Mathematics Paper 2: Form 4 QA Model – Document ID 20250302001

Featured questions from the “KCSE MOCK-MATHEMATICS PAPER 2 QA MODEL”:

Section I (50 Marks)

1. Use logarithm tables to solve:
   639445.23=0.1122(4 marks)\frac{6394}{45.23} = 0.1122 \quad (4 \text{ marks})45.236394​=0.1122(4 marks)
2. Solve for $x$ in the equation:
   sin⁡(4x+10∘)−cos⁡(x+70∘)=0(3 marks)\sin(4x + 10^\circ) – \cos(x + 70^\circ) = 0 \quad (3 \text{ marks})sin(4x+10∘)−cos(x+70∘)=0(3 marks)
3. A quantity $K$ is partly constant and partly varies as $M$. When $K=45$, $M=20$, and when $K=87$, $M=48$:
   a) Find the formulae connecting $K$ and $M$ $(1\text{ mark})$
   b) Find $K$ when $M=36$ $(2\text{ marks})$
4. (i) Expand (2x+1)5(2x + 1)^5(2x+1)5 in ascending powers of $x$ $(1\text{ mark})$
   (ii) Hence use your expansion up to the third term to evaluate (2x+1)5(2x + 1)^5(2x+1)5 at $x=0.98$ $(2\text{ marks})$
5. Find the equation of the normal to the curve y=x2+4x−3y = x^2 + 4x – 3y=x2+4x−3 at point $(1,2)$ $(3\text{ marks})$
6. Using a ruler and a pair of compass only, construct triangle $ABC$ in which $BC=6.6\text{ cm}$, $AC=3.8\text{ cm}$, and $AB=5.6\text{ cm}$. Locate point $E$ inside triangle $ABC$ which is equidistant from points $A$ and $C$ such that angle AEC=90∘AEC = 90^\circAEC=90∘ $(3\text{ marks})$
7. Solve the following trigonometric equation:
   2cos⁡2(x+30∘)=1for 0∘≤x≤360∘(3 marks)2\cos^2(x + 30^\circ) = 1 \quad \text{for } 0^\circ \leq x \leq 360^\circ \quad (3 \text{ marks})2cos2(x+30∘)=1for 0∘≤x≤360∘(3 marks)
8. The position vectors of $A$ and $B$ are given as $a=2i-3j+4k$ and $b=-2i-j+2k$ respectively. Find to 2 decimal places, the length of the vector $AB$ $(3\text{ marks})$
9. A T.V. set was bought on hire purchase. A down payment (deposit) of Ksh 5000 was paid and a 15 monthly installment of Ksh 1500 was required.
   a) Calculate the total amount paid on hire purchase $(1\text{ mark})$
   b) If the hire purchase payment is 20% more than the cash payment, find the cash price $(2\text{ marks})$
10. The figure below shows a triangle $ABC$ inscribed in a circle. $AC=10\text{ cm}$, $BC=7\text{ cm}$ and $AB=10\text{ cm}$. Find the radius of the circle (Leave your answer to the nearest 1 decimal place) $(3\text{ marks})$
11. The floor of a rectangular room measures $4.8\text{ m}\times 3.2\text{ m}$. Estimate the percentage error in the area $(3\text{ marks})$
12. Simplify without using mathematical tables or a calculator:

13. Rationalize the denominator fully and simplify, leaving your answer in surd $(3\text{ marks})$
14. The figure below shows the graph of $\log y$ against $\log x$. If the law connecting $x$ and $y$ is of the form y=axby = ax^by=axb, where $a$ and $b$ are constants, find the values of $a$ and $b$ $(3\text{ marks})$
15. Solve the equation by completing the square method:

16. Find the area bounded by the curve $y=x(x-1)(x+2)$ and the x-axis $(4\text{ marks})$

Section II (50 Marks)

17. Mr. Ouma is a civil servant with a basic salary of Ksh 18,000. Using the tax table below, calculate his PAYE:

• Taxable income and rates provided.
  a) Calculate his total monthly deductions in Ksh $(7\text{ marks})$
  b) Calculate his net monthly pay in Ksh $(3\text{ marks})$

18. The points A1,B1,C1A_1, B_1, C_1A1​,B1​,C1​ are images of $A,B,C$ under a transformation matrix $N$.
    a) Write down the coordinates of A1,B1,C1A_1, B_1, C_1A1​,B1​,C1​ $(3\text{ marks})$
    b) Write down the coordinates of A11,B11,C11A_{11}, B_{11}, C_{11}A11​,B11​,C11​ under a different transformation $(3\text{ marks})$
    c) Determine the transformation matrix $K$ $(4\text{ marks})$
19. The figure shows a solid frustum of a pyramid with a rectangular top and base.
    a) Calculate the height of the frustum $(3\text{ marks})$
    b) Calculate the volume of the solid frustum $(3\text{ marks})$
    c) Calculate the angle between specified lines and planes $(4\text{ marks})$
20. The 2nd and 5th terms of an arithmetic progression (A.P.) are 8 and 17 respectively.
    a) Find the 1st term and the common difference $(3\text{ marks})$
    b) Find the first three terms of the G.P. and the 10th term $(4\text{ marks})$
    c) Calculate the sum of the first 10 terms of the G.P. $(3\text{ marks})$
21. Hospital records for maternity patients are given.
    a) Find the probability that a patient stayed exactly 5 days $(2\text{ marks})$
    b) Find the probability that a patient stayed less than 6 days $(2\text{ marks})$
    c) Find the probability that a patient stayed at most 4 days $(2\text{ marks})$
    d) Find the probability that a patient stayed at least 5 days $(2\text{ marks})$
    e) Find the probability that a patient stayed less than 7 days but more than 4 days $(2\text{ marks})$
22. The positions of two towns X and Y are given.
    a) Find the distance between the two towns along the parallel of latitude in km $(3\text{ marks})$
    b) Find the distance in nautical miles $(3\text{ marks})$
    c) Calculate the speed of a plane traveling from X to Y $(4\text{ marks})$
23. A transporter has a van and a pick-up available for trips.
    a) Write down four inequalities that must be satisfied by the trips $(4\text{ marks})$
    b) Represent the inequalities graphically and determine the maximum profit $(6\text{ marks})$
24. A stone is thrown straight up from the edge of a roof.
    a) How far is the stone 3 seconds later? $(5\text{ marks})$
    b) What time does it hit the ground? $(3\text{ marks})$
    c) What is the velocity of the stone when it hits the ground? $(2\text{ marks})$

These questions cover a wide range of mathematical concepts, including algebra, geometry, trigonometry, statistics, and applications of mathematics in real-world scenarios.