Download Year 9 Term One 2016 – Practice

Year 9 Term One 2016 – Practice - No calculator
Algebra
1. Count the number of dots in each diagram and write this as a number sequence.
Number sequence: ____________________________________________
Describe in words how this sequence was created.
___________________________________________________________________
Work out the next 5 numbers for this sequence.
_____________________________________________________________________
2. Use the rule in the box to work out the ‘output numbers’ to create part of a number
sequence.
Input
numbers
1
2
3
4
Rule
Output numbers
Multiply
the input
number by
3, then
stubtract 1
1 ×3−2 =1
3. C.D.’s can be purchased by mail order. The cost of a purchase is given by the rule:
‘ $ 6.00 for each C.D. plus $3.00 postage’
What would it cost to buy 2 CD’s by mail order? ___________________
What would it cost to buy 10 CD’s by mail order? __________________
Sam spent $33.00 on mail order CD’s. How many CD’s did he buy?
____________________________________________________________________
4. Write an equivalent algebraic expression for each of these.
a) A number with 2 added to it.
b) The sum of 𝑥 and 𝑦.
______________
______________
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c) Three less than 𝑡.
______________
5. The value of 𝑥 is 4. Calculate each of these expressions.
a) 𝑥 + 2 = _______
b) 8𝑥 = _______
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c) 𝑥 = __________
6. Work out what number would go where the letter is in each equation. That is, solve each
equation.
𝑎)
19 + 𝑥 = 26
𝑏)
12 − 𝑦 = 3
𝑐)
𝑑)
9 × 𝑝 = 54
24 ÷ 𝑑 = 8
𝑥 = __________________
𝑦 = __________________
𝑝 = __________________
𝑑 = __________________
7.
A number sequence was made up using the rule ‘ 3 times the term number, plus 5’, as shown
in the table below.
Use this rule to find the Number Sequence in the table. SHOW YOUR WORKING.
Term Number
1st
2nd
3rd
20th
100th
Working
3×1+5= 8
Number Sequence
8
8. 𝑃 = 3, 𝑞 = 5 𝑎𝑛𝑑 𝑟 = 2. Work out the following expressions.
a) 6𝑝 = ______________
c) 4𝑝𝑞𝑟 = ___________
b) 𝑞 + 2𝑟 = ________________
d) 8𝑝 + 4𝑞 − 𝑟 = ___________________
9. Circle the “like” terms from each group:
a) {3𝑝, 3𝑞, 9𝑝}
b) {𝑎𝑏, 4𝑎𝑏, 4𝑎}
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10. Work out what number would go where the letter is in each question. That is, solve each
equation. That is, solve each equation.
𝑎)
6𝑥 = 42
𝑏)
9𝑦 = 72
𝑐)
4𝑝 + 3 = 15
𝑑)
𝑥 = __________________
𝑦 = __________________
𝑝 = __________________
8𝑑 − 2 = 54
𝑑 = __________________
11. Mr and Mrs Smith each have a car. Mr Smith’s car has needed five tyres and four
batteries since new. Mrs Smith’s car has needed six tyres and two batteries. Use t to stand
for a tyre, and b to stand for a battery. Write down an expression, and then simplify it, to
show how to get the tyres and batteries the Smiths have needed altogether. [ 2 marks ]
_____________________________________________________________________
_____________________________________________________________________
12. The general term for a number sequence is given by the rule:
General Term = 𝟐𝒏 + 𝟑
Use this rule to find the first five numbers of this number sequence.
Sequence
order (𝑛)
Number
sequence
1st
2nd
3rd
13. This table shows the start of a number sequence.
Sequence
order
1st
2nd
3rd
Number
sequence
3
7
11
4th
5th
4th
5th
15
19
Find a rule for the general term in this sequence.
____________________________________________________________________
What is the 100𝑡ℎ number in this sequence? ________________________________
14. Simplify:
𝑎) 12𝑥 + 3 − 2𝑥 − 1
𝑏) 3𝑥 + 8𝑦 − 4𝑥 + 7𝑦 − 4
c) 5ab  8ab  ab
𝑑) 3𝑓 + 11𝑔 + 6𝑓 − 4𝑔
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15. A plumber charges a $30 call out fee and then $50 per hour for any work completed. He
uses the formula 𝐶 = 30 + 50𝑡 to calculate how much to charge for a job.
a) What does 𝑡 represent in this formula?
b). Calculate 𝐶 when 𝑡 = 2.
c) Explain in words what you have worked out in part b).
16. A firm of joiners makes doors. Each door needs four hinges. One rule the firm uses is :
𝑦
Number of doors =
4
a) What does 𝑦 represent in this expression?
b) How many doors can be made if they have 28 hinges?
c) Explain whether the rule gives a sensible answer when 𝑦 = 27 .
[2]
___________________________________________________________________________
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