JUNE 2017 CSEC MATHEMATICS PAPER 2

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´╗┐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:

(3.1-1.15)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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