Year 8 Linear Equations test - St Leonard's College

[Pages:3]Year 8 Linear Equations test

Name:

Total: Skills /27 Apps /12 Comm /3 = / 42

45 minutes, no calculator

Communication Marks /3: using inverse operations, setting out underneath, showing units where

appropriate

Section A: SKILLS (27 marks)

_

1. Solve the following equations. .

(a) k 15 23

4 y 32

(b)

(c)

f 3

7

(d) x 10 4

(e) 4g 10

(f)

m 15

3

2. For each question, state whether the solution (bold and in brackets) is TRUE or FALSE.

[ 1 + 1 + 1 + 1 + 1 + 1 = 6 marks ]

(a) ?16 = 12 + 2a (a = ?2)

(b) 4(x + 2) ? 3x = 13

(x = 5)

TRUE/FALSE

TRUE/FALSE

[ 2 marks]

3. A certain number x is multiplied by 6 and the result is subtracted from 3. This answer is then multiplied by 2 to give a final answer of 18. Which of the following equations represents this situation? Circle ONE of them.

(a) 2(6x ? 3 ) = 18 (b) 3 ? 6x 2 = 18 (c) 2(3 ? 6x) = 18 (d) 6(3 ? 2x) = 18 (e) 18 = 12x ? 6

4. Fill in the box in the following equations so that the solution is correct.

[1 marks ]

(a)

+ x = 17

x = 11

(b) 2x +

= 18

(c)

2x = 4 x =2

3x +

= 7 3x = - 3

x = -1

[ 1 + 1 + 1 = 3 marks ]

5. Each of the following equations have been solved INCORRECTLY. There is one error in the calculations for each question which caused the final solution to be incorrect. Read through the solutions and explain, in each case, what error was made in the working out. You DO NOT need to solve the equation.

(a) Step i) 4 x + 2 = -20 ( 4 )

Step ii) x + 2 = -5 (? 2 )

Step iii)

x = -7

(b) Step i) 4(x + 1) ? 6 x ? 7= 12 (expand)

Step ii) 4x + 4 ? 6 x ? 7 = 12 (simplify)

Step iii)

2 x - 3 = 12 (+ 3 )

Step iv)

2 x = 15 ( 2 )

Step v)

x = 7.5

6. Solve the following equations. For full marks, you must show all inverse operations steps.

(a) 4w + 7 = 39

(b) x 1 7 8

[1 + 1 = 2 marks ]

(c) 5 x + 2 = 3x + 16

(d) 6 p 10 4 7

(e) ?2(m ? 3) + 4m = 12

[2 + 2 + 3 + 3 + 3 = 13 marks ]

Section B: APPLICATIONS (12 marks)

NOTE:

For this section you must write an equation first. One mark will be given for the equation and one for the final answer.

1. If 13 is subtracted from a certain number x, the result is 27. 2. Amy bought a fast growing plant from a nursery. After 2

Find the number.

weeks it was 17 centimetres tall, which was triple its

original height less 1 centimetre. How tall was the plant

when Amy bought it?

[ 2 marks ]

[ 2 marks ]

3.

x

x + 6

4. Hamish, Magnus and Tanner have 51 basketball cards in total. Hamish has twice as many cards as Magnus. Tanner has 7 more cards than Magnus. How many cards does Magnus have?

The perimeter of the rectangle above is 84cm. Calculate the

value of x.

[ 2 marks ]

[ 2 marks ]

5. A plumber makes the following charges:

$45 to arrive at your door (call out fee)

$30 per hour

If the total cost of the work was $345, how many hours of

work did the plumber do?

6. Consecutive numbers are numbers that are in order with a difference of one. (For example 12, 13, 14 or 5, 6, 7).

A certain number x is the first of 3 consecutive numbers. The sum of these 3 numbers is 54. Find the number x.

[ 2 marks ]

[ 2 marks ]

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