Mathematics Paper 2 Form 3 End Term 2 Exams 2021 with Marking Schemes
SECTION I (50MARKS)
Answer all questions in this section

- Evaluate using logarithms. [4 Marks]
- A rectangular card measures 5.3 cm by 2.5cm.Find
- The absolute Error in the area of the card. [2 Marks]
- The Percentage Error in the area of the card [2 Marks]
- The length of a room is 4m longer than its width. Find the length of the room if its area is 32m2. [3 Marks
- If 20 Men can lay 36m of a pipe in 8 hours. How long would 25 Men take to lay the next 54m of the pipe? [2 Marks]
- Expand (2 + x)5 in ascending powers of x up to the term in x3. Hence, approximate the value of (2.03)5 to 4s.f. (4 marks)
- Simplify by rationalizing the denominator; [2 Marks]
3
2√3 − √2 - A scientific calculator is marked at sh. 1560. Under hire purchase it is available for a downpayment of sh. 200 and six monthly instalments of sh. 250 each. Calculate;
- The Hire purchase price. [2 Marks]
- The extra amount paid out over the cash price. [1 Mark]
- Solve the equation; [3 Marks]
logâ¡ (2x − 10) − 2 log 8 = 2 + logâ¡ (9 − 2x) - The Equation of a circle is given by x2 + y2 − 6x + 4y − 3 = 0 . Determine the center and the radius of the circle. [3 Marks]
- Make x the subject of the formula in the equation. [3 marks]
- In the figure below, BT is a tangent to the circle to the circle at B. AXCT and BXD are straight lines. AX=6cm, CT=8cm, BX=4.8cm and XD=5cm.
Find the length of;- XC [2 Marks]
- BT [2 Marks]
- Find the value of x if the matrix
is a singular matrix. [3 Marks]
- The first term of an arithmetic sequence is −7 and the common difference is 4.
- List the first 6 terms of the sequence [2 Marks]
- Determine the sum of the first 30 terms of the sequence [2 Marks]
- The coordinates of points A and B are (2,5) and (8, −7) respectively. Find the
- Coordinates of M Which Divides AB in the Ratio 1:2 [2 Marks]
- Magnitude of AB [2 Marks]
- Tap A Fills a tank in 6 hours, tap B fills it in 8 hours and tap C empties it in 10 hours.Starting with an empty tank and all the three taps are opened at the same time, how long will it take to fill the tank. [3 Marks]
- Grade X of Tobacco Costs Sh.81.50 per Kg and grade Y cost sh 109 per Kilogram. In what ratio must the two grades be mixed in order to make a profit of 20% when the mixture sells at sh. 112.80 per kg. [3 Marks]
SECTION II: (50MARKS)
Answer any 5 questions from this section
- The figure below shows triangle OAB in which M divides OA in the ratio 2: 3 and N divides OB .in the ratio 4:1 AN and BM intersect at X.
- Given that OA = a and OB = b, express in terms of a and b: (4mks)
- AN
- BM
- If AX = sAN and BX = tBM, where s and t are constants, write two expressions for OX in terms of.a, b s and t. Find the value of s and t. Hence write OX in terms of a and b (6mks)
- Given that OA = a and OB = b, express in terms of a and b: (4mks)
- Kamau, Njoroge and Kariuki are practicing archery. The probability for Kamau hitting the target is 2/5 , that of Njoroge hitting the target is 1/4 and that of Kariuki hitting the target is 3/7.
Find the probability that in one attempt;- Only one hits the target (2mks)
- All three hit the target (2mks)
- None of them hits the target (2mks)
- Two hit the target (2mks)
- At least one hits the target (2mks)
-
- A matrix T is given by
. Find T-1 [2 Marks]
- Wanjiku bought 20 bags of maize and 25 bags of beans at a total cost of sh. 77,000. If she had bought 30 bags of maize and 20 bags of beans, she would have spent sh. 7,000 more.
- Form a matrix equation from this information. [1 Mark]
- Determine the cost of a bag of maize and a bag of beans. [3 Marks
- She sold all the maize and beans at a profit of 10% on a bag of maize and 12½ % on a bag of beans. Calculate the total percentage profit. [4 Marks]
- A matrix T is given by
- At the beginning of the year 2000, Kanyora bought two houses, one in Thika and the other in Nakuru each at 1,240,000. The value of the house in Thika appreciated at a rate of 12% p.a.
- Calculate the value of the house in Thika after 9 years to the nearest shilling. [2 Marks
- After n years, the value of the house in Thika was 2,741,245 while the value of the house in Nakuru was 2,917,231.
- Find n [4 Marks]
- Find the annual rate of appreciation of the house in Nakuru. [4 Marks]
- The table below shows income tax rates.
Mr. Wafula earns a basic salary of 30,500. He has a house allowance of sh. 6,000 per month, medical allowance of sh. 4,000 per month and transport allowance of sh. 3,000 per month. He claims a tax relief of sh. 1,056 per month.Taxable income
K£ per monthRate in shs. per K£ 1 - 325 2 326 - 650 3 651 - 975 4 976 - 1300 5 1301 - 1625 6 over 1626 7 - Calculate
- Wafula’s taxable income in k£ per month. [2 Marks]
- Gross tax. [3 Marks]
- Net Tax [2 Marks]
- His net income per month has the following deductions
Health insurance fund – sh. 150
Loan interest – sh. 200
Service charge – sh. 200
Sacco loan – sh. 2,500
Calculate his net income per month. [3 Marks]
- Calculate
-
- P varies jointly as Q and the square of R. P = 18 when Q = 9 and R = 15. Find R when P=32 and Q=81. [5 Marks]
- A varies Directly as B and inversely as the square root of C. Find the percentage change in A When B is decreased by 10% and C increased by 21%. [5 Marks]
-
- The first term of an arithmetic progression is 2. The sum of the first 8 terms of the AP is 240.
- Find the common difference of the AP. [2 Marks]
- Given that the sum of the first n terms of the AP is 1,560. Find n [2 Marks]
- The 3rd, 5th and 8th terms of another AP from the first three terms of a G.P. If the common difference of the AP is 3. Find.
- The first term of G. P [4 Marks]
- The sum of the first 9 terms of the G.P to 4 s.f. [2 Marks]
- The first term of an arithmetic progression is 2. The sum of the first 8 terms of the AP is 240.
-
- Complete the table below for the function Y=2x2 + 4x − 3 [2 Marks]
x −4 −3 −2 −1 0 1 2 2x2 32 1 0 8 4x −8 −12 −8 4 8 −3 −3 −3 −3 −3 −3 −3 −3 y 21 −3 - On the grid provided, draw the graph of the function y=2x2 + 4x − 3for −4 ≤ x ≤2 [3 Marks]
- Use your graph to solve the roots of the quadratic equations.
- 2x2 + x − 5 = 0 [2 Marks]
- 2x2+3x − 2 = 0 [2 Marks]
- x2 + 4x − 3 = 0 (1 mark)
- Complete the table below for the function Y=2x2 + 4x − 3 [2 Marks]
