Yr 11 MCAT Algebra Practice 4
1. Solve these equations…
a) 5(a – 3) + 1 = 46
b) (a – 5)(a + 3) = 0
c) 13a – 32 = 7a – 8
2. Expand and simplify…
a) (a – 11)(a – 2) =
b) 7a(a + 3) + 6(a + 4) =
3. Make y the subject of
5x + 6y – 48 = 0
11. Factorise the following…
a) 5a2 + 45a + 100 =
3a
2a + 14
6. Write a simplified expression
for the perimeter of this triangle…
7. Write a simplified expression
for the area of this triangle…
c)
8. If the total area is actually
90m2 what is the value of a?
3a – 3b = 36
c)
36a8b7 =
18a7b4
d)
4a3b5c x 7ab3c2 =
e)
5a - a =
12
12
9(a – 4)2 + 3 = 84
13. Simplify…
a)
b) 7a + 9b + a – b + a – 2b =
3a + b = 48
a) 2a2 = 72
b) 2a4 = 128
9. Simplify… a) (2a4)4 =
5. Simultaneous solve for a and b
c) 2a2 + 5a + 3 =
12. Solve the following…
4. Solve to find both values of a
a2 – 5a - 14 = 0
b) a2 – 81 =
4a5b9 =
14a7b3
b) (4a2)0 =
c) a + 2b =
2
5
14. What two numbers add
to seventeen but subtract to
one?
Yr 11 MCAT Algebra Practice 4
1. Solve these equations… 5(a-3)=45
(a-3)=9
a=12
5 or __
-3
b) (a – 5)(a + 3) = 0 a is __
a) 5(a – 3) + 1 = 46
c) 13a – 32 = 7a – 8 13a-7a=-8+32
6a=24
a=4
2. Expand and simplify…
2
a) (a – 11)(a – 2) = a - 11a - 2a + 22
= a2 – 13a + 22
b) 7a(a + 3) + 6(a + 4) =
= 7a2 + 21a + 6a + 24 = 7a2 + 27a + 24
3. Make y the subject of
5x + 6y – 48 = 0
6y = -5x + 48
y = -5/6x + 8
4. Solve to find both values of a
a2 – 5a - 14 = 0
7 or __
-2
a is __
4b = 12
b=3
a) 5a2 + 45a + 100 =
2a + 14
6. Write a simplified expression
for the perimeter of this triangle…
c) 2a2 + 5a + 3 =
3a + ______
8a + 4 + ______
2a + 14
____
= 13a + 18
7. Write a simplified expression
for the area of this triangle…
3a – 3b = 36
sub b = 3 into eqn 1.
3a + 3 = 48
3a = 45
a = 15
a2 + 9a + 20 = (a + 4)(a + 5)
b) a2 – 81 = (a – 9)(a + 9)
(2a + 3 )(a + 1 )
12. Solve the following…
a2 = 36
a = 6 or - 6
a)
= 72
a4 = 64
4
b) 2a = 128 a = 4 or - 4
2a2
area (triangle) = 1/2 b x h
area (triangle) = 1/2 (2a + 14) x 3a
area (triangle) = (a + 7) x 3a = 3a2 + 21a c)
8. If the total area is actually
90m2 what is the value of a?
3a2 + 21a = 90
3a2 + 21a – 90 = 0
a2 + 7a – 30 = 0
(a + 10)(a - 3 ) = 0
3
a is -10
__ or __
b) 7a + 9b + a – b + a – 2b = 9a - 6b
5. Simultaneous solve for a and b
- (3a – 3b = 36)
3a
9. Simplify… a) (2a4)4 = 16 a16
(a - 7 )(a + 2) = 0
3a + b = 48
11. Factorise the following…
c)
36a8b7 = 2a b3
18a7b4
9(a – 4)2 + 3 = 84
9(a – 4)2 = 81
(a – 4)2 = 9
a – 4 = 3 or - 3
a = 7 or 1
13. Simplify…
a)
4a5b9 =
14a7b3
2b6
7 a2
.
b) (4a2)0 = 1
5a + 4b
c) a + 2b = 10 10
2
5 = 5a+4b
10
.
.
.
d)
4a3b5c x 7ab3c2 = 28a4 b8 c3
e)
5a - a = 4a = a
12
3
12
12
.
.
14. What two numbers add
to seventeen but subtract to
one? a + b = 17
- (a - b = 1 )
2b = 18
b=9
a + 9 = 17
a=8