Part 66 _ Mathematics Question

8/12/2019 Part 66 _ Mathematics Question

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Module 01, Mathematics.

1.1 Arithmetic.

Question Number. 1. A car travels 24 miles in 45 minutes. What is its average speed? Option A. 32 mph.Option . 3! mph.Option ". 1# mph. "orrect Ans$er is. 32 mph.%&planation. 45 minutes ' 3(4 hour. )peed ' distance ( time ' 24(3(4 ' 24 * 4(3 ' 32.

Question Number. 2. %valuate. +esOption A. 4 ,.Option . 3 ,.Option ". 4."orrect Ans$er is. 3 ,.%&planation.

Question Number. 3. 15.4(2 - 2*!.2 - 15.!/.Option A. 11.1.Option . 2!.5.Option ". -11.1."orrect Ans$er is. 2!.5.

%&planation. 0.0-2-.4/0.0--1#.#/0.0 1#.#' 2!.5.

Question Number. 4. A cuboid has dimensions o 4 cm ! cm and 12 cm. What is its volume?. Option A. .2# m3

.

Option . 2.## m3

. Option ". .2## m3

.

"orrect Ans$er is. 2.## m3

.%&planation. 4 * ! * 12 ' 2## then convert the cm to metres divide 2## b6 1 3 times/.

Question Number. 5. What is a scalene triange?. Option A. 2 sides une7ual.Option . All 3 sides une7ual. Option ". 2 sides e7ual."orrect Ans$er is. All 3 sides une7ual. %&planation.

Question Number. !. Wor8 out the ollo$ing sum9 4 :2 5-1/ -3; #. Option A. 2#Option . 30.Option ". 54. "orrect Ans$er is. 2#%&planation. )tart at the inner brac8ets irst and then $or8 out$ards.

Question Number. 0. A rectangle is 11cm & 12cm. What is its area in m

2

?. Option A. .132.Option . 132.Option ". 13.2."orrect Ans$er is. .132.%&planation. 1cm in 1m so divide 132 b6 1 t$ice since it is area/.

Question Number. #.


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Option A. 2.25Option . 2.5.Option".21(#"orrectAns$eris.21(4%&planation. Wor8 out the $holenumbers separate to theractions.emember that 1(4 is2(#.

Question Number. 1. 11(1! 5(# '.Option A. 55(12#.Option . 21(1!.Option ". 1(11."orrect Ans$er is. 21(1!.%&planation. 5(# ' 1(1!. 11(1! 1(1! ' 21(1!.

QuestionNumber.11.3(4multipliedb6.#2ise7ua

lto.OptionA.

1.23.Option . .!15.Option ". 2.4!."orrect Ans$er is. .!15.%&planation. 3(4 ' .05. Appro&imate .# * .05 must be less than .05.

Question Number. 12. 0(! can be e&pressed as.Option A. 1.1!!.Option . 2.!.Option ". 1.!."orrect Ans$er is. 1.1!!.%&planation. !(! $ould be 1. )o 0(! is @ust slightl6 bigger than 1.

Question Number. 13.


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%&planation.


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Option A. 123.Option . !1.5.Option ". #1.5."orrect Ans$er is. !1.5.%&planation. %stimate 3(4 o #2.

Question Number. 30. A circular patch is held together b6 seven e7uall6 spaced rivets. What is their angular spacing?.Option A. 51.5L.Option . 52L.Option ". 51.43L."orrect Ans$er is. 51.43L.%&planation. 3!(0 ' 51.43 degrees.

Question Number. 3#. Add togetherJ 3(4 5(1! 0(# and .305.Option A. 2 5(1!.Option . 2 1(#.Option ". 2 1(4."orrect Ans$er is. 2 5(1!.%&planation. .305 ' 3(#. 3(4 5(1! 0(# 3(# C"D ' 1!/ 12(1! 5(1! 14(1! !(1! ' 30(1! ' 2 5(1!.

Question Number. 3.


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Question Number. 5. One radian is e7ual to.Option A. L.Option . 05L.Option ". 50.5L."orrect Ans$er is. 50.5L.%&planation.


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Option ". # cm3

.

"orrect Ans$er is. !2# cm3

.%&planation. olume ' = * radius-s7uared base area/ * height. 3.14 * 1 * 1 * 2 ' !2#.

Question Number. !4. 1/ >1/ >1'. Option A. 31.Option . 15.Option ". 43. "orrectAns$er is. 43.%&planation. ule 19 Wor8 the innermost brac8ets irst. ule 29 Ater calculating the contents o a brac8et use the multiplier or divider/beore the adder or subtractor.

Question Number. 01. Which number is the lo$est common actor o 3! !! and 12!?.Option A. 23.Option . 12.Option ". !."orrect Ans$er is. !.%&planation.


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"orrect Ans$er is. 1!0.%&planation. )upplementar6 angles add up to 1# degrees. "omplementar6 angles add up to degrees.

Question Number. 00. What is the area o a ring $ith an outer diameter o inches and an inner diameter o # inches?.Option A. 325=.Option . 435=.Option ". 425=."orrect Ans$er is. 425=.

%&planation. adii are 45 and 4. 452-42/ ' 225-1! ' 425. Area ' =r2

.

Question Number. 0#. What is the area o the shape sho$n in centimeters?.Option A. 1.Option . 1225.

Option ". 113. "orrectAns$er is. 1225.%&planation. 12 * 3 ' 3! 2 * 5 ' 1 2#-#/ * 3 ' !. 3! 1 ! ' 1!.


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Option . .3.Option ". .3."orrect Ans$er is. .3.%&planation. 3(1 * .1 ' 3(1 * .1.

Question Number. . %valuate 15.4(2-24.!-15.0/.Option A. 2!.5.Option . 2..Option ". -14.5."orrect Ans$er is. 2..%&planation. 0.0-2-11.1/ 0.0 22.2 2..

Question Number. 1. Ho$ man6 radians are in 3!L?.Option A. 2=.Option . !=.Option ". 4=."orrect Ans$er is. 2=.%&planation. 3!L ' 2= radians.

Question Number. 2. What is the area including the ends/ o a c6linder diameter 1 cm and 1 cm in height?.Option A. 5=.Option . 15=.Option ". 1=."orrect Ans$er is. 15=.%&planation. = * dia. & height 2 * = * radius-s7uared. 1= 5= ' 15= assuming the6 $ant the areas o the ends included/.

Question Number. 3. What is the highest actor o 153?.Option A. !.Option . 3.Option ". ."orrect Ans$er is. .%&planation.


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Question Number. 11!.


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Option A. #1 pounds.Option . 45 pounds.Option ". 54 pounds."orrect Ans$er is. 54 pounds.%&planation. 3F * 1# ' 54.

Question Number. 13. What is the supplement o an angle o 30L?.Option A. #L.Option . 53L.Option ". 143L."orrect Ans$er is. 143L.%&planation. 1#-30 ' 143L.



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Option A. # 5(12.Option . 0 5(12.Option ". 0 5(0."orrect Ans$er is. # 5(12.%&planation. add the $hole numbers9 34 ' 0 add the raction 3(4 2(3 ' (12 #(12 ' 10(12 ' 1 5(12 add on the 09 # 5(12.

Question Number. 143. An aircrat travels 14 nautical miles in 1 hour 45 minutes. What is the average speed o the aircrat?.Option A. 05 8nots.Option . 245 8nots.Option ". # 8nots. "orrectAns$er is. # 8nots.%&planation. Average speed is ound b6 dividing total distance b6 total time. 14 ( 1 3(4.


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Option . != metres.Option ". = metres."orrect Ans$er is. != metres.%&planation. "ircumerence ' 2=.

Question Number. 15!. !0.5cu.m. Option A. !0.5 cu.m.Option . !05 cu.cm.Option ". !.05 cu.m. "orrectAns$er is. !.05 cu.m.

%&planation. volume o a c6linder ' =*r2

* h ' 3 & .05/2

&h vol ' 1.0&4

' !.05 cu.m. emember all units must be the same so15cm is changed to 1.5 m.

Question Number. 150. What is the surace area o a c6lindrical pipe o length 15 cm and diameter 5cm?.

Option A. 15= s7.cm.Option . 05= s7.cm.Option ". 305= s7.cm."orrect Ans$er is. 05= s7.cm.%&planation. )urace Area o a c6linder ' =d & C' = & 5 & 15 ' 05= s7.cm.

Question Number. 15#. Iind the value o 5(# o 4(5.Option A. 1(2.Option . 3(4.Option ". 25(32."orrect Ans$er is. 1(2.%&planation. 5(# o 4(5 is the same as 5(# & 4(5 b6 cancelling top and bottom o the ractions 5Bs cancel leaving 4(# '1(2.

Question Number. 15. What is the s7uare root o 4 raised to the ith po$er?.Option A. 32.Option . 12#.Option ". !4."orrect Ans$er is. 32.%&planation.


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Option . 1!= s7. cm.Option ". 4X s7. cm."orrect Ans$er is. 1!= s7. cm.%&planation. Area o a ring is = 2-r2/ A ' =52-32/.

Question Number. 1!. Iind the area o the triangle sho$n.

Option A. cm2

.

Option . 12 cm2

.

Option ". ! cm2

.

"orrect Ans$er is. ! cm2

.

%&planation. A ' 1(2bh $here b ' base and h ' height. En this case A ' 1(2 * 3 4 ' ! cm2

.

Question Number. 10. What is the area o the shape sho$n in s7uare cm?.Option A. 5.Option . 5.Option ". 5.. "orrectAns$er is. 5..

%&planation. Divide the shape into three rectangles. 1 * 3/ 2 * 0/ 1 * 15/ ' 31415 ' 5 mm2

1 cm2

' 1&1 '

1mm2

so the ans$er is 5(1 ' 5. cm2

.

Question Number. 101. What is the area o the trapeium sho$n?.Option A. Area cannot be calculated rom inormation given.

Option . 20 cm2

.

Option ". 24 cm2

.

"orrect Ans$er is. 24 cm2

.%&planation. Area o a trapeium called trapeoid in K)/ is A ' 1(2ab/h. a and b are the t$o parallel sides. h is the perpendiculardistance bet$een them. A ' 1(250/4 ' !*4 ' 24 cm2.

Question Number. 102. What is the depth o $ater in the tan8 sho$n i the volume o $ater is 4 litres?.Option A. # cm.

Option . 5 m.Option ". 5 cm. "orrectAns$er is. 5 cm.

%&planation. 1 litre ' 1 cm3

4 litres ' 4 cm3

olume o $ater is 4m & 2m & depth "hange to cm 4 * 2 *depth ' 4


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Option . .Option ". 1. "orrectAns$er is. 1.%&planation. Iirst cancel the $/ because the6 are the same.


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%&planation. h(< )7uare root ACC.

Question Number. 15. Iactorise the ollo$ing 9 &2

-&-!'.Option A. &-2/&3/.Option . &-2/&-3/.Option ". &2/&-3/. "orrectAns$er is. &2/&-3/.%&planation. "hoose 2 numbers $here the sum ' -1 the coeicient o &/ and the product multiple/ is -! the constant/. Alternativel6multipl6 out the ans$ers a b c until 6ou get the 7uestion.

Question Number. 1!. Iactorise the ollo$ing 9 4&2

-!&-2# ' .Option A. 4&-14/ &2/.Option . 2&0/ &-2/.

Option ". 2&20/ & 2/."orrect Ans$er is. 4&-14/ & 2/.%&planation. %&pand each ans$er in turn until 6ou get the 7uestion. emember the smile6 ace.

Question Number. 10. )olve or & in the e7uation9 3& 2/ ' 3 2&-4/.Option A. #.Option . 1!.Option ". 15."orrect Ans$er is. 1!.

%&planation. Gultipl6 out the brac8et irst. 3& ! ' 3 2&-#.


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Option A. -1.Option . ab/a-c/b-c/. Option ". 1."orrect Ans$er is. 1.%&planation. ecause this is a series o multiplications on both top and bottom $e can do the ollo$ing9 ab/(ba/ ' 1 a-c/(c-a/ 'a-c/(-a-c/ ' -1 b-c/(-b-c/ ' -1 hence the result is 1&-1&-1 '1.

Question Number. 2. Ga8e the sub@ect o the ormula E '


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Option A. A/!

.

Option . A/2

.Option ". A.

"orrect Ans$er is. A/2

.%&planation. )ubtract the indices.

Question Number. #. log -log 3'.Option A. log !.Option . log 3.Option ". log ."orrect Ans$er is. log 3.%&planation. log ' log 3&3/ ' 2 log 3. 2 log 3-log 3 ' log 3.

Question Number. . What is 6 in the ormula sho$n? a'[/(6.Option A. a [/ ( .Option . [ - / (a.Option ". [ /( a."orrect Ans$er is. [ /( a.%&planation. b.

"orrect Ans$er is. ( r2

> b.%&planation. asic transposition.

Question Number. 14. Ga8e m the sub@ect o the ormula in 6'm&c.Option A. 6-&(c.Option . 6-c(&.Option ". 6c(&."orrect Ans$er is. 6-c(&.%&planation. asic transposition.

Question Number. 15. Ga8e & the sub@ect o the ormula in 6 ' m&c.Option A. 6-c/(m.Option . 6-c(m.Option ". 6-m(c."orrect Ans$er is. 6-c/(m.%&planation. asic transposition.

Question Number. 1!. Ga8e c the sub@ect o the ormula in 6 ' m&c.Option A. 6-m&.Option . m&-6.Option ". 6m&."orrect Ans$er is. 6-m&.%&planation. asic transposition.

Question Number. 10. Octal is to the base o.Option A. 2.Option . 1!.Option ". #."orrect Ans$er is. #.%&planation. Octal is base # numbering s6stem.

Question Number. 1#. 1111 in binar6 is.Option A. 4! base #.Option . 4! base 2.Option ". 4! base 1.

"orrect Ans$er is. 4!1.%&planation. En binar6 each term means 32 1! # 4 2 1. Write do$n 1111 underneath and add up the numbers above the 1Bs.

Question Number. 1. What is octal 13 in base 1?.Option A. 11.Option . 5.Option ". 4."orrect Ans$er is. 11.%&planation. Octal numbering is !4 # 1 etc. )o 13 is 1 & #Bs and 3 & 1Bs ' 11.

Question Number. 2. What t6pe o e7uation is this? a&2

b&c ' .

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Option A. Quadratic e7uation.Option . ol6nomic e7uation.Option ". Zradient o the line."orrect Ans$er is. Quadratic e7uation.%&planation. Quadratic.

Question Number. 21. What is [2

& [3

/3

?.

Option A. [3!.

Option . [15.

Option ". [1.

"orrect Ans$er is. [15.

%&planation. [2

* [3

' [5

[5

raised to the po$er 3 is [15.

Question Number. 22. He&adecimal is base.Option A. 1!.Option . #.Option ". 2."orrect Ans$er is. 1!.%&planation. He&adecimal is base 1!.

Question Number. 23. 6'm&c can also be $ritten.Option A. &'6-c(m.Option . &'6(mc.Option ". &'6(m-c."orrect Ans$er is. &'6-c(m.%&planation. asic transposition.

Question Number. 24. &6/2

] & 6/#

has a base and e&ponent o.

Option A. &6/1.

Option . &6/-

!.

Option ". &6/1(4.

"orrect Ans$er is. &6/-!

.%&planation. E the bases are the same 8eep it the same but subtract the indices e&ponents/ i dividing.Add the indices i multipl6ing/.

Question Number. 25. e$rite the ollo$ing $ith a positive inde&9 p$r-2 and & p$r-3.

Option A. \[2

/2

J and [/3

Option . 1(2

and 1(&3

.Option ". \(22J and 1([

"orrect Ans$er is. 1(\2

and 1([3

.%&planation. Envert the variable e.g. 1( and $rite the po$er $ith the opposite sign/.

Question Number. 2!. 1112'.

Option A. 22.Option . 11.Option ". 351.

"orrect Ans$er is. 11.%&planation. 1 * 1!/ * #/ * 4/ 1 * 2/ 1 * 1/ ' 1.

Question Number. 20. 6 ' 2& 4 When & ' -1 6 '.Option A. 4.Option . 2.Option ". .5."orrect Ans$er is. 2.%&planation. 6'2-1/4'-24 '2.

Question Number. 2#. What is 11112in Octal?.Option A. 341.Option . 324.Option ". 452."orrect Ans$er is. 341.%&planation. A binar6 number ending in 1 must be an odd number $hen converted to an6 base.

Question Number. 2. "D ormat o numbering s6stem has a base o.

Option A. #.Option . 2.Option ". 1."orrect Ans$er is. 2.%&planation. "D is base 2.

Question Number. 3.


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thereore an imaginar6 number.

Question Number. 33. Ziven the log o A e&ceeds that o b6 4 ind the correct statement about A and .Option A. A is 4 times the value o .Option . A is 1 times the value o .Option ". A is 1 times the value o ."orrect Ans$er is. A is 1 times the value o .%&planation. log 1'1 log 1'2 log 1'3 log 1'4 log 1'5.

Question Number. 34. What is 11111 base2 in Octal?.Option A. 02.Option . !#4.Option ". 3!1. "orrectAns$er is. 3!1.

%&planation. Divide into bloc8s o 3 rom right to let/ and convert each bloc8 into D%"EGAC - 6ou have @ust converted to O"


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"orrect Ans$er is. &'2.%&planation. 5&-0 ' 3add 0 to both sides to give 5& ' 1 divide both sides b6 5 to give & ' 2.

Question Number. 4!. Octal is the $ord given to $hat base?.Option A. #.Option . 2.Option ". 1!."orrect Ans$er is. #.%&planation. NEC.

Question Number. 40. Which o the ollo$ing is a 7uadratic e7uation?.

Option A. 3&2

2&1'.Option . 3&264'.

Option ". 3&33&-2 ' ."orrect Ans$er is. 3&

22&1'.

%&planation. A 7uadratic e7uation has onl6 one un8no$n and the highest po$er is t$o.

Question Number. 4#. What is log 1?.Option A. 2.0#0.Option . 1.0#0.Option ". 3.0#0."orrect Ans$er is. 3.0#0.%&planation. Cog 1 ' 1 Cog 1 ' 2 Cog 1 ' 3 Cog 1 ' 4 etc.

Question Number. 4. What is log A?.Option A. log A/.Option . log Alog .Option ". Cog A-Cog ."orrect Ans$er is. log Alog .%&planation. %&ternal $ebsite.

Question Number. 5. What is CogA(?.Option A. log ACog .Option . log A-Cog .Option ". Cog A-/."orrect Ans$er is. log A-Cog .%&planation. %&ternal $ebsite.

Question Number. 51. log 12 '.Option A. 4.Option . Cog 2.Option ". Cog 2."orrect Ans$er is. 4.%&planation. log 1'2 22 ' 4.

Question Number. 52. Cog 1(2 '.Option A. Cog 2.Option . Cog #.Option ". 1."orrect Ans$er is. 1.

%&planation. log 1'2 2(2 ' 1.

Question Number. 53. Cog 1cos!.Option A. .25.Option . 25.Option ". 2.5."orrect Ans$er is. 2.5.%&planation. Cog 1'2 cos!'.5 2.5'2.5.

1.3a Zeometr6.

Question Number. 1. What is the e&ternal angle indicated on the igure belo$?.Option A. !.Option . 12.Option ". 3."orrect Ans$er is. 12.%&planation. NEC.

Question Number. 2. E a $heel o radius revolves 1(2 a turn ho$ man6 radians does it turn through?.Option A. 2= radians.

Option . 22

radians.Option ". = radians."orrect Ans$er is. = radians.%&planation.


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"orrect Ans$er is. 1#o

.%&planation.


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Option . not perpendicular to its base.Option ". parallel to its base."orrect Ans$er is. not perpendicular to its base.%&planation. Nil.

Question Number. 2. An input gear has 2 teeth and the output gear has 12 teeth. E the input gear rotates 3!L the output gear $illrotate.Option A. !L.Option . 45L.Option ". L. "orrectAns$er is. !L.%&planation. atio 19!.


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Question Number. 33. An isosceles triangle has the ollo$ing properties9.Option A.


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Option ". 3! degrees."orrect Ans$er is. 3! degrees.%&planation. %&ternal $ebsite.

Question Number. 40. Which o the 2 angles are called supplementar6?.Option A. ! degrees and 12 degrees.Option . 4 degrees and 4 degrees.Option ". 3 degrees and ! degrees."orrect Ans$er is. ! degrees and 12 degrees.%&planation. Add up to 1# degrees.

Question Number. 4#. An acute angle is.Option A. less than degrees.Option . less than 1# degrees.Option ". more than degrees."orrect Ans$er is. less than degrees.%&planation. NEC. http9((math.about.com(librar6(bldeacuteangle.htm.

Question Number. 4. A straight line $hich goes rom one point on the circumerence to another is called.Option A. an arc.Option . a tangent.Option ". a chord."orrect Ans$er is. a chord.%&planation. NEC. http9((en.$i8ipedia.org($i8i("hordVF2#geometr6F2.

Question Number. 5. What is the name given to a 7uadrilateral $ith t$o pairs o ad@acent sides e7ual and the diagonals intersect atright angles? Note not all the sides are e7ual?.Option A. 8ite.Option . parallelogram.Option ". rhombus."orrect Ans$er is. 8ite.%&planation. Dra$ the igure to chec8.

Question Number. 51. Iind the sie o the other t$o angles o an isoscelese triangle $ith one angle o 1L.Option A. 4L 4L.Option . 3L 3L.Option ". 1L 2L. "orrectAns$er is. 4L 4L.%&planation. Esoscelese triangle has 2 angles e7ual. E one angle is 1L the other t$o add up to #L.


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Question Number. !. A straight line graph has the e7uation 36 ' 12&>3 What is the gradient?.Option A. 1(4.Option . 4(1.Option ". 3(4."orrect Ans$er is. 4(1.%&planation.


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Option ". parallel to the 6 a&is."orrect Ans$er is. parallel to the 6 a&is.%&planation. E & ' 3 then the line $ill pass through all points $here &'3 i.e. 3/J 31/J32/ that is a line parallel to the 6 a&is.

Question Number. 2. What is the e7uation o the graph sho$n?.Option A. 6 ' -2.Option . & ' -2.Option ". 6 ' 2&."orrect Ans$er is. 6 ' -2.%&planation. All the points on he line have a 6 value o -2 hence the e7uation is 6 ' -2.

Question Number. 21. Kse the graphs to solve the simultaneous e7uations 6 ' & 2 and 36 2& ' !.Option A. & ' 2 6 ' .Option . & ' 6 ' 2.Option ". & ' 6 ' ."orrect Ans$er is. & ' 6 ' 2.%&planation.


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Option A. opposite divided b6 [email protected] . ad@acent divided b6 h6potenuse.Option ". opposite divided b6 h6potenuse."orrect Ans$er is. opposite divided b6 ad@acent.%&planation. ).O.H.".A.H.


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Option . degrees.Option ". 45 degrees. "orrectAns$er is. 45 degrees.%&planation. An isosceles right angled triangle has t$o 45 degree angles.


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Part 66 _ Mathematics Question

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