Mathematics Paper 2 Questions - Mumias West Pre Mock Exams 2023

INSTRUCTIONS TO CANDIDATES

• This paper consists of two sections: Section I and Section II.
• Answer ALL questions in section 1 and ONLY FIVE questions from section II
• All answers and workings must be written on the question paper
• Show all the steps in your calculation, giving your answer at each stage in the spaces below each question.
• Non – Programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise.

FOR EXAMINERS USE ONLY
SECTION I

SECTION II

QUESTIONS

SECTION I: Answer all questions in this section.

1. Find the quadratic equation whose roots are ^-3/₄ and ²/₃ and write it in the form
   ax² + bx + c = 0 where a, b and c are integers. (3mks)
2. Given that . Express m in terms of n, q and G. (3mks)
3. The heights, in centimeters of 7 students were; 143, 139, 145, 154, 159, 147,156. Find the mean absolute deviation of the data. (3mks)
4. Triangle ABC has vertices A (4, 1), B (6, 1) and C (8, 3). The image of ABC under a transformation N is A’ (2, 1), B’ (4, 1) and C’ (2, 3). Find the matrix N. (3mks)
5. State the amplitude, period and phase angle of; (3mks)
6. The points P (-6, 5) and Q (2, -1) are the ends of a diameter of a circle centre M. Determine:
   1. The coordinates of M (1mk)
   2. The equation of the circle in the form x² + y² + ax + by + c = 0 (2mks)
7. Without using mathematical table or a calculator, express sin 45o in surd form. Hence simplify;  leaving your answer in surd form. (3mks)
8. Simplify completely; (3mks)
   9x² – 16x +7
   162x² - 98
9. A sum of Ksh 8000 was partly lent at 10% p.a simple interest and 12.5% p.a simple interest. The total interest after 2 years was Ksh. 1775. How much was lent at 10% simple interest? (3mks)
10. The position vectors of points X and Z are 8i + 3j – 4k and 4i + 6j -2k respectively. If Y divides line XZ in the ratio 9: -5, find the coordinates of Y. (3mks)
11. In the figure below AB is a tangent to the circle centre O and radius 12cm. The area of the triangle AOB is 120cm². OXB is a straight line.
    
    Calculate XB (3 mks)
12. A die and a coin are cast simultaneously.
    1. Draw a table to show all possible outcomes. (2mks)
    2. What is the probability of a tail and a number less than 4 showing up. (1mk)
13. Calculate the percentage error in the area of the triangle below given the included angle is exactly 50º. (3mks)
    
14. Use binomial expansion to simplify;
    (√2 + √5)⁴ - (√2 - √5)⁴ (4mks)
15. Solve the simultaneous equation. (4mks)
    2x – y = 3
    x² – xy = - 4
16. Without using logarithms table or calculator, solve for x in Log 5 – 2 + log (2x +10) = log (x-4) (3mks)

SECTION II
Answer ANY FIVE questions in this section.

17. In the figure below OP = p, OQ = q. QX meets OY at R, OX: OP = 2:3 and QY: YP = 1:3.
    
    
    1. Express the following in terms of p and q.
       1. QP (1mk)
       2. OY (2mks)
       3. QX (1mk)
    2. Given that OR = hOY and QR = kQx
       1. Express OR in terms of h, q and p. (1mk)
       2. Express OR in terms of k, q and p. (1mk)
       3. Solve for h and k (4mks)
18. The sum of quantities A and B is y. A varies inversely as x and B varies directly as x. When x=4, Y =17 and when x =6, y = 13.
    1. Express y in terms of x. (7mks)
    2. Find y when x = 10 and x when y = 11.5. (3mks)
19. The figure below is a right pyramid on a rectangle base. TC = TB =TA = 17cm and TO = 15cm. AB is twice BC
    
    Calculate;
    1. The length AB (4mks)
    2. The angle between TC and plane ABCD. (2mks)
    3. The angle between TO and plane TAB. (2mks)
    4. The angle between TAD and ABCD. (2mks)
20.                            
    1. In mathematics, the scores obtained by 30 students were recorded as shown in the table below.
       

       Score x	59	61	65	k	71	72	73	75
       No. of Students	2	3	5	6	7	4	2	1

       Given that Ʃfd = -1.2 where d = x – 69, determine;
                         Ʃf
       1. Score k (4mks)
       2. Standard deviation (4mks)
    2. The data below represents the ages in months at which 9 babies started walking 9, 11, 12, 11, 10, 8, 10, 13, 9. Find quartile. range (2mks)
21. Under a transformation represented by the matrix  , the image of A(-1, 2), B (-1, -1) and c (1, -1) are A’ (-3, 2), B’ (0,-1) and C’ (x, y)
    1. Find the matrix m. (3mks)
    2. Find the coordinates of C’ (1mk
    3. Plot triangles ABC and A’B’C’ on the grid provided below. (2mks)
       
    4. Describe fully the transformation M. (2mks)
    5. Draw the triangle A’’ B’’C’’, the image of A’B’C’ under a stretch of scale factor -2 with the y-axis invariant. (2mks)
22.                
    1. The first term of an arithmetic progression (AP) is 6. The sum of the first 7 terms of the AP is 126.
       1. Find the common difference of the AP (2mks)
       2. Find the 19th term of the AP. (1mk)
    2. The 2nd, 3rd and 11th terms of an increasing arithmetic progression (AP) form the first 3 terms of a geometric progression (GP). The first term of the AP is -2.
       1. Find the common difference of the AP and the common ratio (r) of the GP. (4mks)
       2. Find the sum of the first 5 terms of the geometric progression (GP) (3mks)
23.                      
    1. Complete the table below.
       

       x	0	30	60	90	120	150	180	210	240	270	300	330	360
       y = Sin (x+300)	0.50					0.00	-0.50
       y = 2Cos (x+300)	1.73		0.00		-1.73							2.00	1.73

    2. On the same axes, draw the graphs of y = sin (x+30)º and y = 2Cos (x + 30º) (5mks)
       
    3. Use your graphs to solve the equation. (2mks)
       2 Cos (x + 30º) = 1
        Sin (x + 30º)
    4. State the amplitude of Sin (x + 30º) (1mk)
24. Using a ruler and a pair of compasses only for all constructions in this question.
    1. Construct triangle ABC in which AB = 6cm, BC =7cm and angle ABC = 75º. (3mks)
    2. Find the locus x such that Ax = 3cm. (1mk)
    3. On the same side of BC as ∆ , Construct the locus of P such that angle BPC = 120º. (3mks)
    4. Show by stating the locus of Q inside triangle ABC such that ∟BPC ≥ BQC. (1mk)
    5. On the side of AB opposite C, construct the locus of T such that the area of triangle ATB is 60cm². (2mks)