MIRROR JET JOINT EXAMINATION-2024

Kenya Certificate of Secondary Education.

121/1 PAPER 1
MATHEMATICS
-ALT A-
MARCH 2024
Name: ………………………………………….…….… Adm No: ………………

Stream: ………………Candidate’s Signature: ……….. Date: ………………………..

SCHOOL………………………………………………………………………………..

Instructions to Candidates
(a) Write your name, admission number and class in the spaces provided above.
(b) Sign and write the date of examination in the spaces provided above.
(c) This paper consists of two sections; Section A and Section B.
(d) Answer all the questions in Section A and atleast FIVE questions Section B
(e) Show all the steps in your calculations, giving your answers at each stage in the spaces
provided below each question
(f) Marks may be given for correct working even if the answer is wrong.
(g) Non-programmable silent electronic calculators and KNEC Mathematical tables may be
used, except where stated otherwise.
(h) This paper consists of 11 printed pages.
(i) Candidates should check the question paper to ascertain that all the pages are printed as
indicated and that no questions are missing
For Examiner’s Use Only.
Section A.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total

Section B.
17 18 19 20 21 22 23 24 Total

Grand total.

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 SECTION A.

1. Convert 2. 5̇. into improper fraction hence evaluate (3 marks)

2 23
𝑜𝑓 [2. 5̇ ÷ 27 + −8 × 3].
3

2. The number of students in 20 schools in a certain county were recorded as follows.

200 314 396 451 507
367 263 307 295 507
491 394 281 379 581
520 492 325 590 288
a. Complete the frequency distribution table below for the data (1 mark)
No. of students 200 - 299 300 - 399 400 - 499 500 – 599
No. of schools
b. Find the median of the above data.(3 marks)

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3. The figure below shows quadrilateral QRST in which TS is parallel to QR. QR = 7 cm,
RS = 12cm, QT = 8 cm, < 𝑇𝑄𝑅 = 60° and< 𝑅𝑆𝑄 = 45°. Find the exact length of QS.
(3 mks)

4. The volume of two similar cylindrical solids are 2528 𝑐𝑚3 and 8532 𝑐𝑚3. If the surface
area of the smaller one is 176 𝑐𝑚2 , find the difference in the surface area of the two
cylinders. (3 mks)

5. A regular polygon has internal angle of 150° and a side of length 10 cm.
a. Find the number of sides of the polygon. (1 mark)

b. Find the perimeter of the polygon. ( 1 mark)

3
6. Without using tables or a calculator, find the value of n if
(3 marks)

7𝑛+1 + 7𝑛−1 = 336√7.

7. When sun rays make an angle of 48° with the ground, the shadow cast by a vertical pole
is 4 metres. How long will this shadow be when the suns angle of elevation is 38°.
(3 mks)

8. Under shear transformation, a point A(2,2) is mapped on to 𝐴′(2,4). Find the image of
𝐵(4,3) under the same transformation. (4 mks)

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 9𝑥 2 −1
9. Simplify (3 marks)
3𝑥 2 +2𝑥−1

√5
10. Given that cos 41° sin 𝑥° = sin 49° ,where x is an acute angle, find without using
3
tables and calculator;
tan2 (90 − 𝑥)° (3 mks)

11. Solve the inequality below and represent your answer on a number line.
1 1 1
(5𝑥 − 4) ≤ 𝑥 + 5 < 3𝑥 + 1 . (3 mks)
2 2 2

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12. Use tables of cubes, reciprocals and square roots to evaluate;
(−5)
13.523 − (3 mks)
√0.0512

13. Use the rates below to answer this question.

Buying in ksh Selling in Ksh
1 US dollar 103.00 103.40
1 UK pound 125.30 125.95
A tourist arrived in Kenya from Britain with 9,600 UK pounds. He converted the whole
amount to Kenya shillings. While in Kenya he spent 75% of this money and changed the
balance to US dollars. Calculate the amount of money to the nearest US dollar that he
received. (3 mks)

2
14. Given that 𝑃(−3,9) and 𝑄(4,2), find the coordinates of R if 𝑂𝑅 = 𝑂𝑄 + 3 0𝑃 hence the
distance of R from the origin correct to 3 significant figures. (3 mks)

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15. The equation of a curve is 𝑦 = −𝑥 2 + 3𝑥. Estimate the area bounded by the curve , the
lines 𝑥 = 0, 𝑥 = 5 𝑎𝑛𝑑 𝑥 𝑎𝑥𝑖𝑠 using trapezium rule with 7 ordinates. (3 marks)

16. A line AB = 4.6cm is a side of a trapezium ABCD in which < 𝐴𝐵𝐶 = 105°, 𝐵𝐶 =
4𝑐𝑚, 𝐶𝐷 = 4𝑐𝑚 and CD / / AB. Use a ruler ,a pair of compass only.
a. Construct the trapezium ABCD.(3 mks)

b. Locate a point T on AB such that < 𝐴𝑇𝑃 = 90°.(1 mk)

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 SECTION B
17. The figure below shows rectangle ABCD. Use it to;

a. State the value of m and the x-intercept of line DC . (2 mks)

b. Determine ;
i. The equation of side AD in double intercept form. (3 mks)

ii. The coordinates of the vertices A,B,C.( 3mks)

iii. The area of the triangle.(2 mks)

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18. A train starts from rest and accelerates uniformly for a few minutes then attains its
maximum speed of 90km/h. It maintains this speed for 4 minutes after which it flagged
down and decelerates uniformly coming to rest. If it covered a total distance of 12km.
a. Sketch a speed time graph to show a trains journey.(2 mks)

b. Find the total time taken for the train to recover the whole journey. (3 mks)

c. If the train was moving with the acceleration of 180km/h, calculate the time taken to
cover this maximum speed.

d. Calculate the time taken to cover the half of the journey. (3 mks)

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19. Netia bought 7 exercise books 9 graph books from a shop A at a total cost of sh890. If
she has bought 11 books and 8 graph books , he would have paid sh 140 more.
a. Form two simultaneous equations to represent the information above.(2 mks)

b. Using matrix method, find the price of each exercise book and a graph book that he
bought.(5 mks)

c. The price of an exercise book at shop B is 18% cheaper and that of a graph book is
5% higher than in shop A. How much would he save if he had shopped at shop B.
(3 mks)

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20. The boundaries PQ, QR, RT, TV and VP of an animal conservancy are straight lines
such that Q is 65km on a bearing of 𝑁48°𝑊 from P. R is directly south of Q and on a
bearing of 120° from P. Point Q is 58 km on a bearing of 𝑆50°𝑊 of R.
a. Using a scale of 1cm to represent 10km, show the above information in a scale
drawing. (4 mks)

b. From the scale drawing, determine;

i. The distance in km of PT.(1 mk)

ii. The bearing of T from Q . (1 mk)

c. If the points P,Q ,R, and T are the vertices of a quadrilateral PQRT which represents
the area reserved for endangered species, determine this area in hectares.(4 mks)

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21. Three solids, a cylinder, a sphere and a cone are such that their radii are equal. It is also
given that their surface area are equal. If the volume of the sphere is 310.464𝑐𝑚3 , find
the ;
a. Radius of the sphere.(2 mks)

b. Volume of the cylinder.(3 mks)

c. Volume of the cone.(3 mks)

d. Curved surface area of the cylinder.(2 mks)

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22.
a. On the grid procided below, draw quadrilateral ABCD whose vertices are at
𝐴(2,0), 𝐵(1,3), 𝐶(5, −1)𝑎𝑛𝑑 𝐷(1, −2)(1 mk)

b. On the same axes , draw A’B’C’D’, the image of ABCD under a translation
−1
represented by vector 𝑇 = ( ). (2 mks)
2
c. Draw the quadrilateral 𝐴′′𝐵′′𝐶′′𝐷′′ the image of A′B′C′D′ under a reflection in the line
𝑦 + 𝑥 = 0 on the same axes. State the coordinates of A”B”C”D”. (3 mks)
′′′ (−2,5), ′′′ (4,3), ′′′ (2,11),
d. 𝐴′′′𝐵′′′𝐶′′′𝐷′′′ with vertices 𝐴 𝐵 𝐶 𝐷′′′(−6,3) is the image
′′ ′′ ′′ ′′
of 𝐴 𝐵 𝐶 𝐷 under the transformation X. Draw 𝐴′′′𝐵′′′𝐶′′′𝐷′′′ and describe X fully.
(3 marks)

e. State the type of congruency between quadrilateral ABCD and 𝐴′′𝐵′′𝐶′′𝐷′′.(1 mk)

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23. The figure below represents a piece of land in the shape of an irregular pentagon in which
PQ= 240m, QR = 100m, ST = 160 m, obtuse angle QRS = 105°. < 𝑇𝑅𝑆 = 90° and
< 𝑅𝑆𝑇 = 60°.

Calculate;
a. The size of < 𝑄𝑃𝑅 correct to 2 d.p. (2 mks)

b. The length TP correct to 1 dp. (4 mks)

c. The area of the piece of land in hectares correct to 2 d.p. (4 mks)

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 9
24. The equation of a curve is given as 𝑦 = 2𝑥 3 − 2 𝑥 2 − 5𝑥 + 3.
a. Find
i. The value of y when x = 2. (2 mks)

ii. The equation of the tangent to the curve when x = 2. (4 mks)

b. Determine the turning points of the curve and their nature. (4 mks)

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