SPCS0271

1)!¥Yr11-2U\basics.cat Qn1) 2U84-1i¥

Express the following as integers.

a.5223 102.

b..

c..†

« a) 2 b) 2 c) 3 »

2)!¥Yr11-2U\basics.cat Qn2) 2U84-1ii¥

Given a=,b= and c=2 evaluate .†

« »

3)!¥Yr11-2U\basics.cat Qn3) 2U84-1iii¥

Factorise 2a2+11a+15.†

« (2a+5)(a+3) »

4)!¥Yr11-2U\basics.cat Qn4) 2U84-2iii¥

Solve for x: (2x+3)2=25.†

«x=4or 1 »

5)!¥Yr11-2U\basics.cat Qn5) 2U84-2iv¥

Graph on the number line the solution set of: .†

« »

6)!¥Yr11-2U\basics.cat Qn6) 2U84-3i¥

The volume V of metal in a pipe is given by: V=L(R+r)(Rr) whereL is the length of the pipe, Rthe external radius andr the internal radius. A pipe of length 49cm and internal radius 1·5cm is made out of 616cm3 of metal. Find the external radius of this pipe. Give your answer to the nearest millimetre.†

«25 mm »

7)!¥Yr11-2U\basics.cat Qn7) 2U85-1i¥

Factorise x23x4.†

« (x4)(x+1) »

8)!¥Yr11-2U\basics.cat Qn8) 2U85-1ii¥

Simplify .†

« »

9)!¥Yr11-2U\basics.cat Qn9) 2U85-1v¥

Simplify and express with a rational denominator: .†

« »

10)!¥Yr11-2U\basics.cat Qn10) 2U85-2ii¥

Simplify .†

« »

11)!¥Yr11-2U\basics.cat Qn11) 2U85-2iv¥

Graph on the number line the solution set of: |2x+1|7.†

« »

12)!¥Yr11-2U\basics.cat Qn12) 2U86-1i¥

Find the values of x for which x2x20.†

«x1 or x2 »

13)!¥Yr11-2U\basics.cat Qn13) 2U86-1iii¥

Find the values of x and y if: xy=(52)(2).†

«x=16, y=9 »

14)!¥Yr11-2U\basics.cat Qn14) 2U86-8ii¥

Simplify .†

«1 »

15)!¥Yr11-2U\basics.cat Qn15) 2U86-8iii¥

Graph on the number line the values of x for which |32x|7.†

« »

16)!¥Yr11-2U\basics.cat Qn16) 2U87-1i¥

Solve for n:

a.4n8=12;

b.n215n+16=0;

c.|3n5|=4n7.†

« a) n=5 b) n=13·8 or 12 c) n=2 or »

17)!¥Yr11-2U\basics.cat Qn17) 2U87-1iii¥

Factorize and simplify: .†

« »

18)!¥Yr11-2U\basics.cat Qn18) 2U87-1iv¥

Rationalize the denominator and simplify: .†

«»

19)!¥Yr11-2U\basics.cat Qn19) 2U88-1i¥

Evaluate to 1 decimal place: (1·2)2+(2·1)2..†

«5·9 »

20)!¥Yr11-2U\basics.cat Qn20) 2U88-1ii¥

Express in scientific notation: .†

«1·8105 »

21)!¥Yr11-2U\basics.cat Qn21) 2U88-1iii¥

Simplify †

« »

22)!¥Yr11-2U\basics.cat Qn22) 2U88-1iv¥

If E=(v2u2), find the value ofE when m=4, v=10 and u=7.†

«102 »

23)!¥Yr11-2U\basics.cat Qn23) 2U88-1v¥

Factorise 3x2+8x16.†

« (3x4)(x+4) »

24)!¥Yr11-2U\basics.cat Qn24) 2U88-1vi¥

Express with a rational denominator.†

«1217 »

25)!¥Yr11-2U\basics.cat Qn25) 2U89-1a¥

Find, correct to two decimal places, the value of .†

«0·56 »

26)!¥Yr11-2U\basics.cat Qn26) 2U89-1b¥

Factorise 8p3+64.†

«8(p+2)(p22p+4) »

27)!¥Yr11-2U\basics.cat Qn27) 2U89-1c¥

Solve the equation 2a23a1=0.†

«a= »

28)!¥Yr11-2U\basics.cat Qn28) 2U89-1d¥

The distance travelled (s) of a particle with an initial velocity (u), final velocity (v) and acceleration (a), is given by the formula s=. Find s if v=31, u=17 and a=21.†

«16 »

29)!¥Yr11-2U\basics.cat Qn29) 2U89-1e¥

Solve the equation: .†

«31 »

30)!¥Yr11-2U\basics.cat Qn30) 2U90-1a¥

Find correct to one decimal place, the value of .†

«0·8 »

31)!¥Yr11-2U\basics.cat Qn31) 2U90-1b¥

Simplify the expression 52(3x5)+3x.†

«15  3x »

32)!¥Yr11-2U\basics.cat Qn32) 2U90-1c¥

Find the value of x for which 2x5.†

«x »

33)!¥Yr11-2U\basics.cat Qn33) 2U90-1d¥

Solve the equation 2x25x+1=0 leaving your answer in surd form.†

« »

34)!¥Yr11-2U\basics.cat Qn34) 2U90-1e¥

Simplify the following algebraic expression .†

« »

35)!¥Yr11-2U\basics.cat Qn35) 2U91-1a¥

Calculate correct to 2 decimal places: .†

«220·58 »

36)!¥Yr11-2U\basics.cat Qn36) 2U91-1b¥

Factorise the following expressions:

i.8x4;

ii.x38.†

« i)4(2x1) ii)(x2)(x2+2x+4) »

37)!¥Yr11-2U\basics.cat Qn37) 2U91-1c¥

Rationalise the denominator of the expression: and evaluate it correct to 2significant figures.†

«6·5 »

38)!¥Yr11-2U\basics.cat Qn38) 2U91-1d¥

Solve the following:

i.3x+12;

ii.|6x+4|=2;

iii.x2(x3)=5.†

« i)x ii) x=, 1 iii)x=1 »

39)!¥Yr11-2U\basics.cat Qn39) 2U92-1a¥

Calculate correct to 2 decimal places: .†

«2·92 »

40)!¥Yr11-2U\basics.cat Qn40) 2U92-1b¥

Factorise fully: a2b2+3a+3b.†

« (a+b)(ab+3) »

41)!¥Yr11-2U\basics.cat Qn41) 2U92-1d¥

Graph on the number line the solution set of: |32x|11.†

« »

42)!¥Yr11-2U\basics.cat Qn42) 2U92-1e¥

After a discount of 40% is allowed, the cost of insuring a car is $312. Find the cost of insuring this car when no discount is allowed.†

«$520 »

43)!¥Yr11-2U\basics.cat Qn43) 2U92-3a¥

Solve x+=12.†

«x=14 »

44)!¥Yr11-2U\basics.cat Qn44) 2U93-1a¥

Evaluate correct to one decimal place .†

«0·5 »

45)!¥Yr11-2U\basics.cat Qn45) 2U93-1b¥

Factorise x211x+10.†

« (x10)(x1) »

46)!¥Yr11-2U\basics.cat Qn46) 2U93-1e¥

Solve (x+2)2=9.†

«x=1, x=5 »

47)!¥Yr11-2U\basics.cat Qn47) 2U93-1f¥

Express in the form a+b.†

« »

48)!¥Yr11-2U\basics.cat Qn48) 2U93-1g¥

The value ($V) of a car after n years is given by the formula:

V=V0(1R)n

whereV0 is the initial value of the car andR is the annual percentage rate of depreciation. A car bought 3years ago for $15000 was sold for $9000. Calculate the annual rate of depreciation of this car. (Give your answer to the nearest whole number.)†

«16% »

49)!¥Yr11-2U\basics.cat Qn49) 2U93-7a¥

Simplify .†

«2 »

50)!¥Yr11-2U\basics.cat Qn50) 2U94-1a¥

Solve for x: 5(x1)1=29.†

«x=7 »

51)!¥Yr11-2U\basics.cat Qn51) 2U94-1b¥

Find the value of correct to 3significant figures when t=5·3103 and v=7·8102.†

«4·47 »

52)!¥Yr11-2U\basics.cat Qn52) 2U94-1c¥

Express with a rational denominator.†

« »

53)!¥Yr11-2U\basics.cat Qn53) 2U94-1d¥

Find the values of x for which 5x22x3=0.†

«x= »

54)!¥Yr11-2U\basics.cat Qn54) 2U94-1f¥

Find the values of x for which |52x|3.†

«x1, x4 »

55)!¥Yr11-2U\basics.cat Qn55) 2U95-1a¥

Simplify 5x(23x).†

«8x2 »

56)!¥Yr11-2U\basics.cat Qn56) 2U95-1b¥

Factorise 2x2+5x12.†

« (2x3)(x+ 4) »

57)!¥Yr11-2U\basics.cat Qn57) 2U95-1e¥

At Octopus Communications’ annual sale, all mobile phones were discounted by 40%. Cedric paid $630 for a mobile phone at the sale. What was the original price of the phone?†

«$1050 »

58)!¥Yr11-2U\basics.cat Qn58) 2U95-3a¥

Express in the form a+b.†

«2+ »

59)!¥Yr11-2U\basics.cat Qn59) 2U96-1a¥

Factorise 5x22x3.†

« (5x+3)(x1) »

60)!¥Yr11-2U\basics.cat Qn60) 2U96-1b¥

Evaluate correct to one decimal place .†

«1·3 »

61)!¥Yr11-2U\basics.cat Qn61) 2U96-1d¥

Solve |x5|=6.†

«x=11, 1 »

62)!¥Yr11-2U\basics.cat Qn62) 2U96-1e¥

Simplify .†

« »

63)!¥Yr11-2U\basics.cat Qn63) 2U96-1g¥

Solve 23p7.†

«p »

64)!¥Yr11-2U\basics.cat Qn64) 2U97-1b¥

Simplify .†

« »

65)!¥Yr11-2U\basics.cat Qn65) 2U97-1e¥

Express with a rational denominator.†

« »

66)!¥Yr11-2U\basics.cat Qn66) 2U98-1a¥

Simplify (3x6)(54x).†

«7x11 »

67)!¥Yr11-2U\basics.cat Qn67) 2U98-1b¥

Find the value of correct to 3significant figures.†

«0·0820 »

68)!¥Yr11-2U\basics.cat Qn68) 2U98-1f¥

Solve forx.†

«x=4 »

69)!¥Yr11-2U\basics.cat Qn69) 2U98-2a¥

Simplify .†

« »

70)!¥Yr11-2U\basics.cat Qn70) 2U98-2b¥

Solve .†

«x=0, »

71)!¥Yr11-2U\basics.cat Qn71) 2U99-1a¥

Express with a rational denominator.†

« »

72)!¥Yr11-2U\basics.cat Qn72) 2U99-1b¥

Find the values ofx for which 6x2–x–2=0.†

« »

73)!¥Yr11-2U\basics.cat Qn73) 2U99-1e¥

Find the values ofy for which |9y–11|7.†

«y2, »

74)!¥Yr11-2U\basics.cat Qn74) 2U99-1g¥

A country property increased in value by to a new value of $36000. What was the value of the property before the increase?†

«$32000 »

75)!¥Yr11-2U\basics.cat Qn75) 2U00-1a¥

Find the value of correct to two decimal places.†

«0·30 »

76)!¥Yr11-2U\basics.cat Qn76) 2U00-1b¥

Solve the equation .†

« »

77)!¥Yr11-2U\basics.cat Qn77) 2U01-1a¥

Factorise completely ab–a–bx+x.†

« (a–x)(b–1) »

78)!¥Yr11-2U\basics.cat Qn78) 2U01-1b¥

Simplify |2|+|–5|.†

«7 »

79)!¥Yr11-2U\basics.cat Qn79) 2U01-1c¥

Find integers aandb such that .†

«a=–1, b=2 »

80)!2¥Yr11-2U\basics.cat Qn80) 2U02-1a¥

Evaluate. Give your answer in fractional form.†

« »

81)!2¥Yr11-2U\basics.cat Qn81) 2U02-1b¥

Express as a fraction in its simplest form.†

« »

82)!2¥Yr11-2U\basics.cat Qn82) 2U02-1c¥

Factorise 40–5y3. †

«5(2–y)(4+2y+y2) »

83)!¥Yr11-2U\basics.cat Qn83) 2U03-1a¥

Evaluate correct to one decimal place .†

«36 »

84)!¥Yr11-2U\basics.cat Qn84) 2U03-1b¥

Factorise fully 128x–16x4.†

«16x(2–x)(4+2x+x2) »

85)!¥Yr11-2U\basics.cat Qn85) 2U03-1c¥

Graph on a number line the solution to |2x+1|5.†

« »

86)!¥Yr11-2U\basics.cat Qn86) 2U03-1d¥

Rationalise the denominator of .†

« »

87)!2U¥Yr11-2U\basics.cat Qn87) 04-1a¥

If x5=5000, findx correct to 3significant figures.†

«5∙49 »

88)!2U¥Yr11-2U\basics.cat Qn88) 04-1b¥

Express 0∙3+ in the form , where aandb are integers.†

« »

89)!2U¥Yr11-2U\basics.cat Qn89) 04-1d¥

.†

« »

90)!2U¥Yr11-2U\basics.cat Qn90) 04-1e¥

Solve8x=32, leaving the answer as a fraction.†

« »

91)!2U¥Yr11-2U\basics.cat Qn91) 04-1f¥

Find the integers aandb such that .†

«a=2 and b=1 »

92)!¥Yr11-2U\basics.cat Qn92) 2U05-1a¥

Write down the value of |–6|–|–12|.†

«–6 »

93)!¥Yr11-2U\basics.cat Qn93) 2U05-1b¥

find the value of f when u=–5 and v=7∙5. †

«f=–15 »

94)!¥Yr11-2U\basics.cat Qn94) 2U05-1c¥

Solve the equation (x–3)2=9.†

«x=6 or x=0 »

95)!¥Yr11-2U\basics.cat Qn95) 2U05-1f¥

.†

« Proof »

96)!¥Yr11-2U\basics.cat Qn96) 2U06-1a¥

Evaluate correct to 3decimal places.†

«1∙278 »

97)!¥Yr11-2U\basics.cat Qn97) 2U06-1b¥

By rationalising the denominator, simplify .†

« »

98)!¥Yr11-2U\basics.cat Qn98) 2U06-1d¥

Completely factorise 4xy+xb+8ay+2ab.†

« (x+2a)(4y+b) »

99)!¥Yr11-2U\basics.cat Qn99) 2U06-1f¥

Solve the equation |x–2|=3.†

«x=5 or x=–1 »

100)!¥Yr11-2U\basics.cat Qn100) 2U06-8a¥

If Am = 3, find the value of A4m–5.†

«76 »

[[End Of Qns]]

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