INSTRUCTIONS TO CANDIDATES
 Write your name, index number and class in the spaces provided above.
 The paper contains two sections: Section I and Section II.
 This paper contains 14 PRINTED pages make sure all PAGES ARE PRINTED and NON IS MISSING
 Answer ALL the questions in Section I and ANY FIVE questions from Section II.
 All working and answers must be written on the question paper in the spaces provided below each question.
 Marks may be awarded for correct working even if the answer is wrong.
 Negligent and slovenly work will be penalized.
 Nonprogrammable silent electronic calculators and mathematical tables are allowed for use.
For examiners use only
Section I
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
Total 
Section II
17 
18 
19 
20 
21 
22 
23 
24 
Total 
QUESTIONS
SECTION I (50 marks)
Answer all the questions in this section in the spaces provided.
 Without using Mathematical tables or a calculator, evaluate (3 marks)
 Antony spent one quarter of his net January salary on school fees. He spent a quarter of the remainder on electricity and water bills. He then spent one ninth of what was left on transport. If he finally had sh. 3 400, calculate his net January salary. (3 marks)
 A residential estate is to be developed on a 6 hectares piece of land. 1 500 m^{2} is taken up by the roads while the rest is divided into 40 equal plots. Calculate the area of each plot. (3 marks)
 The equation of a straight line L_{1} is 3y + 4x – 6 = 0. Another straight line L_{2} is perpendicular to L1 and passes through point P (⁻3, 6). Determine the equation of L2 in the form y = mx + c, where m and c are constants. (3 marks)
 A shopkeeper bought a number of eggs for which he paid a total of Ksh. 1000. Four eggs were broken. He sold the rest at 13^{1}/_{3} % profit, thereby making a cash profit of Ksh. 100. Calculate the number of eggs that he had bought at the first place. (3 marks)
 Without using Mathematical tables a calculator evaluate (3 marks)
 The longest side of a rightangled triangle is (2x) cm. The other sides are (x + 3) cm and (2x – 4) cm. Find the value of x and hence the lengths of the sides of the triangle. (4 marks)
 Below is part of sketch of a wedge ABCDEF. Complete the sketch of the solid, showing the hidden edges with broken lines. (3 marks)
 If x is a positive integer, solve the inequality and hence list the integral values that satisfy the inequality. (3 marks)
 The matrix has no inverse. Determine the possible values of k. (3 marks)
 A Kenyan Bank buys and sells foreign currencies at the exchange rates shown below
Buying selling
Kshs Kshs
1 Euro 147.86 148.00
1 US Dollar 74.22 74.50
An American arrived in Kenya with 20000 Euros. He converted all the Euros to Kenya shillings at the Bank. He spent kshs.2,512, 000 while in Kenya and converted the remaining Kenya shillings into US Dollars at the bank. Find the amount in Dollars that he received. (3 marks)  Given that tan (θ + 20)º = ⁻0.7660, find θ, to the nearest degree, in the range 0º ≤ θ ≤ 360º (3 marks)
 The area of an island on a map of scale 1:100 000 is 200 cm^{2}. Calculate the actual area on the ground in square kilometers. (3 marks)
 P(2, ⁻1), Q(8, 11) and R(12, 19) are three points on a Cartesian plane. Show that P, Q and R are collinear. (3 marks)
 A bus leaves Nairobi travelling towards Mombasa at a speed of 70 kmh^{⁻1}. Half an hour later, a car leaves Nairobi travelling in the same direction at a speed of 90 kmh^{⁻1}. Calculate the distance travelled by the car when it overtook the bus. (3 marks)
 Use a ruler and a pair of compasses in this question.
 Construct a quadrilateral PQRS in which PQ = 4 cm, QR = 6 cm, PS = 3cm, angle PQR = 135º and angle SPQ = 60º. (3 marks)
 Measure the length of RS. (1 mark)
SECTION II
Answer five questions only in this section.

 Aisha sold 180 bags of rice in September 2017. The cost of each bag was sh. 2800.
Calculate the amount of money that he received from the sale of rice that month. (1 mark) 
 In October that year, the price of a bag of rice decreased by 24% and the number of bags that she sold increased by 30%. Determine the percentage decrease in the amount of money she received from the sale of rice. (3 marks)
 In November that year, the price of a bag of rice changed in the ratio of 7:8. Find the price of each bag in November. (2 marks)
 The amount that he received from the sale of rice in September was sh. 1260 more than what was received in November. If the number of bags that were sold in November were t% more that those sold in September, find t. (4 marks)
 Aisha sold 180 bags of rice in September 2017. The cost of each bag was sh. 2800.

 Complete the table below for the function y = 2x^{2}  3x  4 = 0 for 4 ≤ x ≤ 2 (2 marks)
x
2
1
0
1
2
3
2x^{2}
2
0
2
8
 3x  4
2
4
13
y
4
5
 On the grid below, draw the graph of y = 2x^{2}  3x  4 = 0 for 2 ≤ x ≤ 3 (3 marks)
 Use your graph to estimate the roots of y = 2x^{2}  3x  4 = 0 (2 marks)
 Use your graph to solve = 4x^{2}  7x = 12 (3 marks)
 Complete the table below for the function y = 2x^{2}  3x  4 = 0 for 4 ≤ x ≤ 2 (2 marks)
 The marks scored by a certain number of students in a mathematics contest are as shown in the table below.
Marks
4549
5054
5559
6064
6569
7074
7579
No. of students
10
11
14
41
27
18
19
 Calculate to 2d.p. the mean of the marks scored. (4 marks)
 State the median class and hence calculate the median. (4 marks)
 Calculate the difference between the mean and the median. (1 mark)
 State the modal class. (1 mark)
 The figure below shows a solid frustum of right pyramid with a rectangular base EFGH measuring 24cm by 7cm. The frustum was obtained by cutting off a small pyramid along plane ABCD that is parallel to base EFGH. Plane ABCD measures 16.8cm by 4.9cm, and is exactly seven tenths way up the vertical height of the original pyramid.
Given that the original pyramid had a slant edge of 32.5cm, find: The altitude (perpendicular height) of the frustum. (4 marks)
 The volume of the frustum (3 marks)
 The surface area of the original pyramid. (3 marks)
 Triangle ABC has vertices A(6,5), B(0,1) and C(2,3). Triangle MNP is the image of triangle ABC under an enlargement. The vertices of triangle MNP are M(4,6), N(1,4) and P(2,2). A reflection then maps triangle MNP onto triangle XYZ whose vertices are X(7,5), Y(5,2) and Z(3,3).
 Plot the three triangles on the grid below. (3 marks)
 Determine the centre and the scale factor of enlargement that maps ABC onto MNP. (3 marks)
 Find the equation of the mirror line of the reflection. (2 marks)
 Given that triangle XYZ has an area of Qcm^{2}, state the area of triangle ABC in terms of Q. (2 marks)
 Plot the three triangles on the grid below. (3 marks)
 In the figure below, AB = 11cm, BC = 8cm, AD = 3cm, AC = 5cm and ‹DAC is a right angle.
Calculate, correct to one decimal place: The length DC (2 marks)
 The size of ‹ADC (2 marks)
 The size of ‹ACB (3 marks)
 The area of the quadrilateral ABCD (3 marks)
 Three warships P, Q and R are at sea such that ship Q is 400km on a bearing of 0300 from ship P. Ship R is 750km from ship Q and on a bearing of 1200 from ship Q. An enemy warship S is sighted 1000km due south of ship Q.
 Taking a scale of 1cm to represent 100km locate the relative positions of ships P, Q, R and S. (4 Marks)
 Find the compass bearing of
 P from S (1 mark)
 S from R (1 mark)
 Use the scale drawing to determine the distance of;
 S from P (1 mark)
 R from S (1 mark)
 Find the bearing of;
 Q from R (1 mark)
 P from R (1 mark)
 A particle moving along a straight line passes through a fixed point P. Its displacement S metres from P after a period at t seconds is given S=t^{3}5t^{2}+3.
Find; The particle’s displacement from P at t=4 (2 marks)
 The particle’s velocity at t = 4. (3 marks)
 The possible Value(s) of t when the particle is momentarily at rest. (3 marks)
 The acceleration of the particle at t = 3. (2 marks)
MARKING SCHEME
SECTION I 

1 

M_{1} M_{1} A_{1} 
Numerator completely simplified Denominator completely simplified 

3 

2 
School fees = 1/4 
B_{1} M_{1} A_{1} 
Remaining fraction Equating to 3 400 

3 

3 
Total area = (6 x 10 000)m^{2} 
B_{1} M_{1} A_{1} 
Conversion of hectares to m^{2} Division by 40 

3 

4 
L_{1} : 3y + 4x – 6 =0 
B_{1} M_{1} A_{1} 
Gradient of L_{2} Or equivalent equations 

3 

5 
Let the total number of eggs bought be x. 
M_{1} M_{1} A_{1} 
Expression for the S.P. per egg Equating total S.P. to 1 100 

3 

6 

M_{1} M_{1} A_{1} 
Removal of all the negative indices Removal of all the roots 

3 

7 
(x + 3)^{2} + 2x – 4)^{2} = (2x)^{2}x^{2} + 6x + 9 + 4x^{2} – 16x +16 = 4x^{2}x^{2} – 10x + 25 = 0 
M_{1} M_{1} A_{1} B_{1} 
Applying Pythagoras theorem Complete factorisation Solving the quadratic equation For all the three sides 

4 

8 
B_{1} B_{1} B_{1} 
Lines AF and ED drawn equal and parallel to BC, 0.1cm For any 2 pairs of lines drawn equal and parallel: AB and FC, AE and DF, BE and CD. Completion of the solid with the broken lines shown. Note: The lines must not be extended 


3 

9 
B_{1} B_{1} B_{1} 
Solving for x Solving for x All the 3 values correct 


3 

10 

M_{1} M_{1} A_{1} 
Equating the determinant to zero Complete factorization. For both values of k 

3 

11 
20,000×147.86 =Ksh 2,957,200 
_{M1} M_{1} _{A1} 
_{ }


3 

12 
For 37^{0} For the pair of 143^{0} and 123^{0} For the pair of 323^{0} and 303^{0} 


3 

13 
L.F.S. = 1 
B_{1} M_{1} A_{1} 
For A.S.F. 

3 

14 
B_{1} B_{1} B_{1} 
For both conditions NB: Follow through the candidate’s work. 


3 

15 
Distance covered by the bus in 30 minutes = 70 x 1/2 = 35 km 
B_{1} M_{1} A_{1} 
For 20 kmh^{⁻}^{1} seen For multiplication C.A.O. 

3 

16 

B_{1} B_{1} B_{1} B_{1} 
Correct location of point R, i.e., construction of PQ = 4.0 ± 0.1 cm, 135 ± 1^{0} and QR = 6.0 ± 0.1 cm. Correct location of point S, i.e., construction of i.e., 60 ± 1^{0} at P and PS = 3.0 ± 0.1 cm. Correct quadrilateral PQRS completed. 

4 
17. 
(a) 180 x 2800 = 504000 (b)(i) October’s sales: 
B1 M1 A1 B1 M1 A1 M1 A1 M1 A1 




10 


18 
(a)
(c) x = 0.85,x = 2.35 (d) 4x^{2}  7x = 12 
B1 B1 B0 S1 P1 C1 B1 B1 B1 B1 
all correct values 68 correct values Less than 6 values Scale plotting curve for Line Each value one mark For Both values 



10 


19 
(a)
140 
B1 B1 M1 A1 B1 M1 M1 A1 B1 B1 
For Fx For cf 



10 


20 
(a) The diagonal of the base =√24^{2} + 7^{2} = 25 
M1 M1 M1 A1 M1 M1 A1 M1M1 A1 




10 


21 
(a) (c) y = x  1 (d) ASF=(LSF)^{2} 2^{2 } = 4 
S1 B1 B1 B1 B1 B1 B1 B1 M1 A1 
Scale Each for each triangle For centre of enlargement Scale factor of enlargement mirror line Drawn eqn of the mirror line 



10 


22 
(a) DC = √3^{2} + 5^{2} (b) Tan α= 5/6 = 1.667 (c) c^{2} = a^{2} + b^{2}  2abcosø (d) Area = (1/2 x 3 x 5) + (1/2 x 5 x 8 x sin113.6) 
M1 A1 M1 A1 M1 M1 A1 M1M1 A1 




10 


23 
(a) (b) (i) 343^{0} ±1 (ii) 226^{0} ±1 c) (i)6.8x100=680km (ii)9x100km=900km d) (i) 300^{0} (ii)272^{0} 
B1 B1 B1 B1 B1 B1 B1 B1 B1 B1 
for each point located 



10 


24 
(a) S = (4)^{3} – 5(4)^{2} + 4(4) + 3 (b) v = ds/dt = 3t^{2}  10t + 4 (c) 3t^{2}10t+4=0 (d) a = dv/dt = 6t  10 
M1 A1 M1 M1 A1 M1 M1 A1 M1 A1 
(both values) 

10 
Download Mathematics Paper 1 Questions and Answers  Asumbi Girls Highschool PreMock Exams May  June 2022.
Tap Here to Download for 50/
Get on WhatsApp for 50/
Why download?
 ✔ To read offline at any time.
 ✔ To Print at your convenience
 ✔ Share Easily with Friends / Students