Calculatorsandmathematicalinstrumentsareallowed but ALL Necessaryworkingmust Be Shown

• Answerallquestions.
• This papercarries 75 marks.
• Calculatorsandmathematicalinstrumentsareallowed but ALL necessaryworkingmust be shown.

______

1. a) Workout the value of. Give your answer as a fraction.

Ans: ______

b) Find the value of nif = 3n

Ans: ______

(2 marks)

1. a) Expandandsimplify:

(i)(y – 9)2(ii) x(2x – 3) – 4(x2 + 3x)

Ans: ______Ans: ______

1. b) Factorisecompletely : 6mt2 – 3mt + 9m2t

Ans: ______

(5 marks)

3. a) Workout the value of (1.4 × 10-3) + (5.8 × 10-2). Giveyouransweras an ordinary

number.

Ans: ______

b) The population of an islandat the beginning of 2012 was 1.3 × 105.

(i)Write 1.3 × 105 as an ordinarynumber.

Ans: ______

At the end of 2012 the populationhaddecreasedby 35 000.

(ii)Find the population of this islandat the end of 2012. Giveyouranswerin standard form.

Ans: ______

(4 marks)

4. a) Write the expression with eachnumberrounded to 1 significantfigure.

Ans: ______

b) Useyouranswer to part (a) to find an estimatefor the value of the expression.

Ans: ______

c) Useyourcalculator to workout a moreaccuratevaluefor the expressiongivingyouranswercorrect to 2 decimalplaces.

Ans:______

(3 marks)

1. a) Solve the equations:

(i)5(y – 6) = −20(ii) 20 – 2(x – 5) – 3x = 5

Ans: ______Ans: ______

b) A solution to the equation x3 – 5x = 8 liesbetween x = 2 and x= 3. Usetrialandimprovement to find the value of xcorrect to 1 decimalplace.

Ans : ______

(8marks)

6.

Ans : ______

(4marks)

1. a) Write the ratio 64g : 4kg initssimplestform.

Ans: ______

7. b) In a gardentulipsanddaffodilsarein the ratio 4 : 5. Thereare 45 daffodils. Howmanytulipsarethere?

Ans: ______

c) A floristhas a delivery of the samenumber of singleroseseveryday. Whenhehas 9 singleroses to a bunchhecanmakeexactly 60bunches. Onedayhedecides to put 12 singlerosesineachbunch. Howmanybuncheswillthere be?

Ans: ______

(5marks)

1. a)

(ii)Calculate the length of BC, givingyouranswercorrect to 2 decimalplaces.

Ans: ______m

8. b) A traintravelsat 50km/h for 2hours, thenslowsdown to do the last 30 minutes of itsjourneyat 40km/h. Whatis the total distance of this journey?

Ans: ______

(6marks)

1. During the month of October, the number of daysoff by 100 factoryworkerswerenotedasfollows.

Calculate a) the modalnumber of daysoff.

Ans: ______

(b) the mediannumber of daysoff.

Ans:______

c) the meannumber of daysoff.

Ans:______

(5marks)

10. a) I think of a number, multiplyitby 8 andsubtract 2. I get the sameansweraswhen

I multiply this numberby 2 andadd 10. Use this information to write an equationandsolveit to find the unknownnumber.

Ans: ______

10. b)

(ii) Solve the equation to findx.

Ans: ______°

(iii)Find the size of the threeangles of the triangle.

Ans: ____°, ____°, ____°

(7marks)

11. a) Simplify:

(i) (5a4)2 (ii) 18a8c6 ÷ 6a3c2

Ans: ______Ans: ______

b)

Ans: ______°

(6 marks)

12. a) The tablebelowshows the amounts of ingredientsin a recipe. The total weight of the ingredientsin this recipeis900 grams.

(i)Complete the tablebyworkingout the angle of eachslice of the piechart.

(ii) Draw andlabel the piechart to show the ingredients.

b) Whatfraction of the total ingredientsin this recipewassugar?

Ans: ______

(8 marks)

13. a) €400 isinvestedfor 18 monthsat an interestrate of 6.5% p.a. Find the simple interestearned.

Ans: €______

b) A salesmanreceives a wage of €3.60 per hourplus 15% commissiononsales. Whatwill be hiswagefor 35 hoursworkifhemakessales of €2900?

Ans:€______

c) In a saleallpricesarereducedby 15%. Matthew buys a shirtin the saleandpays €15.64 for this shirt. Calculate the price of the shirtbeforethe sale.

Ans: €______

(7 marks)

14.

Ans: ______cm

b) Find the area of this sectorgivingyouranswercorrect to the nearest cm2.

Ans:______cm2

(5 marks)

END OF PAPER

Form 3 Mathematics Track 3 Main Paper – Half Yearly 2015 Page 1 of 8