Mathematics Paper 1 Questions and Answers - Sukellemo Joint Pre Mock Exams 2023

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Mathematics Paper 2 Questions - Sukellemo Joint Pre Mock Exams 2023

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Instructions to Candidates

The paper contains TWO sections: Section I and II
Answer ALL questions in section I and STRICTLY ANY FIVE questions from section II.
Show all the steps in your calculations, giving your answers at each stage in the spaces below each question.
Marks may be awarded for correct working even if the answer is wrong.
Non-programmable silent electronic calculators and KNEC Mathematical tables may be used except where stated otherwise.

Section I (50 Marks)

Answer ALL questions in the section in the space provided.

Evaluate −12 ÷ (−3) x 4−(−20) (2 Marks)
– 6 x 6 ÷ 3 + (−6)
Mr. Owino spends ¼ of his salary on school fees. He spends ²/₃ of the remainder on food and a fifth of what is left on transport. He saves the balance. In certain month he saved Sh. 3400. What was his salary? (3 Marks)
Simplify: (3 Marks)
2y² – 3xy – 2x²
4y² – x²
Find x if 3^2x+3 + 1 = 28 (2 Marks)
The circle below whose area is 18.05cm² circumscribes triangle ABC where AB = 6.3cm, BC = 5.7cm and AC = 4.2cm. Find the area of the shaded part. (4 Marks)
A salesman gets a commission of 2.4% on sales up to Sh. 100,000. He gets additional commission of 1.5% on sales above this. Calculate the commission he gets for sales worth Sh. 280,000. (3 Marks)
A rectangle whose area is 96m² is such that its length is 4metres longer than its width.
Find
1. It dimensions (2 Marks)
2. Its perimeter (1 Mark)
The sum of interior angles of a triangle is given by [10x−2y]° while that of a hexagon is given by [30x+24y]° .Calculate the values of x and y (3 Marks)
In triangle ABC below, AC = BC, AB is parallel to DE, AB = 15cm, DE = 7.5cm and BE = 6cm.

Calculate
1. Length CE (2 Marks)
2. Area of quadrilateral ABED. (2 Marks)
A measuring cylinder of base radius 5cm contains water whose level reads 6cm high. A spherical object is immersed in the water and the new level reads 10cm. Calculate the radius of the spherical object (3 Marks)
Using a ruler and pair of compasses only, construct triangle ABC in which AB = 6cm, BC = 8cm and angle ABC = 45°. Drop a perpendicular from A to BC to meet line BC at M. Measure AM and AC. (4 Marks)
In a book store, books packed in cartons are arranged in rows such that there are 50 cartons in the first row, 48 cartons in the next row, and 46 in the next and so on.
1. How many cartons will there be in the 8^th row? (2 Marks)
2. If there are 20 rows in total, find the total number of cartons in the book store. (2 Marks)
Draw the net of the solid below and calculate the total surface area of its faces. (3 Marks)
Solve the following inequalities and state the integral values. (3 Marks)
2x − 2 ≤ 3x + 1 < x + 11
Solve for x in 2^2x − 18 × 2^x = 40 (3 Marks)
A translation maps triangle ABC onto A¹B¹C¹ where A[1,−1], B[2,2], C[3,1] and C¹[−1,3]. Find,
1. Translation vector (1 Mark)
2. The coordinate of A¹ and B¹ [2 Marks]

Section II (50 Marks):

Answer any FIVE questions in this section in the spaces provided.

The distance between towns A and B is 360km. A minibus left town A at 8.15 a.m. and traveled towards town B at an average speed of 90km/hr. A matatu left town B two and a third hours later on the same day and travelled towards A at average speed of 110km/hr.
1. 1. At what time did the two vehicles meet? (4 Marks)
  2. How far from A did the two vehicles meet? (2 Marks)
2. A motorist started from his home at 10.30 a.m. on the same day as the matatu and travelled at an average speed of 100km/h. He arrive at B at the same time as the minibus. Calculate the distance from A to his house. (4 Marks)
Karis owns a farm that is triangular in shape as shown below.
1. Calculate the size of angle BAC (2 Marks)
2. Find the area of the farm in hectares (3 Marks)
3. Karis wishes to irrigate his farm using a sprinkler machine situated in the farm such that it is equidistant from points A, B and C.
  1. Calculate the distance of the sprinkler from point C. (2 Marks)
  2. The sprinkler rotates in a circular motion so that the maximum point reached by the water jets is the vertices A, B and C. Calculate the area outside his farm that will be irrigated. (3 Marks)
A ship leaves port M and sails on a bearing of 050° heading towards island L. Two Navy destroyers sail from a naval base N to intercept the ship. Destroyer A sails such that it covers the shortest distance possible. Destroyer B sails on a bearing of 20° to L. The bearing of N from M is 100° and distance NM = 300KM. Using a scale of 1cm to represent 50km, determine:-
1. The positions of M, N and L. (3 Marks)
2. The distance travelled by destroyer A (3 Marks)
3. The distance travelled by destroyer B. (2 Marks)
4. The bearing of N from L. (2 Marks)
A number of people agreed to contribute equally to buy books worth KSh. 1200 for a school library. Five people pulled out and so the others agreed to contribute an extra Shs. 10 each. Their contributions enabled them to buy books worth Shs. 200 more than they originally expected.
1. If the original numbers of people was x, write an expression of how much each was originally to contribute. (1 Mark)
2. Write down two expressions of how much each contributed after the five people pulled out. (2 Marks)
3. Calculate the number of people who made the contribution. (5 Marks)
4. Calculate how much each contributed. (2 Marks)
Two lines L₁, 2y − 3x − 6 = 0 and L₂, 3y + x − 20 = 0 intersect at a point A.
1. Find the coordinates of A. [3marks]
2. 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. [3marks]
3. Another line L₄ is parallel to L₁ and passes through [−1,3]. Find the x and y-intercept of L₄. [4marks]
The vertices of triangle PQR are P (0,0), Q (6, 0) and R (2, 4)
1. Draw triangle PQR on the grid provided. (1 mark)
2. Triangle P'Q'R' is the image of a triangle PQR under an enlargement scale factor −½ and centre (2, 2). On the same grid draw triangle P'Q'R' and write down its coordinates. (3 marks)
3. On the same grid draw triangle P''Q''R" the image of triangle P'Q'R' under a positive quarter turn about point (1, 1). (3 marks)
4. Draw a triangle P"'Q"'R"' the image of triangle P"Q"R" under reflection in the line y = 1 . (2 marks)
5. State the type of congruence between triangle P"'Q"'R"' and triangle P'Q'R' . (1 mark)
The table shows marks obtained by 100 candidates at Goseta Secondary School in Biology examination.

Marks 15-24 25-34 35-44 45-54 55-64 65-74 75-84 85-94

Frequency 6 14 24 14 x 10 6 4
1. Determine the value of x (1 Mark)
2. State the modal class (1 Mark)
3. Calculate the median mark (4 Marks)
4. Calculate the mean mark (4 Marks)
In the triangle below P and Q are points on OA and OB respectively such that OP:PA = 3:2 and OQ:QB = 1:2 AQ and PQ intersect at T. Given that OA= a and OB= b
1. Express AQ and PQ in terms of a and b (2mks)
2. Taking BT= kBP and AT=hAQ where h and k are real numbers.
  1. Find two expressions for OT in terms of a and b (2mks)
  2. Use the expressions in b (i) above to find the values of h and k. (5mks)
3. In what ratio does T divide AQ.? (1mk)

MARKING SCHEME

NUM
−12 ÷ (−3) × 4 − (−20)
= −12 ÷ −3 × 4 + 20
= 4 × 4 + 20
DEN
−6 × 6 ÷ 3 +(−6)
− 6 × 2 − 6
−18
36
−18
=−2
Food = ½
Transport = 1/20
Remainder
Fraction of saving
1 − (½ + ¹/₂₀ + ¼) = 1 − ¹⁶/₂₀ = ⁴/₂₀
= 3400 × ²⁰/₄ = 17000
NUM
2y² − 3xy − 2x²
2y² − 4xy + xy − 2x²
2y(y−2x) + x(y−2x)
(2y + x) (y − 2x)
DEN
4y² − x²
2²y²− x²
(2y + x) (2y − x)
(2x + x)(y − 2x)
(2y + x) (2y−x)
(y − 2x)
(2y − x)
3^2x+3 + 1 = 28
3^2x+3 = 27
3^2x × 3³ = 3³
27 × 3^2x = 27
3^2x = 1⁰
2x = 0
x = 0
S = 5.7 + 4.2 + 6.3 = 8.1
2
= √(8.1(8.1−5.7)(8.1−4.2)(8.1− 6.3))
= √(8.1 × 2.4 × 3.9 × 1.8) = 11.68
Shaded area = 18.05 − 11.68
= 6.368cm²
2.4 × 100000 = 2400
100
3.9 × 180000 = 7020+
100 9420
1. x(x+4) = 96
  x2 + 4x − 96 = 0
  (x−8) (x+12) = 0
  x = 8
  length = 12
  width = 8
2. 2(8+12)
  = 40
10x − 2y = 180
30x + 24y = 720
5x + y =90
5x + 4y = 120
y = 90 − 5x
5x + 4(90 − 5x) = 120
5x + 360 − 20x = 120
−15x = −240
x = 16
y = 90 − 80
y = 10
1. Length CE
  CE = DE
  BC AB
  x = 7.5
  x+6 15
  x = 6
2. Height of DEC √(6² − 3.75²) = 4.684
  Height of ABC √(12² − 7.5²) = 9.368
  Area of ABED = (½ × 15 × 9.368) − (½ × 7.5 × 4.684)
  = 52.698
²²/₇ × 5²(10 − 6) = 314.29
⁴/₃ × ²²/₇r³ = 314.29
r = 4.217cm
AC = 5.4 ± 1cm
AM = 4.2 ± 1cm
- construction of 45°
- Δ ABC
- ⊥ dropped from A to BC
1. 50, 48, 46... a = 50, d = −2
  T₈ = a + 7d
  = 50 + 7(−2)
  = 36
2. S_n =²⁰/₂ (2×50+(20−1)
  = 620
B1 - correct scale
S.A of the base = 6 × 6 = 36cm²
Area of side flaps = (½×6×8)⁴ = 96cm
Total S.A = 36 + 96 = 132cm²
2x − 2 ≤ 3x + 1 < x + 11
2x−2≤3x + 1
2x − 3x≤1+2
−x≤3
x ≥ −3
3x + 1 ≤ x + 11
3x − x ≤ 11 − 1
2x ≤ 10
x ≤ 5
− 3 ≤ x ≤ 5
−3, −2, −1, 0, 1, 2, 3, 4, 5
2^2x − 18 x 2^x = 40
let 2^x = y
y² − 18y − 40 = 0

Section II (50 Marks);

1. 1. D = ⁷/₂ x 90 = 210km
    Remaning distance = 360 − 210 = 150KM
    A => 90+110 = 200km
    Time for meeting = 150 = 0.75hrs in 45 mins
    Meeting time = 10:35
    + 45
    11:20a.m
  2. Distance from A = 210 + (0.75 × 90)
    = 210 + 67.5
    = 277.5km
2. Time minibus arrived at B = ³⁶⁰/₉₀ = 4hrs M1
  = 8:15 + 4hrs =12:15pm.
  Time taken by motorist to arive at B
  = 12:15pm − 10:30am = 1h 45mins. M1
  =¹⁴⁵/₆₀ X100 = 175km
  ∴ Home to B = 175km M1
  Home to A − 360 − 175
  = 185 Km. A1
1. Calculate the size of angle BAC
  Cos θ = 250² + 320² − 440²
  2 × 250 × 320
  θ = 100·33°
2. Find the area of the farm in hectares
  Area = ½ × 250 × 320sin 100.33° M1
  = 39351.65 M1
  10000
  = 3.9852Ha. A1
3. Karis wishes to irrigate his farm using a sprinkler machine situated in the farm such that it is equidistant from points A, B and
  1. Calculate the distance of the sprinkler from point C.
    440 = 2R M1
    sin100.33
    R = 223.6m A1
  2. Area = ²²/₇ × 223.6² = 157,133.3m² M1
    =157,133.3 − 39351.65 M1
    = 117,781.7m²
1. The position of M, N and L
2. The distance travelled by destroyer A
  6.2cm × 500
  = 310 km ± 5
3. The distance travelled by destroyer B. (2 Marks)
  9.5cm x 50
  = 475km ± 5
4. The bearing of N from L.
  = 235°
1. Sh.1200
  x
2. 120 + 10 = 1400 B1
  x x−5 A1
3. Calculate the number of people who made the contribution.
  1400 − 1200 = 0 M1
  x − 5 x
  1400x − 1200(x−5) = 10
  x(x − 5)
  200x + 6000 =10x² − 50x
  20x + 600 = x² − 5x M1
  x² +15x − 40x − 600 = 0 M1
  x(x+15) − 40(x+15) = 0
4. 1400 = Ksh. 40
  35
1. L₁ = 2y − 3x − 6 = 0
  2y = 3x + 6
  2 2 2
  y = ³/₂x + 3
  L_{2 =} 3y + x − 20 = 0
  3y = −x + 20
  3 3 3
  y = −¹/₃x + ²⁰/₃at A L₁= L₂³/₂x + 3 = −¹/₃x + ²⁰/₃
  ³/₂x + ¹/₃x = ²⁰/₃ − 3
  ¹¹/₆x = ¹¹/₃
  x = 2 M1
  y = ³/₂ × 2 + 3
  y = 6
  A(2,6)
2. L₂ = y = −¹/₃x + ²⁰/₃
  m2 = −¹/₃
  
  y − 6 = 3x − 6
  y = 3x
2. P'(1,1), Q'(4,1) and R'(2,3)
3. P"(1,1), Q"(1,4) and R"(−1,2)
4. P'"(1,1), Q'"(1,−2), R"'(−1, 0)

Determine the value of x
6 +14 + 24+ 14+x+10+ 6 + 4-100
x = 100 − 78
x = 22
35 − 44
Median = 44.5 + (¹⁰/₂ − 44) 10 M1
14
= 44.5 + ⁶/₁₄ × 10 M1
= 48.79 A1

Marks	f	x	xf	cf
15-24	6	19.5	117	6
25-34	14	29.5	413	20
35-44	24	39.5	948	44
45-54	14	49.5	693	58
55-64	22	59.5	1309	80
65-74	10	69.5	695	90
75-84	6	79.5	477	96
85-94	4	89.5	358	100
Σ = 100		Σx = 5010