Algebra (Linear and Quadratic) Revision



Algebra (Linear and Quadratic) Revision

1. Simplify the following expressions.

a) [pic] b) [pic]

c) [pic] d) [pic]

e) [pic] f) [pic]

g) [pic] h) [pic]

i) [pic] j) [pic]

k) [pic] l) [pic]

m) [pic] n) [pic]

o) [pic] p) [pic]

2. Evaluate the following by using substitution.

a) 2pq if p = 4 and q = -3

b) 3k(2k + 1) if k = -4

c) [pic]

3. Expand and then simplify if possible.

a) [pic] b) [pic]

c) [pic] d) [pic]

e) [pic] f) [pic]

g) [pic] h) [pic]

4. Factorise the following expression

a) [pic] b) [pic]

c) [pic] d) [pic]

e) [pic] f) [pic]

g) [pic] h) [pic]

i) [pic] j) [pic]

j) [pic]

5. Solve the following linear equations

a) [pic] b) [pic]

c) [pic] d) [pic]

e) [pic] f) [pic]

g) [pic] h) [pic]

6. Solve the following quadratic equations

a) [pic] b) [pic]

c) [pic] d) [pic]

e) [pic] f) [pic]

g) [pic] h) [pic]

7a) Make y the subject of [pic]

b) Make x the subject of [pic]

c) Make r the subject of [pic]

8. A printer, quoting to offset print a single sided leaflet for a local sports club, charges $250 for the paper and an hourly rate of $42.

a) If h equals the number of hours of labour required to print the leaflets, complete the equation:

Cost of leaflets = …………. h + …………..

b) The sports club has only $1300 budgeted for the printing job. How many hours of labour will this amount afford?

c) The club expects to get 10000 leaflets printed. What is the cost of a single leaflet if the club spends all of its proposed budget?

9. Three children in a family are related as follows:

Ben is three years older than Carol

Abe is half Carol’s age

The sum of all their ages is 33

a) If Carol’s age is represented by the letter c, then write an expression for the sum of the three children’s ages in terms of Carol.

b) Calculate the age of each of the children by solving the last expression you have written.

10. A piece of wire is attached and hung between two

poles. A ball is threaded onto the wire and released

from point A and travels through to the other side.

The height (metres) the ball is above the ground at any

time (t seconds) is given by the formula [pic]

a) How high is the ball above the ground when it is first released from the point labeled A?

b) To find out at what time the ball touches the ground set h = 0 and solve the quadratic equation.

c) After how many seconds from the start is the ball again at its highest point above the ground?

d) At what times is the ball exactly 1 metre above the ground?

11. A rectangular extension is to be built onto an existing house. The length of the extension is to be 3 metres more than the width, which is x metres.

a) Give an expression for the area of the proposed extension.

b) If it is known that the area of the proposed extension is 10 m2 calculate the value of x.

c) It is estimated that the cost of building is $1250 per metre squared. What is the cost of the proposed extension.

12. The table below gives the length of a spring when different weights are attached from it.

|Weight (kg) |Spring length (cm) |

|1 |13 |

|2 |16 |

|3 |19 |

|4 |22 |

|5 |25 |

a) Is this sequence of spring lengths a linear or quadratic relationship? Explain.

b) Find the rule that relates the spring length (L) to the weight attached to it (W).

c) How long is the spring with no weight attached?

d) How long would the spring be if a 12 kg was attached to it?

e) How heavy would the attached weight be if the length of the spring was 64 cm?

13. Study the three stacks of blocks drawn below

a) Complete the table below for the stack number and the number of blocks in the stack.

|Stack Number (N) |Number of blocks (B) |

|1 |2 |

|2 |5 |

|3 | |

|4 | |

|5 | |

b) Is the sequence of bricks a linear or quadratic relationship? Explain.

c) Find the rule that relates the stack number (N) to the number of bricks in the stack (B)

d) How many blocks would stack number 25 have?

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