Yr 11 MCAT Algebra Practice 6
(all previous year’s NCEA questions) 8. Solve the equation to
find the values of a…
5. Solve the following…
a2 + 8a – 9 = 0
0 or ___
-4
a) 3a(a + 4) = 0 a is ___
1. Factorise completely…
a) a2 – 7a + 6 = ( a - 1 )( a - 6)
b)
2
2a2 – 4a – 16 = 2(a – 2a - 8 )
c)
c2
– 5c - 24
b) (2a – 1)(a + 3) = 0 a is
= 2( a - 4 )(a + 2 )
c) 6a – 2 = 2a + 9
= ( c - 8 )( c + 3 )
6a – 2a = 9 + 2
2. Josh estimates the area of a
circle by using the formula
A = 3(5)2 = 3(25) = 75
3. Simplify Fully…
b)
_ + 5a
_ = 8a
a + a = 3a
15
15 15
5 3
4. Make b the subject of this
formula…
P = 2b + 2h
2b + 2h = P
2b = P – 2h
b = (P – 2h)
2
4a = 11
a = 11/4
cd’s as Mary. Together they have 97
cd’s. What is the least number of cd’s
Peter has. Write equations and solve,
showing working…
What is the area if r = 5cm?
3a2 – 15ab = 3a(a – 5b) = a – 5b
3a(2a)
2a
6a2
-3
or ___
6. Peter has more than twice as many
A = 3r2
a)
1/
2
___
.
( a - 9 )( a + 1 ) = 0
9 or ___
-1
a is ___
9. Simultaneously Solve to
find values of p and m…
12p + 4m = 159.2
2p + 4m = 39.70 minus these
- _____________
_____________
3p + m == 119.5
39.80 x by four
10p
p = 11.95 sub back in
2(19.5) + 4m = 39.70
4m = 15.80
m = 3.95
P ≥ 2M and M = 97 – P
10. Expand and simplify…
substitute 97 - P for M
P ≥ 2(97 – P)
a) 5(a+1) + 2(a-3) =
5a +5 +2a -6 =7a-6
P ≥ 194 – 2P P ≥ 64 2/3
=
2P + P ≥ 194
Peter would have b) (3a-1)(2a+5)
2
6a +15a-2a-5 =6a2 +13a-5
3P ≥ 194
at least 65 cd’s
c) (a – 2)2 = (a – 2)(a – 2)
7. Simplify Fully…
=a2 -4a +4
a) 3a4 x 2a3 = 6 a7
b) (2a2)3 = 8a6
c)
d)
11. James is 5 years old, Emma
is 4 years older.
a2 + 5a + 6 = (a + 3 )(a + 2 ) = a + 2 How many years will it be from
now unit James and Emma’s ages
a+3
a+3
multiply to 725? Show equations
and working. simultaneous eqn’s
9a5 = 3a
E = J + 4 E x J = 725
4
12a3
sub J + 4 for E (J+4) x J = 725
e) 4(a2)n x 3a4 = 12a16
what is the value of n? n = 6
J2 + 4J = 725
+ 4J – 725 = 0
(J-25 )(J+29) = 0
can’t be -ve J is ___
-29 or ___
25
J2
Yr 11 MCAT Algebra Practice 6
1. Factorise completely…
a) a2 – 7a + 6
b)
2a2 – 4a – 16
c)
c2 – 5c - 24
2. Josh estimates the area of a
circle by using the formula
A = 3r2
What is the area if r = 5cm?
(all previous year’s NCEA questions) 8. Solve the equation to
find the values of a…
5. Solve the following…
a2 + 8a – 9 = 0
a) 3a(a + 4) = 0
b) (2a – 1)(a + 3) = 0
c) 6a – 2 = 2a + 9
6. Peter has twice as many cd’s as Mary.
Together they have 97 cd’s. What is the
least number of cd’s Peter has. Write
equations and solve, showing working…
b)
3a2 – 15ab =
6a2
a + a =
5 3
4. Make b the subject of this
formula…
P = 2b + 2h
2p + 4m = 39.70
3p + m = 39.80
10. Expand and simplify…
a) 5(a+1) + 2(a-3) =
3. Simplify Fully…
a)
9. Simultaneously Solve to
find values of p and m…
b) (3a-1)(2a+5) =
7. Simplify Fully…
a) 3a4 x 2a3 =
b) (2a2)3 =
c)
a2
+ 5a + 6 =
a+3
d)
9a5 =
12a3
e) 4(a2)n x 3a4 = 12a16
what is the value of n?
c) (a – 2)2 =
11. James is 5 years old, Emma
is 4 years older.
How many years will it be from
now unit James and Emma’s ages
multiply to 725? Show equations
and working.