MOCK 2025 CANDIDATE’S NAME
GENERAL
MATHEMATICS/
MATHEMATICS
(CORE) 2
2 DATE:
INDEX NUMBER SIGNATURE
21/2 hours
THE OBOSS EXAMINATIONS COMMITTEE
OTI BOATENG SENIOR HIGH SCHOOL MOCK EXAMINATION FOR STUDENT
MK 2025 GENERAL MATHEMATICS/MATHEMATICS (CORE) 2 hours
[100 marks]
For Examiner’s Use
Only
Question Mark
Write your name and index number in ink in the spaces provided above. Number
Answer ten questions in all. All the questions in section A and five questions
in from section B.
In each question, all necessary details of working including rough work
must be shown with the answer.
Give answers as accurately as data and tables allow.
Graph papers are provided for use in the examination.
The use of non – programmable, silent and cordless calculator is allowed.
Write in the space provided below, the QUESTION NUMBERS OF THE
QUESTION YOU HAVE ANSWERED, in the order in which you have
answered them.
TOTAL
© The Oboss Examinations Committee
SECTION A
[40 marks]
Answer all the questions in this section. All questions carry equal marks.
𝑐𝑜𝑠 𝜃
1. (a) If 𝑠𝑖𝑛 𝜃 = 0.6, 00 < 𝜃 < 900 . Evaluate tan 𝜃 − sin 𝜃.
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
…………………………………………..…………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………….………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
(b) Two angles are complementary. If one of the angles is 180 less than thrice the other, find the
angles.
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………..……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
1|Page
2. (a) Find the truth set of the equation 3(2𝑥) − 3(𝑥+2) = 3(1+𝑥) − 27
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
…………………………………………..…………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………….………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………….....................................................................
(b) The ordered ages (in years) of 8 classmates are 10,10, (𝑝 + 6), (2𝑝 + 2),
(3𝑝 − 3), 13,14 𝑎𝑛𝑑 3𝑝. If the median age is 12𝑦𝑒𝑎𝑟𝑠, find the value of 𝑃.
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
…………………………………………..…………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
2|Page
3. (a) If 𝑙𝑜𝑔 2 = 0.3010 and log 3 = 0.4771, calculate without using calculators or mathematical
tables the value of log 0.72, correct to 2 significant figures.
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
…………………………………………..…………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
(b) A basket contains 21 fruits of the same size. The fruits are coconuts and watermelons. The
3
probability of selecting a coconut randomly from the basket is . Find the number of each
7
fruits in the basket.
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
…………………………………………..…………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………
𝐴
4. (a)
𝐵 2𝑥
𝐸
0
56
𝑦
𝐷
𝐶
Not drawn to scale
3|Page
In the diagram, 𝐶𝐸 is a tangent to the circle 𝐴𝐵𝐷 at 𝐷. < 𝐴𝐵𝐷 = 2𝑥, < 𝐴𝐷𝐸 = 560 ,
7
< 𝐵𝐴𝐷 = 4 𝑥 𝑎𝑛𝑑 < 𝐵𝐷𝐶 = 𝑦. Find the value of ;
(i) 𝑥;
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
(ii) 𝑦
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………….
ℎ𝑑5
(b) Express 𝑑 in terms of 𝑎, 𝑏, ℎ, 𝑘 𝑎𝑛𝑑 𝑔 of the relation; 𝑔 = 𝑎√ 𝑘𝑏
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
4|Page
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
5. (a) The line 𝑝𝑥 + 𝑞𝑦 + 𝑟 = 0 passes through the points 𝐴(−2, −4) and 𝐵(3,7). Find the values of
𝑝, 𝑞 𝑎𝑛𝑑 𝑟.
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………….......................................................................................
.................................................................................................................................................................
.................................................................................................................................................................
(b) Simplify √(11001𝑡𝑤𝑜 ) leaving your answer in base two.
…..………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………
5|Page
SECTION B
[60 marks]
Answer five questions only from this section. All question carry equal marks
6. The uncompleted table has the relation 𝑦 = 𝑝𝑥 2 + 𝑞𝑥 + 10.
𝑥 −4 −3 −2 −1 0 1 2 3 4
𝑦 −26 0 10 −5 −18
(a) Find the values of 𝑝 𝑎𝑛𝑑 𝑞.
(b) With the values of 𝑝 𝑎𝑛𝑑 𝑞 found in (a), complete the table.
(c) Using a scale of 2𝑐𝑚 𝑡𝑜 1 𝑢𝑛𝑖𝑡 on the 𝑥 − 𝑎𝑥𝑖𝑠 and 2𝑐𝑚 𝑡𝑜 5 𝑢𝑛𝑖𝑡𝑠 on the 𝑦 − 𝑎𝑥𝑖𝑠 draw the
graphs of the relations; 𝑦 = 𝑝𝑥 2 + 𝑞𝑥 + 10 𝑎𝑛𝑑 𝑦 = 2𝑥 + 5, in the interval −4 ≤ 𝑥 ≤ 4.
(d) Use the graph to find the range of values of 𝑥 for which 𝑦 = 𝑝𝑥 2 + 𝑞𝑥 + 10 is positive.
7. The angles of depression of the top (T) and bottom (B) of a vertical building from the top (A) of a
mast are 510 and 620 respectively. The building, 70𝑚 high is on the same horizontal level as the
foot (𝑂) of the mast.
(a) Illustrate the information in a diagram.
(b) Calculate, correct to 1 decimal place
(i) |𝑂𝐴|; (ii) |𝑂𝐵|
8. (a) Fifteen counters are in a bag, 4 are red, 6 are green and the rest are black. Two counters are
taken out at random one after the other without replacement. Calculate the probability that;
(i) the counters are black
(ii) one is green and the other is red
(b) If 5 sin(2𝑘 − 220 ) − 4 cos(2𝑘 − 220 ) = 0, 00 ≤ 𝑘 ≤ 900 , find the value of 𝑘.
9. The marks obtained in test by 40 pupils are as follows;
78 60 78 66 33 81 67 84 72 60
54 42 27 33 24 66 27 63 18 30
39 44 30 30 33 45 39 33 30 45
27 36 42 18 42 36 60 72 72 63
(a) Construct a frequency table using the class intervals 10 − 19, 20 − 29, 30 − 39, …
(b) Draw a histogram for the distribution.
(c) Use the histogram to find the mode.
(d) Calculate the mean of the distribution.
6|Page
10. a) In the diagram ̅̅̅̅ ̅̅̅̅ and ̅̅̅̅
𝐴𝐵 //𝐶𝐷 ̅̅̅̅ , if ∠𝐽𝑀𝐵 = 1400 and ∠𝐻𝐾𝐹 = 1200 . Find the values of ;
𝐶𝐷//𝐸𝐹
i) 𝑥;
ii) 𝑦. 𝐽 𝐺
𝐴 1400
𝐵
𝑀
𝑥
𝐶 𝐷
𝑦
𝐾
𝐸 𝐹
𝐻
𝑵𝒐𝒕 𝒅𝒓𝒂𝒘𝒏 𝒕𝒐 𝒔𝒄𝒂𝒍𝒆
3 𝑎3 𝑏
b) If log 𝑎 = 2 , log 𝑏 = 3 𝑎𝑛𝑑 log 𝑐 = −1, evaluate log √( )
𝑐2
11. The table shows the ages (in years) of 50 pupils in a school.
Age 4 5 6 7 8 9
2
Frequency 3𝑥 + 1 8 9 3𝑥 − 2 5𝑥 6
(a) Find the value of 𝑥
(b) Find correct to 2 significant figures, the;
(i) Mean;
(ii) Standard deviation.
12. a) The mean of ten numbers is 8. If an eleventh number is now included, the mean becomes 9.
What is the value of the eleventh number?
b) The ratio of the ages of Akua and Yaw is 5 ∶ 3. If Akua is 25 years old, how many years later
will their ratio be 3 ∶ 2?
1 1 1
13. Mr. Abekah spent 10 of his salary on tithe, 2 of the remainder on food, 3 of the remainder on
savings and still had 𝐺𝐻𝑆 8400.00 on him for other purposes. Find;
(i) fraction spent on other purposes
(ii) his monthly salary;
(iii) the money he will pay in the year as tithe.
END OF PAPER
7|Page
