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Linear Algebra Revision Sheet #2
Linear equations
Name: ___________________________
Section A Multiple Choice
1
The solution to the equation
is:
A
B
C
D
E
2
2x
 3  1
5
5
If a number is multiplied by 5 and then
divided by 6, the result is 7. The
equivalent mathematical statement is:

7
A 5x =
6
B 5x = 42
6x 
C
= 7
5
5x
D
=7
6
5x 
E
= 7
6
6
If twice a number subtracted from 6
gives 10, then the number is:
A 10
B 6
C 2
D 2
E 3
7
The perimeter of a regular hexagon is
15 cm more than the perimeter of a
square with the same side length. The
length of the side of the hexagon is:
A 7.5 cm
B 3.75 cm
C 2.5 cm
D 4 cm
E 15 cm
2
2
3
3
none of these.
2x
 6 the following
3
operations should be performed to both
sides:
A Add 10, multiply by 3 and divide
by 2.
B Subtract 10, multiply by 3 and
divide by 2.
C Subtract 10, divide by 3 and divide
by 2.
D Subtract 10, divide by 3 and
multiply by 2.
E Add 10, multiply by 3 and divide
by 2.
To solve 10 
3
Which of the following is the same as
3(2x  1) = 4x + 5?
A 2x = 8
B 6x = 4x + 5
C 6x  4x = 5
D 6x = 5x + 3
E 6x = 4x + 3
4
Which of the following satisfies the
1  3x x
  2?
equation
4
5

A
4
B 2
C 2
D 3
E none of these.
Maths Quest 11 Standard General Mathematics
8
2R  5
is transposed to make R
6
the subject, then:
6P  5
A R=
2
B R = 3P  5
5
C R = 3P 
2
5
D R = 6P 
2
E R = 2(6P  5)
If P =
Page 1 of 7
9
If x = 3, then the value of y in the
relation 2x  3y = 6 is:
A 1
B 2
C 3
D 4
E 4
10
The general form of the gradientintercept equation is y = mx + c. If
y = 4, x = 3 and c = 2, then m is equal
to:
A 2
B 2
C 3
D 3
E 4
11
The sum of solutions to the
simultaneous equations y  x = 12 and
2y + x = 6 is:
A 0
B 12
C 6
D 36
E 6
12
Three bottles of Coke and three
ice-creams cost $10.50, while 1 bottle
of Coke and 4 ice-creams cost $8. Find
the cost of a bottle of coke and an
ice-cream.
A Coke $2, ice-cream $1
B Coke $1, ice-cream $2
C Coke $1.50, ice-cream $2
D Coke $2, ice-cream $1.50
E Coke $2.50, ice-cream $1
Maths Quest 11 Standard General Mathematics
Page 2 of 7
Linear equations Test B
Name: ___________________________
Section B Short/Extended answer
1
Solve for x:
7(5  3x) = 28
3
2
Solve for x:

x 1 3  2x
1


2
3
3
3
3
Reena is buying tulip bulbs. Red tulip bulbs
cost $5 each while a yellow tulip bulb costs $4.
If 36 bulbs cost Reena $164, how many of each
type did she buy?
3
Maths Quest 11 Standard General Mathematics
Page 3 of 7
4
The formula for the conversion of temperature
from Celsius (°C) to Fahrenheit (°F) is given by
9
the formula F = C + 32. When C = 25 °C,
5
find the value of F.
2
5
Peter is 4 years older than Diane. In 6 years
time, Peter will be 3 times as old as Diane was
2 years ago. Find their present ages.
3
6
Transpose v = u + at to make a the subject and
hence find a when v = 30, u = 10 and t = 4.
4
7
Simon has invested $2000 at 4% simple
interest, credited to his account at the end of
each financial year. Write the difference
equation to represent this situation.
2
Maths Quest 11 Standard General Mathematics
Page 4 of 7
8
The cost of 2 hamburgers and a bottle of Coke
is $7.50. The difference between 3 hamburgers
and 2 bottles of Coke is $6. Find the cost of a
hamburger and a bottle of Coke.
3
9
Solve the pair of simultaneous equations:
2x  3y = 5 and
3x + y = 2
2
Maths Quest 11 Standard General Mathematics
Page 5 of 7
10

9
1
Sketch the graphs of y + x = 2 and y =
x+1
2
and hence state the coordinates of the point of
intersection.
Maths Quest 11 Standard General Mathematics
4
Page 6 of 7
11
1Tom and his girlfriend Sarita wish to rent a car
0for a long weekend. The cost, C, of renting a
Nissan Pulsar from company A is given by
C  20  0.08n and from company B,
C  30  0.06n where n is the number of
kilometres travelled.
6
(a) Which company, A or B, does line (1)
represent?
(b) What could the numbers 20 and 30
represent?
(c) What does the point of intersection of lines
(1) and (2) represent?
(d) Find the coordinates of the point of
intersection.
(e) If Sarita decides to travel along the Hume
Highway for about 400 km each way, from
which company, A or B, should they rent
to pay less?
Maths Quest 11 Standard General Mathematics
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