Algebra 1
Extra questions for before the assessment
Try these questions.
(You’ll find the answers on the last four pages)
Key Skill 1: Add and subtract like terms
Simplify the following:
Qu
unsimplified expression
a
5x + 3x + 7x + x
b
6y + 9z + 3y + 11z
c
15x + 7 + 5x + 8
d
x2 + 4x + 3x2 + 7x + 4x2
e
5a + 7b – 3a – 4b
f
a + 2a + 3a – 10a + 17
g
6d – 8d + e – 9e + 4
h
a2 + b 2 + a 2 + b 2 + a2
i
10k – 5k – 3k – 2k
j
6de + 10df - 8de – 9df
k
-7p – 4r – 3r – 3p – 9r – 3p
l
2e + 3 - 6e + 7f + 9 - 11f
m
5w2 - 3w + w - 19w2 + 6w2
n
- t – 4t + 1 + 3t – 7 - 2 + t
o
6m – 16n + 7n + 3m – 2m
simplified expression
Written by John Donnelly
Key Skill 2: Perform basic calculations after substituting letters with numbers
If x = 5, y = 3, z = 10 evaluate the following expressions:
(a)
x+y+z
(b)
2x + 4y
(c)
5y - z
(d)
xy + 5
(e)
xyz
(f)
x2 + y2
(g)
(y + z)2
(h)
2x2 – 5z
(i)
z3
(j)
z - xy
(k)
3xy
(l)
2x2z2
If p = - 3, q = - 4, r = 10 evaluate the following expressions:
(m)
p+q+r
(n)
2r + 4p
(o)
5p – r
(p)
pq + 5
(q)
pqr
(r)
p2 + r2
(s)
(r + q)2
(t)
2q2 – 5p
(u)
p3
(v)
r – pq
(w)
qp2
(x)
5pr2
Written by John Donnelly
Key Skill 3: Solve a variety of algebraic equations
Solve the following algebraically:
(a)
3x + 10 = 40
(b)
5x + 3 = 23
(c)
10x + 15 = 45
(d)
4x – 2 = 42
(e)
7x – 3 = 18
(f)
6x – 9 = 39
(g)
7x + 12 = - 2
(h)
8x + 30 = 6
(i)
11m – 12 = - 23
(j)
5x + 3 = 3x + 15
(k)
10y – 13 = 3y + 22
(l)
7y – 3 = 4y – 12
(m)
3n + 18 = 5n – 22
(n)
8g + 18 = 2g - 36
(o)
d – 49 = 11d - 9
Written by John Donnelly
Key Skill 4: Read and interpret a problem in order to construct an algebraic equation
(a)
I think of a number. I double this number and add seven. This is equal to twenty-one.
(i)
(ii)
(b)
Create an equation to illustrate the above scenario.
Solve this equation to find the number I originally thought of.
I think of a number. I multiply this number by four and subtract six. This is equal to thirty.
(i)
(ii)
(c)
Create an equation to illustrate the above scenario.
Solve this equation to find the number I originally thought of.
I think of a number. I multiply this number by seven and take it away from twenty-nine.
This is equal to fifty.
(i)
(ii)
Create an equation to illustrate the above scenario.
Solve this equation to find the number I originally thought of.
Answers overleaf
Written by John Donnelly
Answers
Key Skill 1
Qu
unsimplified expression
simplified expression
a
5x + 3x + 7x + x
16x
b
6y + 9z + 3y + 11z
9y + 20z
c
15x + 7 + 5x + 8
20x + 15
d
x2 + 4x + 3x2 + 7x + 4x2
8x2 + 11x
e
5a + 7b – 3a – 4b
2a + 3b
f
a + 2a + 3a – 10a + 17
- 4a + 17
g
6d – 8d + e – 9e + 4
- 2d – 8e + 4
h
a2 + b 2 + a 2 + b 2 + a2
3a2 + 2b2
i
10k – 5k – 3k – 2k
0
j
6de + 10df - 8de – 9df
- 2de + df
k
-7p – 4r – 3r – 3p – 9r – 3p
- 13p – 16r
l
2e + 3 - 6e + 7f + 9 - 11f
- 4e – 4f + 12
m
5w2 - 3w + w - 19w2 + 6w2
- 8w2 – 2w
n
- t – 4t + 1 + 3t – 7 - 2 + t
-t–8
o
6m – 16n + 7n + 3m – 2m
7m – 9n
Written by John Donnelly
Key Skill 2
(a)
x+y+z
= 5 + 3 + 10
= 18
(b)
=
=
=
2x + 4y
2(5) + 4(3)
10 + 12
22
(c)
5y - z
= 5(3) – 10
= 15 – 10
= 5
(e)
=
=
xyz
(5)(3)(10)
150
(f)
=
=
=
xy + 5
(5)(3) + 5
15 + 5
20
x2 + y2
= (5)2 + (3)2
= 25 + 9
= 34
(h)
2x2 – 5z
= 2(5)2 – 5(10)
= 50 – 50
=
0
(i)
=
=
=
(y + z)2
(3 + 10)2
132
169
z3
= (10)3
= 1000
(k)
3xy
= 3(5)(3)
=
45
(l)
=
=
=
z - xy
10 – (5)(3)
10 – 15
-5
(d)
(g)
(j)
=
=
=
2x2z2
2(5)2(10)2
2(25)(100)
5000
(m)
p + q + r
= (-3) + (-4) + 10
= 3
(n)
2r + 4p
= 2(10) + 4(-3)
= 20 + (-12)
= 8
(o)
5p – r
= 5(-3) - 10
= (-15) - 10
= - 25
(p)
pq + 5
= (-3)(-4) + 5
=
12 + 5
=
17
(q)
pqr
= (-3)(-4)(10)
= 120
(r)
p2 + r2
= (-3)2 + (10)2
=
9 + 100
=
109
(s)
(t)
2q2 – 5p
= 2(-4)2 – 5(-3)
= 32 - (-15)
= 47
(u)
=
=
=
(r + q)2
(10 + (-4))2
(6)2
36
p3
= (-3)3
= -27
(v)
=
=
=
r – pq
10 – (-3)(-4)
10 – 12
-2
(w)
qp2
= (-4)(-3)2
= (-4)(9)
= - 36
(x)
5pr2
= 5(-3)(10)2
= (-15)(100)
= -1500
Written by John Donnelly
Key Skill 3
(a)
3x + 10 = 40
3x
(b)
= 30
5x + 3 = 23
5x
x = 10
(d)
(e)
= 44
7x
(h)
= -14
x=-2
(j)
= 21
6x – 9 = 39
6x
5x + 3 = 3x + 15
(k)
= 48
x=8
(i)
= - 24
11m – 12 = - 23
11m
x=-3
= - 11
m=-1
10y – 13 = 3y + 22
(l)
7y – 3 = 4y – 12
5x
= 3x + 12
10y
= 3y + 35
7y
= 4y - 9
2x
=
7y
=
3y
=
12
x=6
(m)
(f)
8x + 30 = 6
8x
= 30
x=3
x=3
7x + 12 = - 2
7x
10x
7x – 3 = 18
x = 11
(g)
= 20
10x + 15 = 45
x=4
4x – 2 = 42
4x
(c)
3n + 18 = 5n – 22
35
y=5
(n)
y=-3
8g + 18 = 2g - 36
3n + 40 = 5n
8g
= 2g – 54
40 = 2n
6g
=
n = 20
-9
- 54
g=-9
(o)
d – 49 = 11d – 9
d
- 10d
= 11d + 40
=
40
d=-4
Written by John Donnelly
Key Skill 4
(a)
(i)
Let n be the original number
(ii)
2n + 7 = 21
2n
2n + 7 = 21
= 14
n=7
(b)
(i)
Let n be the original number
(ii)
4n – 6 = 30
4n
4n - 6 = 30
= 36
n=9
(c)
(i)
Let n be the original number
(ii)
29 – 7n = 50
29 – 7n = 50
- 7n = 21
n=-3
Written by John Donnelly