S2/3 Revision Pack 2 Gradients and Straight Lines (1) 1. Calculate the gradient of each ladder below : 2. Calculate the gradient of each line below, leaving your answer as a fraction in its simplest form where necessary. 2 m 4 m 8 m 2 m 3 m 10 m 12 m 2 m 6 m 8 m 1 m 8 m (a) (b) (c) (d) (e) (f) (a) (b) (c) (d) (e) (f) (g) (h) (i) (j)
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Gradients and Straight Lines (1) - Dunblane High School · S2/3 Revision Pack 2 Gradients and Straight Lines (2) 1. A straight line has as its equation y 2x. (a) Copy and complete
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S2/3 Revision Pack 2
Gradients and Straight Lines (1)
1. Calculate the gradient of each ladder below :
2. Calculate the gradient of each line below, leaving your answer as a fraction in its simplest
form where necessary.
2 m
4 m
8 m
2 m
3 m
10 m
12 m
2 m
6 m
8 m
1 m
8 m
(a) (b) (c)
(d) (e) (f)
(a)
(b)
(c)
(d)
(e) (f)
(g) (h)
(i)
(j)
S2/3 Revision Pack 2
Gradients and Straight Lines (2)
1. A straight line has as its equation xy 2 .
(a) Copy and complete the table for this line.
(b) Plot the points from the table on a coordinate diagram and draw the line through them.
2. A straight line has as its equation xy 3 .
(a) Copy and complete the table for this line.
(b) Plot the points from the table on a coordinate diagram and draw the line through them.
3. A straight line has as its equation xy2
1 .
(a) Copy and complete the table for this line.
(b) Plot the points from the table on a coordinate diagram and draw the line through them.
4. A straight line has as its equation xy3
1 .
(a) Copy and complete the table for this line.
(b) Plot the points from the table on a coordinate diagram and draw the line through them.
5. A straight line has as its equation xy .
(a) Copy and complete the table for this line.
(b) Plot the points from the table on a coordinate diagram and draw the line through them.
x 0 1 2 3 4 5
y 2 10
x 0 1 2 3 4 5
y 3
x 0 2 4 6 8 10
y 1 4
x 0 3 6 9 12
y 0 3
x 1 2 3 4 5 6
y 1 5
S2/3 Revision Pack 2
Gradients and Straight Lines (3)
1. A straight line has as its equation 2 xy .
(a) Copy and complete the table for this line.
(b) Plot the points from the table on a coordinate diagram and draw the line through them.
2. A straight line has as its equation 12 xy .
(a) Copy and complete the table for this line.
(b) Plot the points from the table on a coordinate diagram and draw the line through them.
3. A straight line has as its equation 42
1 xy .
(a) Copy and complete the table for this line.
(b) Plot the points from the table on a coordinate diagram and draw the line through them.
4. A straight line has as its equation 54
1 xy .
(a) Copy and complete the table for this line.
(b) Plot the points from the table on a coordinate diagram and draw the line through them.
5. A straight line has as its equation 23 xy .
(a) Copy and complete the table for this line.
(b) Plot the points from the table on a coordinate diagram and draw the line through them.
x 0 1 2 3 4 5
y 2 5
x 0 1 2 3 4 5
y 3 9
x 0 2 4 6 8 10
y 4 8
x 0 4 8 12
y 6
x 1 2 3 4 5
y 1 10
S2/3 Revision Pack 2
Worksheet Name : ___________________________
Class : _____________
x
y
0 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
5
6
7
8
9
10
11
12
13
x
y
0 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
5
6
7
8
9
10
11
12
13
x
y
0 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
5
6
7
8
9
10
11
12
13
x
y
0 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
5
6
7
8
9
10
11
12
13
This worksheet can be used along with the gradient, straight line and scatter diagrams worksheets
S2/3 Revision Pack 2
Trigonometry (1)
You need a scientific calculator for this worksheet.
1. Calculate the angle marked x in each triangle below :
(a) (b) (c)
(d) (e) (f)
2. Calculate the angle marked x in each triangle below :
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
19 21
x
12
14
x
4 9
x
3 11
x
5
8
x
10
17
x
15
14
3
4
9 16
7
12
5
5 27
34
4 5.6
7.3
8.9
3.2 12.8
x x x
x x
x
x
x x
Remember
SOH CAH TOA
S2/3 Revision Pack 2
Trigonometry (2)
You need a scientific calculator for this worksheet.
1. Calculate the length of the side marked x in each triangle below :
(a) (b) (c)
(d) (e) (f)
2. Calculate the side marked x in each triangle below :
(a) (b) (c)
(d) (e) (f)
x
x
x
x x
x
32o
45o
50o 48o
78o
24o
16
7
12
14
11
20
7
80o
x 35o
20
x
20o
26
x
25o
15 x
3
42o
x
9
32o
x
Remember
SOH CAH TOA
S2/3 Revision Pack 2
Trigonometry (3) - Angles & Sides
You need a scientific calculator for this worksheet.
Calculate the value of x in each triangle below :
5 8
xo
3
11
xo
x
19 9 x
x
8
11
16
4.5
2.7
27 x
12
37
x
17
4.7
3.5
xo
20o
58o xo
xo
xo
xo
75o
26o 28o
(a) (b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
12
8
xo 27
x
72o
(m) (n)
11
7
S2/3 Revision Pack 2
Trigonometry (4)
You need a scientific calculator for this worksheet.
1. To test the stability of a bus a tilting platform is used.
It is known that a bus will topple if the angle between the platform and the ground is greater that 20o.
Which of the buses below would topple?
Each answer must be accompanied with the appropriate working.
(a) (b) (c) (d)
(e) (f) (g) (h)
2. To comply with building regulations a roof must have
an angle of between 22o and 28o to the
horizontal (see diagram opposite).
Which of the roofs below comply, and which do not comply,
with building regulations?
(a) (b)
(c) (d)
(e) (f)
(g) (h)
8 m
2 m
10 m
4 m
14 m
4.8 m
6.2 m
2 m
7.45 m
2.7 m
9.8 m
3.6 m
8.43 m
3 m
6.8 m
2.6 m
x
x must lie between 22o and 28o
4 m
1.8 m
3.6 m
1.4 m
6.2 m
1.5 m
6.8 m
1.9 m
6 m
2.1 m
8 m
4.5 m
7.4 m
2.2 m
12.3 m
2.4 m
S2/3 Revision Pack 2
Fractions, Decimals and Percentages (1)
** You need a calculator for this worksheet.
1. Calculate :
kgofotonnesofnofm
oflmmofkofj
ofikgofhofg
gramsoffofecmofd
ofckgofbofa
525)(480)(2540£)(
08.1£)(984)(10.5£)(
92.10£)(45)(96.15£)(
558)(136£)(48)(
40.36£)(65)(96£)(
17
5
16
9
20
11
12
9
8
3
6
5
7
3
10
9
3
2
9
7
8
5
4
3
7
1
5
1
3
1
2. Calculate :
tonnesofoofnofm
oflofkgofj
ofiofhofg
cmoffofekgofd
ofcgofbofa
1200%7)(12£%4)(1500£%78)(
360£%94)(250£%80)(4500%8)(
880£%65)(340£%5)(64£%19)(
85%21)(10£%17)(60%42)(
45£%13)(300%54)(90£%26)(
3. Calculate each of the following rounding your answers to the nearest penny.
pofoofnofm
poflofkofj
ofiofhofg
poffofepofd
ofcofbofa
97%57)(08.12£%3)(53.1£%71)(
88%34)(57.2£%9)(45.3£%81)(
65.834£%5)(20.341£%4)(30.18£%12)(
51%41)(43.10£%57)(89%47)(
35.6£%18)(71.12£%24)(20.13£%36)(
4. Change each of the following fractions to percentages.
Round your answer to the nearest percent when necessary.
29
6
95
48
365
38
31
6
7
3
15
2
13
8
32
4
12
5
23
18
11
3
9
5
20
19
100
17
10
7
25
7
4
3
5
4
)()()()()()(
)()()()()()(
)()()()()()(
rqponm
lkjihg
fedcba
5. John's schedule marks are shown in the table below :
(a) Copy and complete the table by calculating John's "percentage mark" for each subject.
Round each answer to the nearest percent where necessary.
(b) Which was John's best subject ?
(c) Which was his worst ?
Subject Maths English Tech Science Art History French
Mark 45 out of 60 64 out of 72 40 out of 65 38 out of 55 75 out of 90 27 out of 40 63 out of 95
%
S2/3 Revision Pack 2
Fractions, Decimals and Percentages (2)
** You need a calculator for this worksheet.
1. Increase each of the following by 15%.
(a) £250 (b) 160kg (c) 25cm (d) £36
(e) 2100g (f) 210oC (g) £8 (h) £3500
2. Decrease each of the amounts in Q1 by 20%.
3. The nine workers in a small factory are given different percentage wage rises dependant upon
their length of service. The table below represents their weekly wages.
Copy and complete the table .......
Name Old Wage % Increase Increase New Wage
John Hughes £230 4% £9.20 £239.20
Steven Higgins £168 6%
Susan Marshal £210 4%
Stewart Aitken £145 2%
Pamela Grant £360 3.5%
Neil McShane £225 6%
James Mackie £235 8%
Lorna Graham £210 4.5%
Pat Lavery £468 5%
4. For each diagram below, write down i) the fraction shaded; ii) the percentage shaded .
(a) (b) (c) (d)
(e) (f) (g)
5. Calculate the percentage of vowels in each word below.
(a) (b) (c)
6. (a) In a class of thirty pupils, 6 were absent. Calculate the percentage absent.
(b) A machine produces 300 heating elements in a morning. Six are found to be defective.
What percentage of the elements are defective ?
(c) A small farm has 160 sheep. During a severe storm the farmer loses 8 sheep.
What percentage of the sheep got lost ?
S2/3 Revision Pack 2
Fractions, Decimals and Percentages (3)
** You need a calculator for this worksheet.
1. VAT is charged at %172
1 . Calculate the VAT on each item below.
(a) A stereo costing £230 (b) A fridge costing £148
(c) A cooker costing £456 (d) A watch costing £68
(e) A computer costing £650 (f) A gold ring costing £134
2. Find the total cost of each item in Q1 after the VAT has been added.
3. A man places £2300 in a savings account which has an annual interest rate of 4%.
(a) How much interest will he earn in the first year ?
(b) Assuming he does not touch his money, how much does he now have in the bank
at the beginning of year two ?
(c) Hence calculate the interest he will get at the end of year two.
4. A woman places £22100 in a Post Office savings account which has an annual interest rate of 5%.
(a) How much interest will she earn in the first year ?
(b) Assuming she does not touch her money, how much does she now have in the bank
at the beginning of year two ?
(c) Hence calculate the interest she will get at the end of year two.
5. Steven places £800 in a Building Society at an annual interest rate of 3%.
How much will he have in his account after two years ?
6. Susan invests £800 in a Building Society at an annual interest rate of 6%.
How much will she have in her account after two years ?
7. Mr Banks places £1300 in a savings account which has an annual interest rate of 2%.
How much will he have in his account after three years ?
8. Miss Anderson places £5600 in a Building Society at an annual interest rate of 7%.
How much will she have in her account after three years ?
S2/3 Revision Pack 2
Solving Equations (1)
1. Solve each of the following equations :
37710)(3829)(2158)(
2623)(2062)(2516)(
3137)(1756)(2243)(
1314)(1132)(1885)(
ylxkaj
xiphhg
dfaeyd
mctbxa
2. Solve each of the following equations :
3610)(3369)(16412)(
2758)(1839)(2426)(
3527)(306)(2037)(
1624)(1536)(1235)(
yylxxkaaj
xxipphhhg
ddfaaeyyd
mmcttbxxa
3. Solve each of the following equations :
11486)(40749)(5198)(
405411)(364127)(238716)(
513315)(192111)(432312)(
356710)(32629)(2658)(
1628)(244610)(30446)(
16217)(29256)(12547)(
21318)(15336)(8325)(
xxuxxtmms
aarddqyyp
xxohhnppm
yylxxkaaj
xxipphhhg
ddfaaeyyd
mmcttbxxa
S2/3 Revision Pack 2
Solving Equations (2)
1. Solve each of the following equations :
27312)(4316)(2378)(
2447)(2912)(3246)(
1927)(3118)(576)(
1554)(932)(1644)(
ylxkyj
uiphhg
dfaeyd
mctbxa
2. Solve each of the following equations :
5512)(3057)(16210)(
14455)(11158)(12426)(
14470)(536)(12528)(
9204)(9186)(7125)(
yylxxkaaj
xxirrhhhg
xxfyyeyyd
mmcttbxxa
3. Solve each of the following equations :
?4486)(38345)(33128)(
406410)(38427)(238714)(
33395)(21267)(432)(
173)(347211)(3427)(
263112)(2489)(21476)(
19216)(35358)(15517)(
20518)(17337)(8325)(
xxuxxtaas
aarkkqyyp
xxohhnppm
yylxxkxxj
xxiyyhhhg
ddfkkemmd
mmcttbxxa
S2/3 Revision Pack 2
Solving Equations (3)
1. Solve each of the following equations :
80)2(10)24)2(6)45)1(9)
48)5(8)25)1(5)21)2(3)
12)3(6)16)2(4)10)1(5)
30)6(2)35)1(7)24)3(6)
40)6(5)12)4(2)20)2(4)
rownem
zlkkyj
xiphag
hfwegd
fcebca
2. Solve each of the following equations :
80)210(4)24)62(3)20)31(2)
28)77(2)22)35(2)21)21(3)
12)32(4)28)13(2)27)15(3)
35)14(7)52)35(4)20)42(2)
60)24(6)12)42(2)28)13(4)
rownem
ulzkkj
yiphhg
wfgetd
fcebca
3. Solve each of the following equations :
)15(2)32(4))1(4)2(7))4(6)1(8)
213)1(7)33)2(6)73)1(5)
)28(4)2(8))5(4)2(7))8(2)1(4)
342)1(6)293)3(8)153)1(7)
242)3(5)302)3(4)12)2(3)
xxoxxnwwm
uulxxkddj
aaixxhaag
yyfhheddd
mmcxxbaaa
S2/3 Revision Pack 2
Equations (Extension Examples)
1. Solve each of the following equations (a warm up) :
3235)(611312)(517)(
1219)(6159)(5248)(
1627)(15337)(2645)(
vvimmhxxg
yyfddevvd
mmcttbxa
2. Solve each of the following equations :
35278)(15315)(19453)(
12246)(5279)(1331)(
52462)(226414)(2126)(
24558)(5213)(32112)(
4406)(2202)(425)(
221)(3245)(123)(
xxrvvqxxp
xxoxxnccm
ddlaakxxj
rripphyyg
xxfaaettd
yycmmbxxa
3. Solve each of the following equations :
21831222445137
42936220523122
6230861855113
6166421042688
11573123275
cc)o(kk)n(xx)m(
aa)l(yy)k(xx)j(
ee)i(mm)h(xx)g(
aa)f(hh)e(vv)d(
y)c(x)b(x)a(
S2/3 Revision Pack 2
Statistics - Stem-and-Leaf Diagrams
1. A sample of tomato plants are measured for height. Their heights are recorded
to the nearest centimetre.
The stem-and-leaf diagram shows the results.
(a) How many plants were in the sample?
(b) What height is the tallest plant?
(c) Write out level 5 in full.
(d) What fraction of the plants were more
than 50cm tall?
2. Susan decided to visit various shops in her surrounding area in order to
compare the price of an identical CD player.
Her results, shown below, are given to the nearest pound.