Yr 11 MCAT Algebra Practice 2
6. Write an expression for the
area of the following shape…
6a
1. Expand and Simplify…
a2 + 8a – 20 =
a + 10
3a
(3a + 8)(a – 1) =
10. Simplify fully…
2.
(2a2 x 3a3)2 = 36ak
What is the value of k?
3. Rearrange to make x the
subject of…
y = 3x – 6
4.
Simplify fully…
a) 8ab – 3ab +
5c3
+
b)
24a10b6 =
30a4b8
c)
8a2 x 2a3 x 3a =
c3
=
7. If the above area is 450cm2
what is the value of a?
8. Factorise fully…
a)
a2 + 22a + 40 =
b)
15ab + 20a =
c)
a2 – 100 =
9. Solve the following…
5. Simultaneously solve for a & b.
6a + 5b = 108
3a + 5b = 84
a)
13a – 16 = 10a + 2
b)
5a4 = 80
c)
(a – 4)(a + 9) = 0
d)
a2 + 14a + 40 = 0
11. Three consecutive numbers
beginning with a are added
together. Write a simplified
expression for the sum of these
three numbers.
12. If these three numbers total
up to 171. What is the value of
the first number (a).
13. Simplify fully…
a + a =
3 5
3a2 ÷ 9a =
4b
20b3
Yr 11 MCAT Algebra Practice 2
6. Write an expression for the
area of the following shape…
6a
1. Expand and Simplify…
(3a + 8)(a – 1) =
(2a2 x 3a3)2 = 36ak
k = 10
7. If the above area is 450cm2
what is the value of a?
3. Rearrange to make x the
subject of…
3x – 6 = y
y = 3x – 6
3x = y + 6
4.
x= y+6
3
Simplify fully…
a) 8ab – 3ab +
5c3
+
4 a6
5 b2
c3
450 = 18a2
18a2 = 450
a2 = 25
a = √25 a = 5
.
8. Factorise fully…
= 5ab + 6c3
b)
24a10b6 =
30a4b8
c)
8a2 x 2a3 x 3a = 48a6
.
6a + 5b = 108
3a + 5b = 84
3a
= 24
a=8
eqn 1
eqn 2
subtract eqn 2 off eqn 1
1st + 2nd + 3rd
= a + a + 1+ a + 2
= 3a + 3
12. If these three numbers total
up to 171. What is the value of
the first number (a).
a2 + 22a + 40 = (a + 2 )(a + 20)
b)
15ab + 20a = 5a ( 3b + 4)
c)
a2 – 100 = (a + 10)(a - 10 )
a)
13a – 16 = 10a + 2 3a = 18
b)
13a – 10a = 2 + 16
a=6
a = 4√16
5a4 = 80
a = 2 and -2
a4 = 16
c)
(a – 4)(a + 9) = 0
d)
a2 + 14a + 40 = 0
substitute a back into eqn 1
6(8) + 5b = 108
5b = 60
b = 12
11. Three consecutive numbers
beginning with a are added
together. Write a simplified
expression for the sum of these
three numbers.
a)
9. Solve the following…
5. Simultaneously solve for a & b.
.
=a–2
Area (rectangle) = base x height
Area = 6a x 3a
Area = 18a2
What is the value of k?
(6a5)2 = 36a10
a2 + 8a – 20 = (a + 10)(a – 2)
a + 10
a + 10
3a
- 3a + 8a - 8
= 3a2 + 5a - 8
2.
3a2
10. Simplify fully…
3a + 3 = 171
3a = 168
a = 56
13. Simplify fully…
a + a = 5a + 3a = 8a
15
15
15
3 5
4 or ___
-9
a is ___
-10 or ___
-4
(a + 10)(a + 4) = 0 a is ___
.
3a2 ÷ 9a = 3a2 x 20b3
4b
9a
4b
20b3
= 60a2b3
36ab
2
= 1 /3ab2