9 \)

Question 2

Evaluate:

\[ 18 + 6 \times 3 - 4 \]

A. \(68\)

B. \(32\)

C. \(36\)

D. \(28\)

Question 3

Express \(0.625\) as a fraction in its simplest form.

A. \( \frac{5}{8} \)

B. \( \frac{3}{5} \)

C. \( \frac{2}{5} \)

D. \( \frac{5}{6} \)

Question 4

Find the highest common factor (HCF) of \(24\) and \(36\).

A. \(6\)

B. \(8\)

C. \(12\)

D. \(18\)

Question 5

Find the lowest common multiple (LCM) of \(6\) and \(8\).

A. \(12\)

B. \(18\)

C. \(24\)

D. \(48\)

Question 6

Simplify:

\[ \frac{3}{4}+\frac{2}{3} \]

A. \( \frac{5}{7} \)

B. \( \frac{17}{12} \)

C. \( \frac{6}{12} \)

D. \( \frac{13}{12} \)

Question 7

Calculate:

\[ \frac{5}{6}-\frac{1}{4} \]

A. \( \frac{7}{12} \)

B. \( \frac{4}{2} \)

C. \( \frac{2}{10} \)

D. \( \frac{3}{12} \)

Question 8

Express \(0.08\) as a percentage.

A. \(0.8\%\)

B. \(8\%\)

C. \(80\%\)

D. \(800\%\)

Question 9

Find \(35\%\) of \(240\).

A. \(72\)

B. \(84\)

C. \(96\)

D. \(105\)

Question 10

Divide GH₵360 in the ratio \(2:3\). What is the smaller share?

A. GH₵120

B. GH₵144

C. GH₵180

D. GH₵216

SECTION B: Algebraic Expressions

Question 11

Simplify:

\[ 5x+3x-2x \]

A. \(10x\)

B. \(6x\)

C. \(8x\)

D. \(6x^2\)

Question 12

Expand:

\[ 4(x+3) \]

A. \(4x+3\)

B. \(4x+12\)

C. \(7x\)

D. \(4x+7\)

Question 13

Factorise:

\[ 6x+12 \]

A. \(6(x+2)\)

B. \(3(2x+12)\)

C. \(6(x+12)\)

D. \(2(3x+12)\)

Question 14

Simplify:

\[ 3a+2b-a+5b \]

A. \(2a+7b\)

B. \(4a+3b\)

C. \(2a+3b\)

D. \(5ab\)

Question 15

If \(x=4\), evaluate:

\[ 2x^2-3 \]

A. \(13\)

B. \(29\)

C. \(32\)

D. \(61\)

Question 16

Expand:

\[ (x+2)(x+3) \]

A. \(x^2+5x+6\)

B. \(x^2+6\)

C. \(x^2+6x+5\)

D. \(x^2+5x-6\)

Question 17

Factorise:

\[ x^2+7x+12 \]

A. \((x+2)(x+6)\)

B. \((x+3)(x+4)\)

C. \((x-3)(x-4)\)

D. \((x+1)(x+12)\)

Question 18

Simplify:

\[ 2(x+4)-3x \]

A. \(5x+8\)

B. \(8-x\)

C. \(x+8\)

D. \(8-5x\)

Question 19

Which of the following is a like term of \(7x^2\)?

A. \(5x\)

B. \(3x^2\)

C. \(7y^2\)

D. \(2x^3\)

Question 20

Simplify:

\[ \frac{12x^2y}{3xy} \]

A. \(4xy\)

B. \(4x\)

C. \(9xy\)

D. \(4x^2\)

SECTION C: Linear Equations and Inequalities

Question 21

Solve for \(x\):

\[ 3x+5=20 \]

A. \(3\)

B. \(5\)

C. \(7\)

D. \(15\)

Question 22

Solve for \(x\):

\[ 5x-7=18 \]

A. \(3\)

B. \(4\)

C. \(5\)

D. \(7\)

Question 23

Solve for \(x\):

\[ 2(x-3)=10 \]

A. \(2\)

B. \(5\)

C. \(8\)

D. \(13\)

Question 24

Solve for \(x\):

\[ \frac{x}{4}+3=7 \]

A. \(4\)

B. \(12\)

C. \(16\)

D. \(28\)

Question 25

If \(2x+3=11\), find the value of \(x+1\).

A. \(4\)

B. \(5\)

C. \(6\)

D. \(7\)

Question 26

Solve the inequality:

\[ 2x+1<9 \]

A. \(x<4\)

B. \(x>4\)

C. \(x<5\)

D. \(x>5\)

SECTION D: Number Patterns, Sequences and Applications

Question 27

Find the next number in the sequence:

\[ 4,\ 8,\ 12,\ 16,\ \ldots \]

A. \(18\)

B. \(20\)

C. \(22\)

D. \(24\)

Question 28

Find the \(n\)th term of the sequence:

\[ 3,\ 6,\ 9,\ 12,\ 15,\ \ldots \]

A. \(n+3\)

B. \(3n\)

C. \(3n+1\)

D. \(n^2\)

Question 29

A student scores \(45\) marks out of \(60\) in a mathematics examination. What is the student's percentage score?

A. \(65\%\)

B. \(70\%\)

C. \(75\%\)

D. \(80\%\)

Question 30

The sum of two consecutive integers is \(41\). What are the integers?

A. \(19\) and \(22\)

B. \(20\) and \(21\)

C. \(18\) and \(23\)

D. \(21\) and \(22\)

Answer Key

Marking Scheme

• Each correct answer carries 1 mark.
• Total marks: 30.
• Percentage score is calculated using:

\[ \text{Percentage Score}=\frac{\text{Number of Correct Answers}}{30}\times100\% \]

Example: A student who answers 24 questions correctly obtains:

\[ \frac{24}{30}\times100\%=80\% \]

Conclusion

Regular practice helps students improve their understanding of fractions, number systems, algebraic expressions, equations, and mathematical sequences. Attempt the questions before checking the answer key, and revisit any topic you find difficult.

Important note: These questions are for revision and educational practice. They are not official examination questions from any College of Education. Students should also consult their lecturers' notes and official course outlines.

References and Further Study

• Khan Academy – Mathematics: Lessons and practice on arithmetic, fractions, algebra, and equations.
• OpenStax – Mathematics Textbooks: Free mathematics learning materials and textbooks.
• Tumu College of Education: Institutional programme information. Confirm your specific course title and syllabus with your own college.