Download 1. Solve these equations. (a) = 12

1.
Solve these equations.
(a)
x = 12
2
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Answer x = …………………………….
(1)
(b)
3y – 11 = 4
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.....................................................................................................................................
Answer y = ……………………………..
(2)
(c)
4z + 8 = 3 – z
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer z = ………………….…………..
(3)
(d)
2t  5  7
3
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.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer t = ………………….…………..
(3)
(Total 9 marks)
The Robert Smyth School
1
2.
Solve the following equations.
(a)
2x + 5 = 3
.....................................................................................................................................
.....................................................................................................................................
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Answer x = ....................................................
(2)
(b)
4(y – 3) = 18
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.....................................................................................................................................
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Answer y = ....................................................
(3)
(c)
z4
= 11
2
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.....................................................................................................................................
Answer z = ....................................................
(2)
(Total 7 marks)
3.
(a)
Solve the equation
23 – 2 x
3
5
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.....................................................................................................................................
Answer x = ..............................................................
(3)
(b)
Solve the inequality 3x + 8 < 29
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.....................................................................................................................................
Answer ......................................................
(2)
(Total 5 marks)
The Robert Smyth School
2
4.
Solve the equations
(a)
4v – 1 = 9
.....................................................................................................................................
.....................................................................................................................................
Answer v = ...............................................................
(2)
(b)
3w + 4 = 19 – 2w
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.....................................................................................................................................
Answer w = ..............................................................
(3)
(c)
x
 2  11
5
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.....................................................................................................................................
Answer x = ...............................................................
(2)
(d)
4( y + 3) = 9( y – 2 )
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Answer y = ...............................................................
(3)
(Total 10 marks)
5.
Solve these equations
(a)
6r + 2 = 8
...............……………………………………………………………………………..
...............……………………………………………………………………………..
Answer r = ............................................
(2)
The Robert Smyth School
3
(b)
7s + 2 = 5s + 3
...............……………………………………………………………………………..
...............……………………………………………………………………………..
...............……………………………………………………………………………..
Answer s = ............................................
(3)
(c)
12 – y
5
3
...............……………………………………………………………………………..
...............……………………………………………………………………………..
...............……………………………………………………………………………..
Answer y ............................................
(3)
(Total 8 marks)
6.
Solve the equations
20
(a)
4
x
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer x =...............................................................................
(2)
(b)
y
5  9
3
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.....................................................................................................................................
.....................................................................................................................................
Answer y =...............................................................................
(2)
(c)
4(z – 1) = 2(z + 3)
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Answer z =...............................................................................
(3)
(Total 7 marks)
The Robert Smyth School
4
1.
(a)
24
B1
Allow embedded answers
throughout this question provided they are not
contradicted on the answer line
(b)
(c)
(d)
3y = 4 + 11 or 15
M1
5
A1
4z + z or 3 – 8 seen
M1
5z = –5
M1
–1
A1
2t + 5 = 7 × 3 or 21
2t 5
or   7
3
3
M1
2t = 21 – 5 or 16
2t
5
7–
3
3
8
Ml dep
A1
[9]
2.
(a)
x = –l
M1,A1
M1 for 2x = –2
A1 answer cao
(b)
y = 7.5
M1,M1,A1
M1 for 4y – 12 = 18
M1 for 4y = 30
A1 answer cao
(c)
z = 18
M1,A1
M1 for z + 4 = 22
A1 answer cao
[7]
3.
(a)
23 – 2x = 15
M1
4.6 – 0.4x = 3 gets M1 allow one error
23 – 15 = 2x
A1
1.6 = 0.4x A1
4
A1ft
f.t. if M1 awarded.
(b)
3x < 21
M1
3x = 21 gets M1 iff recovered
x<7
A1
Must have inequality in answer.
Accept ..
[5]
The Robert Smyth School
5
4.
(a)
4v = 9 + 1 (or 10)
M1
v = 2.5
A1
oe
(b)
3w + 2w = 19 – 4
oe Allow one sign error
M1
5w = 15
M1dep
Gathering terms
w=3A
(c)
x = 5× (11 + 2)
x = 5× 11 + 10
M1
65
(d)
A1
4y + 12 = 9y – 18
Allow one error
M1
30 = 5y, –5y = –30
ft if M1 awarded and equation in form ay = b with no further
errors
A1ft
6
A1ft
ft only if M1, A0 previously and their equation of form ay = b is
solved correctly
[9]
5.
(a)
6r = 8 – 2
1
M1
A1
(b)
2s or 1 seen
2s = 1
½ or 0.5
M1
A1
A1
7s – 5s or 3 – 2 or 5s – 7s or – 2s or 2 – 3 or – 1
–1 = –2s
(c)
12 – y = 3 × 5
12 – 15 = y
–3
4 – y/3 = 5
M1
DM1
A1
–y/3 = 1, allow y = 15 – 12
[8]
6.
(a)
20 = 4x
M1
20
=x
4
5
(b)
(c)
A1
y+5×3=9×3
y/3= 9 – 5, y/3 = 9 + 5,
M1
(3y + 15 = 27 is M0)
12
A1
4z – 4 = 2z + 6
2z – 2 = z+ 3
M1
2z = 10
A1
2z –- z =3 + 2
5
A1
[7]
The Robert Smyth School
6