08. CSEC Maths June 2015 nsite.com

CSEC MATHEMATICS MAY-JUNE 2015

SECTION I 1. (a) (i) Using a calculator, or otherwise, determine the EXACT value of:

2 2 -11 +31 53 2

SOLUTION: 21 1

Required to calculate: The exact value of 2 -1 + 3 . 53 2

Calculation:

om 2 2 -11 + 3 1 = 2 2 + 3 1 -11 532 5 23 .c = 4 + 2 + 1 - 1 523 ths = 4 + 6(2) +15(1) -10(1) 30 a = 4 + 12 +15 -10 30 m = 4 + 17 s 30 s = 4 17 (in exact form) 30

pa (ii) Using a calculator, or otherwise, determine the EXACT value of: .fas(4.14 ?5.75) +(1.62)2

SOLUTION:

wRequired to calculate: The exact value of (4.14 ? 5.75) + (1.62)2 . wCalculation: w (4.14 ? 5.75) + (1.62)2 = (4.14 ? 5.75) + (1.62 ?1.62)

= 0.72 + 2.6244 (by the calculator) = 3.3444 (in exact form)

(iii) Using a calculator, or otherwise, determine the EXACT value of

2 ? 3.142 ?1.25

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SOLUTION:

Required to calculate: The exact value of 2 ? 3.142 ?1.25. Calculation: 2 ? 3.142 ?1.25 = 7.855 (in exact form by calculator)

(iv) Using a calculator, or otherwise, determine the EXACT value of

2.89 ? tan 45?

SOLUTION:

m Required to calculate: The exact value of

Calculation:

o Taking the positive root .c 2.89 ? tan45? = 1.7 ?1

s = 1.7 (in exact form)

2.89 ? tan 45?.

th (b) The table below shows a shopping bill for Mrs. Rowe. The prices of some items are missing.

ma Item s 3 kg sugar s 4 kg rice a 2 kg flour

Shopping Bill Unit Cost Price

X Y $1.60

Total Cost Price $10.80 Z $3.20

p (i) Calculate the value of X, the cost of 1 kg of sugar.

.fas SOLUTION:

Data: Table showing Mrs. Rowe's shopping bill. Required to calculate: The value of X

wCalculation: w3 kg of sugar cost $10.80 w \Cost of 1 kg of sugar = $10.80

3

= $3.60

\X = $3.60

(ii) If the cost price of 1 kg of rice is 80 cents MORE than for 1 kg of flour, calculate the value of Y and of Z.

SOLUTION: Data: 1 kg of rice costs 80? more than 1 kg of flour.

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Required to calculate: The value of Y and of Z Calculation: 1 kg of flour costs $1.60 \the cost of 1 kg of rice = $1.60 + $0.80

= $2.40 \Y = $2.40

The cost of 4 kg of rice at $2.40 per kg = $2.40 ? 4 = $9.60

\Z = $9.60

(iii) A tax of 10% of the total cost price of the three items is added to Mrs.

m Rowe's bill. What is Mrs. Rowe's TOTAL bill, including the tax? .co SOLUTION: s Data: 10% of the cost of the items is added on as tax.

Required to calculate: Mrs. Rowe's total bill

th Calculation:

Cost of 3 kg of sugar, 4 kg of rice and 2 kg of flour, before tax =

a $ 10.80 m$ 9.60 + s$ 3.20 s$2 3. 6 0 a Tax = 10% of $23.60 sp = 10 ?$23.60

100

.fa= $2.36

Hence, Mrs. Rowe's total bill

w= $23.60 +

$ 2.36

ww $25.96

2. (a) Given that a = 4, b = 2 and c = -1, find the value of:

(i) a - b + c

SOLUTION:

Data: a = 4, b = 2 and c = -1

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Required to calculate: a - b + c Calculation:

a - b + c = 4 - (2) + (-1)

=1

(ii) 2ab

SOLUTION: Required to calculate: 2ab Calculation:

m ( ) 2ab = 2 4 2 = 2 ? 16 o = 32

s.c (b) A bottle contains 500 ml of orange juice. Write an expression for EACH of the following. The amount of juice left in the bottle after pouring out th (i) p ml a SOLUTION: m Data: The amount of orange juice in a bottle before pouring is 500 ml. s Required to calculate: The amount of juice after p ml has been poured out s Calculation: The amount of juice left in the bottle a = The initial amount of juice ? The amount of juice poured out p = (500 - p) ml .fas (ii) q glasses each containing r ml. SOLUTION: wRequired to calculate: The amount of juice left after pouring q glasses, weach containing r ml w Calculation: The amount of juice in q glasses with r ml each = (q ? r) ml = qr ml

\The amount of juice, remaining = The initial amount before pouring ? The amount poured out

= (500 - qr) ml

(c) Write as a single fraction, as simply as possible

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2k + 2 - k 35

SOLUTION:

Required to write: 2k + 2 - k is a single fraction 35

Solution:

2k + 2 - k

35

5(2k ) + 3(2 - k ) = 10k + 6 - 3k

m 15

15

o = 10k - 3k + 6 .c 15

= 7k + 6 (as a single fraction in its simplest form)

s 15

th (d) Four mangoes and two pears cost $24.00, while two mangoes and three pears cost a $16.00.

m (i) Write a pair of simultaneous equations in x and y to represent the information given above.

ss SOLUTION:

a Data: 4 mangoes and 2 pears cost $24.00. 2 mangoes and 3 pears costs p $16.00. s Required to write: The information in terms of x and y. .fa Solution:

x and y needed to have been defined first and hence part (ii) should have been part (i). Let the cost of 1 mango be $x and the cost of 1 pear be $y.

wHence, the cost of 4 mangoes and 2 pears = w(4 ? x) + (2 ? y) = 24 w 4x + 2y = 24

?2

2x + y = 12 ...(1)

And, the cost of 2 mangoes and 3 pears =

(2 ? x) + (3? y) = 16

2x + 3y = 16 ...(2) (ii) State clearly what x and y represent.

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