SPCS0271
1)!¥Yr11-2U\basics.cat Qn1) 2U84-1i¥
Express the following as integers.
a.5223 102.
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)(Rr) 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 x23x4.†
« (x4)(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 x2x20.†
«x1 or x2 »
13)!¥Yr11-2U\basics.cat Qn13) 2U86-1iii¥
Find the values of x and y if: xy=(52)(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 |32x|7.†
« »
16)!¥Yr11-2U\basics.cat Qn16) 2U87-1i¥
Solve for n:
a.4n8=12;
b.n215n+16=0;
c.|3n5|=4n7.†
« a) n=5 b) n=13·8 or 12 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: .†
«1·8105 »
21)!¥Yr11-2U\basics.cat Qn21) 2U88-1iii¥
Simplify †
« »
22)!¥Yr11-2U\basics.cat Qn22) 2U88-1iv¥
If E=(v2u2), find the value ofE when m=4, v=10 and u=7.†
«102 »
23)!¥Yr11-2U\basics.cat Qn23) 2U88-1v¥
Factorise 3x2+8x16.†
« (3x4)(x+4) »
24)!¥Yr11-2U\basics.cat Qn24) 2U88-1vi¥
Express with a rational denominator.†
«1217 »
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)(p22p+4) »
27)!¥Yr11-2U\basics.cat Qn27) 2U89-1c¥
Solve the equation 2a23a1=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 52(3x5)+3x.†
«15 3x »
32)!¥Yr11-2U\basics.cat Qn32) 2U90-1c¥
Find the value of x for which 2x5.†
«x »
33)!¥Yr11-2U\basics.cat Qn33) 2U90-1d¥
Solve the equation 2x25x+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.8x4;
ii.x38.†
« i)4(2x1) ii)(x2)(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.x2(x3)=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: a2b2+3a+3b.†
« (a+b)(ab+3) »
41)!¥Yr11-2U\basics.cat Qn41) 2U92-1d¥
Graph on the number line the solution set of: |32x|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.†
«$520 »
43)!¥Yr11-2U\basics.cat Qn43) 2U92-3a¥
Solve x+=12.†
«x=14 »
44)!¥Yr11-2U\basics.cat Qn44) 2U93-1a¥
Evaluate correct to one decimal place .†
«0·5 »
45)!¥Yr11-2U\basics.cat Qn45) 2U93-1b¥
Factorise x211x+10.†
« (x10)(x1) »
46)!¥Yr11-2U\basics.cat Qn46) 2U93-1e¥
Solve (x+2)2=9.†
«x=1, x=5 »
47)!¥Yr11-2U\basics.cat Qn47) 2U93-1f¥
Express in the form a+b.†
« »
48)!¥Yr11-2U\basics.cat Qn48) 2U93-1g¥
The value ($V) of a car after n years is given by the formula:
V=V0(1R)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(x1)1=29.†
«x=7 »
51)!¥Yr11-2U\basics.cat Qn51) 2U94-1b¥
Find the value of correct to 3significant figures when t=5·3103 and v=7·8102.†
«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 5x22x3=0.†
«x= »
54)!¥Yr11-2U\basics.cat Qn54) 2U94-1f¥
Find the values of x for which |52x|3.†
«x1, x4 »
55)!¥Yr11-2U\basics.cat Qn55) 2U95-1a¥
Simplify 5x(23x).†
«8x2 »
56)!¥Yr11-2U\basics.cat Qn56) 2U95-1b¥
Factorise 2x2+5x12.†
« (2x3)(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 5x22x3.†
« (5x+3)(x1) »
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 |x5|=6.†
«x=11, 1 »
62)!¥Yr11-2U\basics.cat Qn62) 2U96-1e¥
Simplify .†
« »
63)!¥Yr11-2U\basics.cat Qn63) 2U96-1g¥
Solve 23p7.†
«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 (3x6)(54x).†
«7x11 »
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 .†
«36 »
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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