Formula sheet (10 Mathematics â€“ Standard)
Mensuration
circumference of a
circle C = 2Ï€ r area of a circle A = Ï€ rÂ²
area of a
parallelogram A = b h area of a trapezium A = Â½(a + b)h
area of a triangle A = Â½ b h volume of a prism V = A h
total surface area of a
cylinder S = 2Ï€ r h + 2Ï€ rÂ² volume of a cylinder V = Ï€ rÂ² h
Finance
simple interest ?? = ?????? compound interest ?? = ??(1 + ??)??
Trigonometry
trigonometric ratios ?????? ??= ????????????????
â„Ž??????????????????
?????? ??= ????????????????
â„Ž??????????????????
?????? ??= ????????????????
????????????????
Pythagorasâ€™ theorem ??2 + ??2 = ??2
Statistics
mean ?? = ?????? ???? ?????? ???????? ????????????
???????????? ???? ???????? ????????????
?? = âˆ‘????
??
median ï¿½??+1
2
ï¿½
??â„Ž
data value
Probability
probability of an event
occu
ing ??(??????????) =
???????????? ???? ???????????????????? ????????????????
?????????? ???????????? ???? ????????????????
probability of
independent events ??(?? ?????? ??) = ??(??) Ã— ??(??)
conditional probability ??(??|??) =
??(?? âˆ© ??)
??(??)
YEAR 10 STANDARD MATHEMATICS â€“ SA5 - EXAM â€“ TERM 4, XXXXXXXXXXPAGE 1
WORKING is to be completed on this paper. If you need extra room or to redo a question,
note this on this paper and attach the extra pages used. Be sure to label your work
clearly.
Question XXXXXXXXXXSF/UF â€“ 1Â½ marks)
Given the line whose equation is y = 3x + 5
(a) Write an equation for a line parallel to the given line
(b) Write an equation for a line perpendicular to the given line
(a) Solve the following simultaneous equations graphically XXXXXXXXXX?? âˆ’ ?? = 5
?? + 1.5?? = 9
(b) Check your solution alge
aically
Question XXXXXXXXXXSF/UF - 2Â½ marks)
YEAR 10 STANDARD MATHEMATICS â€“ SA5 - EXAM â€“ TERM 4, XXXXXXXXXXPAGE 2
Question 3 (SF/UF - 1 mark)
Graph the following inequality on the number line below
?? > 12
Question XXXXXXXXXXSF/UF â€“ 2 marks)
Solve the following inequality for x
(2??âˆ’3)
5
â‰¥ 2
YEAR 10 STANDARD MATHEMATICS â€“ SA5 - EXAM â€“ TERM 4, XXXXXXXXXXPAGE 3
Question XXXXXXXXXXSF/UF - 3Â½ - marks)
Leeâ€™s soccer team played 38 games this season. Their results are shown in the two-way table
elow.
a) Complete the table by determining the missing values
Win Draw Loss Total
Home 11 6 3
Away XXXXXXXXXX
Total 17 7
) Determine the probability that a randomly selected game was won.
c) Calculate the probability that a randomly selected game was won, given that it was at home.
YEAR 10 STANDARD MATHEMATICS â€“ SA5 - EXAM â€“ TERM 4, XXXXXXXXXXPAGE 4
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Question XXXXXXXXXXSF/PS 4 marks)
In a bag there are four balls: two green, one blue and one red. In a second bag, there are two
alls, one yellow and one green. One ball is chosen from each bag.
a) In the space below, complete a tree diagram to show all possible colour combinations
that may be selected. Ensure you list the sample space.
SAMPLE SPACE
) Determine the probability that two green balls are selected.
c) Calculate the probability of at least one of the balls selected being green.
YEAR 10 STANDARD MATHEMATICS â€“ SA5 - EXAM â€“ TERM 4, XXXXXXXXXXPAGE 5
Question 7 (SF/PS â€“ 4 marks)
The admission fee at a small fair is $1.50 for kids and $4.00 for adults. On a certain day,
2200 people enter the fair and $5050 is collected. How many children and how many adults
attended?
(Mathematically justify your solution by showing all working.)
a) Complete the following:
i) Let A = Number of Adults and K = _____________________________
ii) A + K = _______
) Write an equation for the total cost of Adult and Childrenâ€™s tickets in terms of A and K
__________________________________________________________________________
c) Use this information to mathematically determine the number of adults and children to visit the
fair. (Note: to get full marks youâ€™ll need to show a method other than guess and check)
YEAR 10 STANDARD MATHEMATICS â€“ SA5 - EXAM â€“ TERM 4, XXXXXXXXXXPAGE 6
Question 8 (CF/UF â€“ 2Â½ marks)
Solve the following equations simultaneously. (Be sure to Check your solution)
4?? + ?? = 8
?? = ?? âˆ’ 2
Solve the following equations using the elimination method. (Be sure to Check your solution)
2?? + ?? = 8
4?? âˆ’ 3?? = 6
Question XXXXXXXXXXCF/UF - 4 marks)
YEAR 10 STANDARD MATHEMATICS â€“ SA5 - EXAM â€“ TERM 4, XXXXXXXXXXPAGE 1
Question XXXXXXXXXXCU/PS - 5 marks)
Jason paints signs on buildings using the following letters:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
He can paint the letters which contain all straight edges quite easily but the letters which contain a curved edge
take longer
Straight letters Curved letters
A E F H I K L M N T V W X Y Z B C D G J O P Q R S U
It takes Jason 25 minutes to paint the word CHEMIST and 29minutes to paint the word BUTCHER.
Calculate how long would it take Jason to paint the word ACCOUNTANT.
END OF EXAM
YEAR 10 STANDARD MATHEMATICS â€“ SA5 - EXAM â€“ TERM 4, XXXXXXXXXXPAGE 2
SF CF CU
1 1.5
2 2.5
3 1
4 2
5 3.5
6 4
7 4
8 2.5
9 4
10 5
Total (% XXXXXXXXXX