Algebra 1
Extra questions for after 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
6x + 3x + 10x + x
b
5y + 7z + 7y + 14z
c
14x + 5 + 4x + 8
d
x2 + 3x + 5x2 + 9x + 6x2
e
8a + 6b – 5a – 4b
f
4a + 5a + 6a – 10a + 13
g
8d – 10d + 3e – 12e + 7
h
b2 + a 2 + b 2 + a 2 + b2
i
20k – 10k – 6k – 4k
j
6ef + 10df - 8ef – 9df
k
-9p – 3r – r – 2p – 6r – 4p
l
3e + 6 - 2e + 9f + 8 - 18f
m
7w2 - 3w + w - 21w2 + 5w2
n
- t – 5t + 3 + 2t – 6 - 3 + 2t
o
5m – 18n + 9n + 2m – 3m
simplified expression
Written by John Donnelly
Key Skill 2: Perform basic calculations after substituting letters with numbers
If x = 4, y = 2, z = 5 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)
2x2y2
If p = - 2, q = - 5, r = 6 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)
6x + 10 = 40
(b)
4x + 3 = 23
(c)
3x + 15 = 45
(d)
11x – 2 = 42
(e)
3x – 3 = 18
(f)
4x – 9 = 39
(g)
14x + 12 = - 2
(h)
6x + 30 = 6
(i)
11m – 67 = - 78
(j)
5x + 3 = 2x + 24
(k)
9y – 18 = 4y + 22
(l)
7y – 3 = 4y – 21
(m)
3n + 8 = 6n – 22
(n)
7g + 14 = 2g - 36
(o)
4d – 59 = 14d - 19
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 four. This is equal to twenty-six.
(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 five and subtract seven. This is equal to eighteen.
(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 eight and take it away from twenty-eight.
This is equal to fifty-two.
(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
6x + 3x + 10x + x
20x
b
5y + 7z + 7y + 14z
12y + 21z
c
14x + 5 + 4x + 8
18x + 13
d
x2 + 3x + 5x2 + 9x + 6x2
12x2 + 12x
e
8a + 6b – 5a – 4b
3a + 2b
f
4a + 5a + 6a – 10a + 13
5a + 13
g
8d – 10d + 3e – 12e + 7
- 2d – 9e + 7
h
b2 + a 2 + b 2 + a 2 + b2
2a2 + 3b2
i
20k – 10k – 6k – 4k
0
j
6ef + 10df - 8ef – 9df
- 2ef + df
k
-9p – 3r – r – 2p – 6r – 4p
-15p - 10r
l
3e + 6 - 2e + 9f + 8 - 18f
e – 9f + 14
m
7w2 - 3w + w - 21w2 + 5w2
- 9w2 – 2w
n
- t – 5t + 3 + 2t – 6 - 3 + 2t
- 2t - 6
o
5m – 18n + 9n + 2m – 3m
4m – 9n
Written by John Donnelly
Key Skill 2
(a)
x+y+z
= 4+2+5
= 11
(b)
=
=
=
2x + 4y
2(4) + 4(2)
8 + 8
16
(c)
5y - z
= 5(2) – 5
= 10 – 5
= 5
(d)
(e)
=
=
xyz
(4)(2)(5)
40
(f)
=
=
=
xy + 5
(4)(2) + 5
8 +5
13
x2 + y2
= (4)2 + (2)2
= 16 + 4
= 20
(h)
2x2 – 5z
= 2(4)2 – 5(5)
= 32 – 25
=
7
(i)
=
=
=
(y + z)2
(2 + 5)2
72
49
z3
= (5)3
= 125
(k)
3xy
3(4)(2)
24
(l)
=
=
=
z - xy
5 – (4)(2)
5–8
-3
2x2z2
= 2(4)2(2)2
= 2(16)(4)
= 128
(g)
(j)
=
=
(m)
p + q + r
= (-2) + (-5) + 6
= -1
(n)
2r + 4p
= 2(6) + 4(-2)
= 12 + (-8)
= 4
(o)
5p – r
= 5(-2) - 6
= (-10) - 6
= - 16
(p)
(q)
pqr
= (-2)(-5)(6)
= 60
(r)
p2 + r2
= (-2)2 + (6)2
=
4 + 36
=
40
2q2 – 5p
= 2(-5)2 – 5(-2)
= 50 - (-10)
= 60
(u)
p3
= (-2)3
= -8
pq + 5
= (-2)(-5) + 5
=
10 + 5
=
15
(t)
=
=
=
(r + q)2
(6 + (-5))2
(1)2
1
=
=
=
r – pq
6 – (-2)(-5)
6 – 10
-4
(w)
qp2
= (-5)(-2)2
= (-5)(4)
= -20
(s)
(v)
(x)
=
=
=
5pr2
5(-2)(6)2
5(-2)(36)
-360
Written by John Donnelly
Key Skill 3
(a)
6x + 10 = 40
6x
(b)
= 30
4x + 3 = 23
4x
x=5
(d)
(e)
= 44
3x
(h)
= - 14
x = -1
(j)
= 21
4x – 9 = 39
4x
5x + 3 = 2x + 24
(k)
= 48
x = 12
(i)
= - 24
11m – 67 = - 78
11m
x=-4
= - 11
m=-1
9y – 18 = 4y + 22
(l)
7y – 3 = 4y – 21
5x
= 2x + 21
9y
= 4y + 40
7y
= 4y – 18
3x
=
5y
=
3y
=
21
x=7
(m)
(f)
6x + 30 = 6
6x
= 30
x = 10
x=7
14x + 12 = - 2
14x
3x
3x – 3 = 18
x=4
(g)
= 20
3x + 15 = 45
x=5
11x – 2 = 42
11x
(c)
3n + 8 = 6n – 22
3n + 30 = 6n
40
y=8
(n)
7g + 14 = 2g - 36
7g + 50 = 2g
30 = 3n
50 = - 5g
n = 10
g = - 10
- 18
y=-6
(o)
4d – 59 = 14d - 19
4d
-10d
= 14d + 40
=
40
d=-4
Written by John Donnelly
Key Skill 4
(a)
(i)
Let n be the original number
(ii)
2n + 4 = 26
2n
2n + 4 = 26
= 22
n = 11
(b)
(i)
Let n be the original number
(ii)
5n – 7 = 18
5n
5n - 7 = 18
= 25
n=5
(c)
(i)
Let n be the original number
(ii)
28 – 8n = 52
28 – 8n = 52
- 8n = 24
n=-3
Written by John Donnelly