

2017 Mathematics Paper 1
Section I (50 marks)
Answer all the questions in this section in the spaces provided.
1. Evaluate i~—, correct to four decimal places, hence Write the answer in 4.0836—3.71l2 standard form. (3 marks)
2. Two numbers p and q are such that p3 >< q = 189. Find p and q. (3 marks)
3. A trader bought maize for Ksh 20 per kilogram and beans for Ksh 60 per kilogram. She mixed the maize and beans and sold the mixture at Ksh 48 per kilogram. If she made a 60% proﬁt, determine the ratio maize to beans per kilogram in the mixture. (4 marks)
In the triangle ABC below, BC = 12 cm, A ABC = 80° and L ACB = 30°.
Caculate correct to 4 signiﬁcant ﬁgures. the area of trianglc ABC. (3 marks)
Given that the exterior angle of a regular hexagon is x. ﬁnd the size of each interior angle of the hexagon. (2 marks)
6.Use logarithms to evaluate,
(4 marks)7. A line L is perpendicular to the line Ex + ; y = l . Given that L passes through (4,l l), ﬁnd:
(a) gradient of L; ( l mark)
(b) equation of L in the form y = mx + c, where m and c are constants. (2 marks)
7 C 8. Convert 2πC/9 into degrees. (2 marks)
9. A garden is in the shape of a right angled triangle. The length of the shortest side is l7 m and the area of the garden is 346.8 ml. Calculate the length of the longest side of the garden. (3 marks)
10. The diagram below shows a region R bounded by three lines L1 L2 L3
Form the three inequalities that satisfy the given region R. (3 marks)
11. Murimi and Naliaka had each 840 tree seedlings. Murimi planted equal number of seedlings per row in x rows while Naliaka planted equal number of seedlings in (x + 1) rows. The number of tree seedlings planted by Murimi in each row were 4 more than those planted by Naliaka in each row. Calculate the number of seedlings Murimi planted in each row. (4 marks)
12. A Kenyan bank buys and sells foreign currencies as shown below:
Buying (Ksh) Selling (Ksh)
1 Sterling pound (£) 130.10 130.54
1 South African Rand 9.52 9.58
A businessman on a trip to Kenya had £50 000 which he converted to Kenya shillings. While in Kenya, he spent 80% of the money and changed the balance to South African Rand.
Calculate, to the nearest Rand, the amount he obtained. (3 marks)
13. Use the mid ordinate rule with six strips to ﬁnd the area bounded by the curve y =x2 + 1, the lines
x = 4 , x = 8 and the xaxis. (3 marks)
14. Given that a = [ j,c = K _i J and 3a — 2b + 4c =[ 1109 1, ﬁnd b. (3 marks)
15. A triangle T With vertices A (2,4), B (6,2) and C (4,8) is mapped onto triangle T’ with vertices
A’(l0,0) , B'(8,—4) and C'(14,—2) by a rotation. (a) On the grid provided draw triangle T and its image. (2 marks)
(b) Determine the centre and angle of rotation that maps T onto T’. (2 marks)16. A construction company employs technicians and artisans. On a certain day 3 technicians and 2 artisans were hired and paid a total of Ksh 9000. On another day the ﬁrm hired 4 technicians and 1 artisan and paid a total of Ksh 9500‘ Calculate the cost of hiring 2 technicians and 5 artisans in a day. (3 marks)
SECTION II (50 marks)
Answer any ﬁve questions from this section in the spaces provided.
17. Two lines L‘: 2y — 3x 6 = 0 and L2: 3y + x — 20 =
0 intersect at a point A.
(a) Find the coordinates of A. (3 marks)
(b) A third line L3 is perpendicular to L2 at point A. Find the equation of L3 in the form y = mx + c, Where m and c are constants. (3 marks)
(c) Another line L4 is parallel to Ll and passes through (—l,3). Find the x and y intercepts of L é. (4 marks)
18. The masses, in kilograms, of patients who attended a clinic on a certain day were recorde follows.
38 52 46 48 60 59 62 73 49 54
49 41 57 58 69 72 60 58 42 41
79 62 58 67 54 60 65 61 48 47
69 59 70 52 63 58 59 49 51 44
67 49 5l 58 54 59 39 59 54 52
(a) Starting with the class 35 — 39, make a frequency distribution table for the data. (2 marks)
(b) Calculate:
(i) the mean mass; (3 marks)
(ii)the median mass (3 marks)
(c) On the grid provided below draw a histogram to represent the data
20. In the ﬁgure below (not drawn to scale), AB I llcm, BC = 8cm, AD = 3 cm, AC I 5cm and A DAC is a right angle.
Calculate, correct to one decimal place:
(a) the length DC; (2 marks)
(b) the size of 4 ADC; (2 marks)
(0) the size of A ACB; (3 marks)
(d) the area of the quadrilateral ABCD. (3 marks)
21. The comer points A, B, C and D of a ranch are such that B is 8km directly East of A and C is 6km from B on a bearing of 30°. D is 7km from C on a bearing of 300°.
(a) Using a scale of lcm to represent lkm, draw a diagram to show the positions of A, B, C and D. (4 marks)
(b) Use the scale drawing to determine:
(i) the bearing of A from D; (1 mark)
(ii) the distance BD in kilometres. (2 marks)
22. (a) Given that A = 3 x and B = 1 2 , ﬁnd values of x for which AB is a x +1 2 3 0 singular matrix. (4 marks) (b) Mambo bought 3 exercise books and 5
pens for a total of Ksh 165. 11’ Mambo had bought 2 exercise books and 4 pens, he would have spent Ksh 45 less. Taking x to represent the price of an exercise book and y to represent the price of a pen:
(i) Form two equations to represent the above information. (1 mark)
(ii) Use matrix method to ﬁnd the price of an exercise book and that of a pen. (3 marks)
(m) A teacher of a class of 36 students bought 2 exercise books and 1 pen for each student. Calculate the total amount of money the teacher paid for the books and pens. (2 marks)
23. An institution intended to buy a certain number of chairs for Ksh 16 200. The supplier agreed to 0ﬂ°er a discount 0fKsh 60 per chair which enabled the institution to get 3 more chairs.
Taking x as the originally intended number of chairs,
(a) Write an expressions in terms of x for:
(i) original price per chair; (1 mark)
(ii) price per chair after discount. (1 mark)
(b) Determine:
(i) the number of chairs the institution originally intended to buy; (4 marks)
(ii) price per chair after discount; (2 marks)
(iii) the amount of money the institution would have saved per chair if it bought the intended number of chairs at a discount of 15%. (2 marks)
24. The equation of a curve is given as y = 2x3 —9/2 x2 — 15x + 3.
(a) Find:
(i) the value of y when x = 2; (2 marks)
(ii) the equation of the tangent to the curve at x = 2. (4 marks)
(b) Determine the turning points of the curve. (4 marks)

Questions and Answers
2017 Mathematics Paper 1
1. Evaluate i~—, correct to four decimal places, hence Write the answer in 4.0836—3.71l2 standard form. (3 marks)
I 0.0961 i————— =\/0.2581 4.0836—3.7ll2 = 0.5080 Standard form = 5.080 x 10
2. Two numbers p and q are such that p3 >< q = 189. Find p and q. (3 marks)
189=3x3x3x7
=3x7
pxq=3x7
p=3,q=7
3. A trader bought maize for Ksh 20 per kilogram and beans for Ksh 60 per kilogram. She mixed the maize and beans and sold the mixture at Ksh 48 per kilogram. If she made a 60% proﬁt, determine the ratio maize to beans per kilogram in the mixture. (4 marks)
Let the number of kg of maize be m and numberof kg of beans be b Buying price = 20111" + 60b Selling price = 48(m+b) Q _ 48(m+b) ~(20m + 60b) 100 ‘ 20m+60b 0'6 = 28m—l2b 20m+6Ob :> 12m + 36b =_ 28m — 12b l6m=48b 22 b 1 Ratio mzb = 3:1
In the triangle ABC below, BC = 12 cm, A ABC = 80° and L ACB = 30°.
Caculate correct to 4 signiﬁcant ﬁgures. the area of trianglc ABC. (3 marks)
Given that the exterior angle of a regular hexagon is x. ﬁnd the size of each interior angle of the hexagon. (2 marks)
6.Use logarithms to evaluate,
(4 marks)7. A line L is perpendicular to the line Ex + ; y = l . Given that L passes through (4,l l), ﬁnd:
(a) gradient of L; ( l mark)
(b) equation of L in the form y = mx + c, where m and c are constants. (2 marks)
7 C 8. Convert 2πC/9 into degrees. (2 marks)
9. A garden is in the shape of a right angled triangle. The length of the shortest side is l7 m and the area of the garden is 346.8 ml. Calculate the length of the longest side of the garden. (3 marks)
10. The diagram below shows a region R bounded by three lines L1 L2 L3
Form the three inequalities that satisfy the given region R. (3 marks)
11. Murimi and Naliaka had each 840 tree seedlings. Murimi planted equal number of seedlings per row in x rows while Naliaka planted equal number of seedlings in (x + 1) rows. The number of tree seedlings planted by Murimi in each row were 4 more than those planted by Naliaka in each row. Calculate the number of seedlings Murimi planted in each row. (4 marks)
12. A Kenyan bank buys and sells foreign currencies as shown below:
Buying (Ksh) Selling (Ksh)
1 Sterling pound (£) 130.10 130.54
1 South African Rand 9.52 9.58
A businessman on a trip to Kenya had £50 000 which he converted to Kenya shillings. While in Kenya, he spent 80% of the money and changed the balance to South African Rand.
Calculate, to the nearest Rand, the amount he obtained. (3 marks)
13. Use the mid ordinate rule with six strips to ﬁnd the area bounded by the curve y =x2 + 1, the lines
x = 4 , x = 8 and the xaxis. (3 marks)
14. Given that a = [ j,c = K _i J and 3a — 2b + 4c =[ 1109 1, ﬁnd b. (3 marks)
15. A triangle T With vertices A (2,4), B (6,2) and C (4,8) is mapped onto triangle T’ with vertices
A’(l0,0) , B'(8,—4) and C'(14,—2) by a rotation. (a) On the grid provided draw triangle T and its image. (2 marks)
(b) Determine the centre and angle of rotation that maps T onto T’. (2 marks)16. A construction company employs technicians and artisans. On a certain day 3 technicians and 2 artisans were hired and paid a total of Ksh 9000. On another day the ﬁrm hired 4 technicians and 1 artisan and paid a total of Ksh 9500‘ Calculate the cost of hiring 2 technicians and 5 artisans in a day. (3 marks)
SECTION II (50 marks)
Answer any ﬁve questions from this section in the spaces provided.
17. Two lines L‘: 2y — 3x 6 = 0 and L2: 3y + x — 20 =
0 intersect at a point A.
(a) Find the coordinates of A. (3 marks)
(b) A third line L3 is perpendicular to L2 at point A. Find the equation of L3 in the form y = mx + c, Where m and c are constants. (3 marks)
(c) Another line L4 is parallel to Ll and passes through (—l,3). Find the x and y intercepts of L é. (4 marks)
18. The masses, in kilograms, of patients who attended a clinic on a certain day were recorde follows.
38 52 46 48 60 59 62 73 49 54
49 41 57 58 69 72 60 58 42 41
79 62 58 67 54 60 65 61 48 47
69 59 70 52 63 58 59 49 51 44
67 49 5l 58 54 59 39 59 54 52
(a) Starting with the class 35 — 39, make a frequency distribution table for the data. (2 marks)
(b) Calculate:
(i) the mean mass; (3 marks)
(ii)the median mass (3 marks)
(c) On the grid provided below draw a histogram to represent the data
20. In the ﬁgure below (not drawn to scale), AB I llcm, BC = 8cm, AD = 3 cm, AC I 5cm and A DAC is a right angle.
Calculate, correct to one decimal place:
(a) the length DC; (2 marks)
(b) the size of 4 ADC; (2 marks)
(0) the size of A ACB; (3 marks)
(d) the area of the quadrilateral ABCD. (3 marks)
21. The comer points A, B, C and D of a ranch are such that B is 8km directly East of A and C is 6km from B on a bearing of 30°. D is 7km from C on a bearing of 300°.
(a) Using a scale of lcm to represent lkm, draw a diagram to show the positions of A, B, C and D. (4 marks)
(b) Use the scale drawing to determine:
(i) the bearing of A from D; (1 mark)
(ii) the distance BD in kilometres. (2 marks)
22. (a) Given that A = 3 x and B = 1 2 , ﬁnd values of x for which AB is a x +1 2 3 0 singular matrix. (4 marks) (b) Mambo bought 3 exercise books and 5
pens for a total of Ksh 165. 11’ Mambo had bought 2 exercise books and 4 pens, he would have spent Ksh 45 less. Taking x to represent the price of an exercise book and y to represent the price of a pen:
(i) Form two equations to represent the above information. (1 mark)
(ii) Use matrix method to ﬁnd the price of an exercise book and that of a pen. (3 marks)
(m) A teacher of a class of 36 students bought 2 exercise books and 1 pen for each student. Calculate the total amount of money the teacher paid for the books and pens. (2 marks)
23. An institution intended to buy a certain number of chairs for Ksh 16 200. The supplier agreed to 0ﬂ°er a discount 0fKsh 60 per chair which enabled the institution to get 3 more chairs.
Taking x as the originally intended number of chairs,
(a) Write an expressions in terms of x for:
(i) original price per chair; (1 mark)
(ii) price per chair after discount. (1 mark)
(b) Determine:
(i) the number of chairs the institution originally intended to buy; (4 marks)
(ii) price per chair after discount; (2 marks)
(iii) the amount of money the institution would have saved per chair if it bought the intended number of chairs at a discount of 15%. (2 marks)
24. The equation of a curve is given as y = 2x3 —9/2 x2 — 15x + 3.
(a) Find:
(i) the value of y when x = 2; (2 marks)
(ii) the equation of the tangent to the curve at x = 2. (4 marks)
(b) Determine the turning points of the curve. (4 marks)

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