JUNE 2017 CSEC MATHEMATICS PAPER 2
JUNE 2017 CSEC MATHEMATICS PAPER 2
SECTION 1
1. (a) Using a calculator, or otherwise, calculate the EXACT value of
(i)
? ??
4
1 3
1
2 5
? ??
?
4 15
SOLUTION:
m Required
to
calculate:
? ??
4
1 3
12 5
? ??
?
4 15
in
exact
form
Calculation:
.co 41 12 = 13  7 3 5 35
s 5(13) 3(7)
=
th 15
= 65  21
a 15
= 44
m 15 s So, now we have
s ? a ??
4
1 3
1
2 5
? ??
?
4 15
=
44 15
?
4 15
p= 1144 ? 15 s 15 41
.fa =11 (in exact form)
( 3.1  1.15)2
w (ii) 0.005
wwSOLUTION:
( 3.1  1.15)2
Required to calculate:
in exact form
0.005
Calculation:
(3.11.15)2 (1.95)2
=
0.005
0.005
(By calculator)
= 3.8025 0.005
= 760.5 (in exact form)
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Pg 1 of 40
(b) A store is promoting a new mobile phone under two plans. Plan A and Plan B. The plans are advertised as shown in the table below.
Deposit Monthly installment Number of months to repay Tax on ALL payments
Plan A $400 $65 12 0%
Plan B $600 $80
6 5%
(i) Calculate the TOTAL cost of a phone under Plan A.
m SOLUTION:
Data: Table showing two mobile phone plans as advertised by a store.
.co Required to calculate: The total cost of a phone under Plan A s Calculation: th Total cost under Plan A
= The deposit + (Monthly installments ? No. of months to repay) + Tax
a = $400 + ($65?12) + $0 m = $(400 + 780) s = $1180 as (ii) Determine which of the two plans, A or B, is the better deal. Justify your
answer.
sp SOLUTION: .fa Required to find: The better deal of the two plans
Solution: Total cost under Plan B
w=The deposit + (Monthly installments ? No. of months to repay) + Tax w= $600 + ($80? 6) + 5 ($600 + ($80? 6))
100
w = $(600 + 480) + 5 ($600 + $480) 100 = 1.05? $(600 + 480)
= $1134
If the better deal is supposed to mean the plan that has a lesser cost, then Plan B is the better deal as there is a savings of $1180  $1134 = $46 .
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Pg 2 of 40
(c) John's monthly electricity bill is based on the number of kWh of electricity that he consumes for that month. He is charged $5.10 per kWh of electricity consumed. For the month of March 2016, two meter readings are displayed in the table below.
Beginning 01 March Ending 31 March
Meter Readings (kWh) 0 3 0 1 1 0 3 3 0 7
(i) Calculate the TOTAL amount that John pays for electricity consumption for the month of March 2016.
m SOLUTION: o Data: Table showing John's electricity meter readings, in kWh, at the .c beginning and end of March 2016. John is charged $5.10 per kWh for
electricity used.
s Required to calculate: The total amount John pays for electricity for th March 2016 a Calculation:
Number of kWh used
m = End reading on 31 March  Beginning reading on 01 March s= 0 3 3 0 7 s0 3 0 11 a 296
sp The cost at $5.10 per kWh = 296?$5.10 = $1509.60 .fa \If John pays the full amount that is required, then he would pay
$1 509.60.
w (ii) For the next month, April 2016, John pays $2 351.10 for electricity wwconsumption. Determine his meter reading at the end of April 2016.
SOLUTION: Data: John pays $2 351.10 for electricity in April 2016.
Required to calculate: John's meter reading at the end of April 2016 Calculation: For the month of April John pays $2 351.10. At $5.10 per kWh, the number of kWh used in April = $2 351.10
$5.10 = 461kWh
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Pg 3 of 40
Hence, the meter reading at the end of April should be the reading at the end of March + 461
=03307 + 4 61
03768
2. (a) Factorise the following expressions completely. (i) 6y2 18xy
om SOLUTION: .c Required to factorise: 6y2 18xy
Solution:
s 6y2 18xy = 6y ? y  6y ?3x th = 6y( y 3x)
a (ii) 4m2 1 m SOLUTION: s Required to factorise: 4m2 1 s Solution: a 4m2 1= (2m)2 (1)2 p This is now in the form of the difference of two squares. s So, 4m2 1= (2m 1)(2m +1)
.fa (iii) 2t2 3t 2 wSOLUTION:
Required to factorise: 2t2  3t  2
wSolution: w 2t2  3t  2 = (2t +1)(t  2)
?2t2  4t + t  2? We may even expand to confirm our result
? ?2t
2

3t

2
? ?
(b) Write as a single fraction and simplify
5p + 2  3p 1
3
4
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Pg 4 of 40
SOLUTION:
Required to write: 5 p + 2  3 p 1 as a simplified single fraction.
3
4
Solution:
5p + 2  3p 1
3
4
4(5 p + 2)  3(3 p 1) = 20 p + 8  9 p + 3
12
12
= 20 p  9 p + 8 + 3 12
m = 11p +11 12
.co = 11( p+1) 12
ths (c) A formula is given as d = 4h . 5
a (i) Determine the value of d when h = 29 . Give your answer correct to 3
significant figures.
sm SOLUTION: s Data: d = 4h and h = 29
a 5 p Required to calculate: d
s Calculation: .fa When h = 29
4 ( 29 )
d= 5
ww= 116 5
w = 23.2
(using the calculator)
= 4.816
= 4.82 (correct to 3 significant figures)
(ii) Make h the subject of the formula.
SOLUTION: Required to make: h the subject of the formula Solution:
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Pg 5 of 40
d = 4h 5
Squaring both sides to remove the hindrance of the root sign d 2 = 4h 5
\5? d 2 = 4h
4h = 5d 2
h = 5d 2
4
.com 3. (a)
The Universal set, U, is defined as follows:
U = {x : x ? N, 2 < x ................
................
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