VCE General Maths (Further) Unit 1

Linear Algebra

2015 Test

Name: _______________________________

Total: / 60 marks ( %)

Conditions: 45 min, Casio Classpad and up to 2 double sided, handwritten, Summary Sheets permitted.

Multiple Choice Section ( 5x 2 marks = 10 marks)

1. The solution to the simultaneous equations below is:

A. (3 ,−2 )B. (−2 , 3 )C. (1 ,1 )D. (4 ,2 )E. (1 , 2 )

2. The solution to 3 ( x−5 )=12is:

A.173

B. 6 C. 8 D. 9 E. 10

3. When solving 2 x5

−4=10 the first step could be:

A. Multiply both sides by 2.B. Divide both sides by 5.C. Subtract 4 from both sides.D. Add 4 to both sides.E. Add 10 to both sides.

4.

A. 2 B. 3 C. 5 D. 6 E. 7

4

2 x+1The area of this rectangle is 28 cm2. The value of x is therefore:

5. If, M=4ab (h+3)then the value of M when: a=3 , b=5 and h=−8, is:

A. 42 B. 660 C. -75 D. 300 E. -300

Short Answer Section. Show ALL working.

1. Solve the following linear equations

a. 3 x−9=12 b. 4 (3 x−2 )=28

c.2 a5

+1=7 d.4 w−3

3=9

e. 4 f −5=2 f −1 f. 9−3 a=12

(6 ×2=12 marks )

2. a. Write an equation for the perimeter, P, of the shape shown and simplify the equation where possible.

b. Given that the perimeter of the object is 52m, find the value of x.

2 x4

x

4

8

3 x

(2+2=4marks )3. Tickets to a movie cost $15 for adults and $9 for children.

a. Write an equation for the total cost, C, of x adults and y children.

b. How much money was paid altogether for 44 adults and 62 children?

c. On another night a total of $633 was paid. If there were 17 children that night, how many adults attended?

(1+2+2=5marks )

4. A number is doubled and then 5 is subtracted giving a result of 27.a. Write an equation using n to represent the number.

b. Solve the equation to find the number, n.

(1+2=3 marks ¿

5. Use an appropriate method (elimination or substitution) to solve the following pairs of simultaneous equations. Show ALL Working.

a. 3 x+2 y=13y=2 x−4

b. 3 x+2 y=3x−2 y=9

c. 3 x−5 y=94 x−3 y=1

d. y=1−x3 x−4 y=−18

(3+3+4+3=13 marks )

6. A farmer bought 2 pigs and 5 sheep for $200 and 3 pigs and 4 sheep for $230.

a. Using the letter p for the cost of one pig and s for the cost of one sheep, write two equations from the information above.

b. Using an appropriate method, (elimination or substitution), solve the two simultaneous equations and hence state the cost of one pig and one sheep.

(2+4=6 marks )

7. The sum of two numbers is 93 and their difference is 13. a. Write two equations, using x and y to represent the two numbers.

b. Solve the simultaneous equations to find the two numbers.

(2+3=5marks)

8. Use your Classpad to answer the following. No working is required for this question.

a. Solve 3 x2

=4 x−13 +2 b. Solve the simultaneous equations

x+ y=1 and 5 x−3 y=17

(1+1=2 marks)