Yr 11 MCAT Algebra Practice 3 – based on NCEA externals 2009 and 2010
1. Jonathan found this equation…
4(a2)n x 3a4 = 12a16
What is the value of n?
2.
Factorise
3.
Solve these equations…
a)
a/
3
a2
6. Solve for a…
a) (4a – 5)(a + 2) = 0
+ 7a – 60
–4=5
b)
3a + 5 = 3 – 5a
c)
(1 – 2a)(a + 3) = 0
4. Solve this inequation…
5a – 8 > 12
5. Make r the subject of this
formula A = 4πr2
b)
4(a + 3) = 11
c)
4a – 7 = 8 + 2a
7. Find the whole numbers that
can replace a, b and c so that this
equation is true…
x2 + ax – 8 = (x + 8)(x + c)
11. if 8a9 = 2a4 what is n =?
4an
12. Expand and simplify…
(a + 5)(a – 7) =
13. Pam sends Christmas cards to
her friends. Stamps cost 50 cents
for each. Cards cost $2.75 for
each. Pam spends a total of
$68.25. She writes this equation
0.50f + 2.75f = 68.25
How many friends has Pam got?
8. Two square fields are side by
side. They are the same length
but one is 3m wider. Together
they have an area of 860m2.
Calculate the value of a
14. Anne was told that one
factor of a2 + 48a – 100 is a – 2.
What is the other factor?
15. Simplify 2a + 4a =
3
5
a
16. Solve for both a and b…
a
9. Solve
a
3
a2 – 10a – 39 = 0
10. Expand and simplify…
(2a + 3)2 =
3a + 8b = 79
and
a=b+8
Yr 11 MCAT Algebra Practice 3 – based on NCEA externals 2008, 2009 and 2010
1. Jonathan found this equation…
4(a2)n x 3a4 = 12a16
What is the value of n?
2.
3.
= 4a2n x 3a4
= 12a2n + 4
so 2n + 4 = 16
2n = 12
n=6
Factorise a2 + 7a – 60
(a + 12)(a - 5)
a/
b)
c)
3
–4=5
a/
3
=9
a = 27
3a + 5 = 3 – 5a
3a + 5a = 3 - 5
8a = -2
c)
4(a + 3) = 11
a + 3 = 2.75
a = -0.75
4a – 7 = 8 + 2a
4a – 2a = 8 + 7
2a = 15
a = 7.5
What multiplies to – 8?
a = -1/4
1/
-3
a is ___
2 or ___
4. Solve this inequation…
5a – 8 > 12
5a > 20
a>4
5. Make r the subject of this
formula A = 4πr2
-1x8 1x-8
-2x4 2x-4
because a is positive we can eliminate…
therefore a = 7or2, b/c = -1or-2, 8or4
8. Two square fields are side by
side. They are the same length
but one is 3m wider. Together
they have an area of 860m2.
Calculate the value of a
(1 – 2a)(a + 3) = 0
4πr2 = A
r2 = A/4π
r = ± √(A/4π)
b)
5/
-2
a is ___
4 or ___
7. Find the whole numbers that
can replace a, b and c so that this
equation is true…
x2 + ax – 8 = (x + b)(x + c)
Solve these equations…
a)
6. Solve for a…
a) (4a – 5)(a + 2) = 0
a
11. if 8a9 = 2a4 what is n =?
4an
n=5
12. Expand and simplify…
(a + 5)(a – 7) = a2 - 7a + 5a - 35
= a2 – 2a – 35
13. Pam sends Christmas cards to
her friends. Stamps cost 50 cents
for each. Cards cost $2.75 for
each. Pam spends a total of
$68.25. She writes this equation
0.50f + 2.75f = 68.25
How many friends has Pam got?
3.25f = 68.25
f = 21
14. Anne was told that one
factor of a2 + 48a – 100 is a – 2.
What is the other factor?
what x – 2 is -100? 50
base x height
(a+a+3) x a
so the other factor is (a + 50)
(2a+3) x a
15. Simplify 2a + 4a = 10a + 12a
2a2+3a
15
15
=22a
3
5
2a2 + 3a = 860
15
a
a
3
2 + 3a – 860 = 0
2a
16. Solve for both a and b…
(2a + 43)(a - 20) = 0
20
a is-21.5
___ or ___
area =
area =
area =
area =
9. Solve
a2 – 10a – 39 = 0
(a + 3 )(a- 13)
10. Expand and simplify…
(2a + 3)2 = (2a+3)(2a+3) =4a2+12a+9
3a + 8b = 79
sub b + 8 in
and
3(b+8) + 8b = 79
3b + 24 + 8b = 79
11b = 55
a=b+8
b=5
a=5+8
a = 13