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1 section · 10 questions · 100 marks · Mock ExaminationNo sections — ten compulsory questions of ten marks each.

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EXAMSTZ SECONDARY SCHOOL

FORM TWO MOCK EXAMINATION

043 MATHEMATICS

Time: 2:30 HoursYear: 2026

INSTRUCTIONS

  1. This paper consists of ten (10) questions.
  2. Answer the questions as instructed in each section.
  3. This paper carries a total of 100 marks.
  4. All necessary working and answers for each question must be shown clearly.
  5. All writing must be in blue or black ink, except drawings which must be in pencil.
  6. Cellular phones and any unauthorised materials are not allowed in the examination room.
  7. Write your Examination Number on every page of your answer booklet(s).
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Answer ALL questions. Each question carries ten (10) marks.

  1. 1.
    (a)

    Solve the simultaneous equations 2x + y = 11 and x − 2y = 1.

    (b)

    Factorise completely: x² + 5x + 6. (10 marks)

  2. 2.
    (a)

    Given the universal set U = {15, 30, 45, 60, 75} and the subsets A = {15, 45} and B = {30, 60}, find (A ∪ B)′ and hence represent this information using a Venn diagram.

    (b) (i)

    In a class of 41 students, 20 are boys and 21 are girls. If a student is chosen at random, what is the probability that the student is a boy?

    (b) (ii)

    Rehema has two shirts, blue and red, and three pairs of trousers: black, green and yellow. Using a tree diagram, find the probability of putting on a blue shirt and black trousers. (10 marks)

  3. 3.
    (a)

    A rectangular plot of land is 56 metres long. If the length of its diagonal is 79 metres, how wide is the plot?

    (b) (i)

    Given that A is an acute angle for which 29 cos A − 20 = 0, find the value of tan A without using mathematical tables.

    (b) (ii)

    A triangular pond ABC is such that AB = 7 m, AC = 4 m and ∠BAC = 60°. Determine the length of BC. (10 marks)

  4. 4.
    (a)

    Simplify the expression given below under mathematical language.

    (b)

    Apply mathematical language to the practical situation given, and interpret your answer. (10 marks)

  5. 5.
    (a)

    Arrange the given fractions in ascending order of magnitude: 1/3, 2/8, 3/6 and 4/9.

    (b)

    In the year 2017 the population of Dodoma village was 7500. If it increased by 12%, find the population in the following year. (10 marks)

  6. 6.
    (a)

    List the first twelve multiples of 3 and 7 and hence identify their common multiples.

    (b)

    Evaluate 7.62 × 5.98 correct to (i) one significant figure (ii) three decimal places. (10 marks)

  7. 7.
    (a)

    Two angles of a triangle are (2x)° and (4x + 12)°. If the third angle is 52°, find the value of x.

    (b)

    Prove that the base angles of an isosceles triangle are equal, giving reasons for each step. (10 marks)

  8. 8.
    (a)

    Find the gradient and the y-intercept of the line joining the points (4, 5) and (8, 9).

    (b)

    Draw the graph of y = 3x − 2 for values of x from −3 to 3 and use it to find the value of x when y = 0. (10 marks)

  9. 9.
    (a)

    State two situations in which circles cannot be used.

    (b)

    Draw the graph described above and use it to answer the questions that follow on circles. (10 marks)

  10. 10.
    (a)

    Show that the triangle whose vertices are A(5, −4), B(−6, −1) and C(2, 6) is isosceles.

    (b)

    A man walks 4 km from village P to village Q and then 5 km to village R. If Q is N60°E of P and R is N30°W of Q, (i) represent this information on a well labelled diagram (ii) find the resultant displacement from P to R. (10 marks)