Fixing your maths mistakes Exercises
STUDYSmarter
Question 1: detecting common errors
Decide whether each of the following equations are TRUE or FALSE.
1
3
2
7
(a) 4/0 = 0
(e) −24 = 16
(i) (−2)3 = −8
(m)
(b) 0/(−2) = 0
(f ) (−3)2 = 9
(j) (−3)3 = −9
(n) 30 = 1
(c) 0/(−4) = 0
(g) (−1)2 = 1
(k)
(d) −22 = −4
(h) −23 = −8
(l)
1
1
2
7
1
1
+
+
3
2
2
2
=
=
5
14
+
=
13
21
(o) (−5)0 = −1
(p) −50 = −1
Question 2: getting algebraic steps right
Think of each of the following algebraic equations as a single step of working out from
the left side to the right side. State whether you think the working out is True or
False. If false, give a reason why.
(a) (x − 3)2 = x2 + 9
(o)
4x 4
4x
=
+
3 + 2x
3
2
(p)
3 + 2x
3 2x
= +
4
4
4
(q)
9xy + y
=9+y
xy
(r)
3x2 + 2x
= 3x + 2
x
(b) (x − 3)2 = x2 − 9
(c) (x − 3)2 = x2 − 6x + 9
(d) x4 x2 = x6
(e) x3 x3 = x6
(f ) x5 x5 = x25
3x
= 4x + 3
x
(g) (x2 )9 = x18
(s) 4x2 +
(h) (x2 )7 = x11
(j) (3x + 3) = 3(x + 1)
(t) (x + h)3 = x3 + h3
√
(u) x2 + 9 = x + 3
√
(v) x2 = x
(k) (2x + 4)7 = 2(x + 2)7
(w)
(i) (x2 x3 )2 = x10
(l) (2x + 2)2 = 4(x + 1)2
1
x
+
1
x
=
2
x
(m) −6(x + 2) = −6x − 12
(x) 4(x + 3)3 = (4x + 12)3
√
(y) x2 + 2x + 1 = x + 1
(n) −4x(−3x − 2) = 12x2 − 8x
(z) 9x2 + x3 = 9x5
G Coates/A Dudek
1
July 2016
Fixing your maths mistakes Exercises
STUDYSmarter
Question 3
A student has been asked to solve the equation (x + 2)2 − 9 = 0. We show their working
out below. What is wrong with their working?
⇒ (x + 2)2 − 9
⇒ (x + 2)2
⇒x+2
∴x
G Coates/A Dudek
2
=
=
=
=
0
9
3
1
July 2016
Fixing your maths mistakes Exercises
STUDYSmarter
Solutions
Question 1
(a) False (undefined)
(g) True
(m) True
(b) True
(h) True
(n) True
(c) True
(i) True
(o) False (0)
(d) True
(j) False (-27)
(p) True
(e) False (-16)
(k) False
(f ) True
(l) False
2
1
or 2
25
14
Question 2
(a) False, we can not distribute powers to each term in the brackets.
(b) False, the same reason as above.
(c) True
(d) True
(e) True
(f ) False, we should add powers here.
(g) True
(h) False, we should multiply powers here.
(i) True
(j) True
(k) False, Indices come before multiplication.
(l) True
(m) True
(n) False, because (−4x)(−2) should equal 8x, and not −8x.
(o) False, we can not split denominators.
(p) True
(q) False, xy is not a common factor of both lines.
G Coates/A Dudek
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July 2016
Fixing your maths mistakes Exercises
STUDYSmarter
(r) True
(s) False, only the 3x is being divided by x here.
(t) False, we can not distribute powers.
(u) False, the square root of the sum is not the sum of the square roots.
(v) True (unless x is negative)
(w) True
(x) False, cube first and then distribute.
(y) True (unless x < −1)
(z) False, can not add unlike terms.
Question 3
The mistake occurs in the step from (x+2)2 = 9 to x+2 = 3. Here, the student has taken
the square root of both sides, and as a result, has lost one of the solutions to this problem!
This step can only be made by realising that there are two numbers which square to 9,
which are 3 and −3. The correct working is as follows:
⇒ (x + 2)2 − 9
⇒ (x + 2)2
⇒x+2
⇒x
∴x
=
=
=
=
=
0
9
±3
−2 ± 3
1, −5
Using STUDYSmarter Resources
This resource was developed for UWA students by the STUDYSmarter team for the
numeracy program. When using our resources, please retain them in their original form
with both the STUDYSmarter heading and the UWA crest.
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July 2016