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Hello, i hope you're all doing well, can you please answer these questions in the PDF. Thank you for all your help

Formula sheet (10 Mathematics – Standard) Mensuration circumference of a circle C = 2π r area of a circle A = π r² area of a parallelogram A = b h area of a trapezium A = ½(a + b)h area of a triangle A = ½ b h volume of a prism V = A h total surface area of a cylinder S = 2π r h + 2π r² volume of a cylinder V = π r² h Finance simple interest ?? = ?????? compound interest ?? = ??(1 + ??)?? Trigonometry trigonometric ratios ?????? ??= ???????????????? ℎ?????????????????? ?????? ??= ???????????????? ℎ?????????????????? ?????? ??= ???????????????? ???????????????? Pythagoras’ theorem ??2 + ??2 = ??2 Statistics mean ?? = ?????? ???? ?????? ???????? ???????????? ???????????? ???? ???????? ???????????? ?? = ∑???? ?? median �??+1 2 � ??ℎ data value Probability probability of an event occurring ??(??????????) = ???????????? ???? ???????????????????? ???????????????? ?????????? ???????????? ???? ???????????????? probability of independent events ??(?? ?????? ??) = ??(??) × ??(??) conditional probability ??(??|??) = ??(?? ∩ ??) ??(??) YEAR 10 STANDARD MATHEMATICS – SA5 - EXAM – TERM 4, 2023 - PAGE 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 1 (SF/UF – 1½ 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 2?? − ?? = 5 ?? + 1.5?? = 9 (b) Check your solution algebraically Question 2 (SF/UF - 2½ marks) YEAR 10 STANDARD MATHEMATICS – SA5 - EXAM – TERM 4, 2023 - PAGE 2 Question 3 (SF/UF - 1 mark) Graph the following inequality on the number line below ?? > 12 Question 4 (SF/UF – 2 marks) Solve the following inequality for x (2??−3) 5 ≥ 2 YEAR 10 STANDARD MATHEMATICS – SA5 - EXAM – TERM 4, 2023 - PAGE 3 Question 5 (SF/UF - 3½ - marks) Lee’s soccer team played 38 games this season. Their results are shown in the two-way table below. a) Complete the table by determining the missing values Win Draw Loss Total Home 11 6 3 Away 8 4 18 Total 17 7 b) 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 – SA5 - EXAM – TERM 4, 2023 - PAGE 4 _________ _________ _________ _________ _________ _________ _________ _________ Question 6 (SF/PS 4 marks) In a bag there are four balls: two green, one blue and one red. In a second bag, there are two balls, 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 b) 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 – SA5 - EXAM – TERM 4, 2023 - PAGE 5 Question 7 (SF/PS – 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 = _______ b) Write an equation for the total cost of Adult and Children’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 you’ll need to show a method other than guess and check) YEAR 10 STANDARD MATHEMATICS – SA5 - EXAM – TERM 4, 2023 - PAGE 6 Question 8 (CF/UF – 2½ marks) Solve the following equations simultaneously. (Be sure to Check your solution) 4?? + ?? = 8 ?? = ?? − 2 Solve the following equations using the elimination method. (Be sure to Check your solution) 2?? + ?? = 8 4?? − 3?? = 6 Question 9 (CF/UF - 4 marks) YEAR 10 STANDARD MATHEMATICS – SA5 - EXAM – TERM 4, 2023 - PAGE 1 Question 10 (CU/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 – SA5 - EXAM – TERM 4, 2023 - PAGE 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 (%) 18.5 6.5 5

Formula sheet (10 Mathematics – Standard) Mensuration circumference of a circle C = 2π r area of a circle A = π r² area of a parallelogram A = b h area of a trapezium A = ½(a + b)h area of a triangle A = ½ b h volume of a prism V = A h total surface area of a cylinder S = 2π r h + 2π r² volume of a cylinder V = π r² h Finance simple interest ?? = ?????? compound interest ?? = ??(1 + ??)?? Trigonometry trigonometric ratios ?????? ??= ???????????????? ℎ?????????????????? ?????? ??= ???????????????? ℎ?????????????????? ?????? ??= ???????????????? ???????????????? Pythagoras’ theorem ??2 + ??2 = ??2 Statistics mean ?? = ?????? ???? ?????? ???????? ???????????? ???????????? ???? ???????? ???????????? ?? = ∑???? ?? median �??+1 2 � ??ℎ data value Probability probability of an event occurring ??(??????????) = ???????????? ???? ???????????????????? ???????????????? ?????????? ???????????? ???? ???????????????? probability of independent events ??(?? ?????? ??) = ??(??) × ??(??) conditional probability ??(??|??) = ??(?? ∩ ??) ??(??) YEAR 10 STANDARD MATHEMATICS – SA5 - EXAM – TERM 4, 2023 - PAGE 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 1 (SF/UF – 1½ 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 2?? − ?? = 5 ?? + 1.5?? = 9 (b) Check your solution algebraically Question 2 (SF/UF - 2½ marks) YEAR 10 STANDARD MATHEMATICS – SA5 - EXAM – TERM 4, 2023 - PAGE 2 Question 3 (SF/UF - 1 mark) Graph the following inequality on the number line below ?? > 12 Question 4 (SF/UF – 2 marks) Solve the following inequality for x (2??−3) 5 ≥ 2 YEAR 10 STANDARD MATHEMATICS – SA5 - EXAM – TERM 4, 2023 - PAGE 3 Question 5 (SF/UF - 3½ - marks) Lee’s soccer team played 38 games this season. Their results are shown in the two-way table below. a) Complete the table by determining the missing values Win Draw Loss Total Home 11 6 3 Away 8 4 18 Total 17 7 b) 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 – SA5 - EXAM – TERM 4, 2023 - PAGE 4 _________ _________ _________ _________ _________ _________ _________ _________ Question 6 (SF/PS 4 marks) In a bag there are four balls: two green, one blue and one red. In a second bag, there are two balls, 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 b) 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 – SA5 - EXAM – TERM 4, 2023 - PAGE 5 Question 7 (SF/PS – 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 = _______ b) Write an equation for the total cost of Adult and Children’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 you’ll need to show a method other than guess and check) YEAR 10 STANDARD MATHEMATICS – SA5 - EXAM – TERM 4, 2023 - PAGE 6 Question 8 (CF/UF – 2½ marks) Solve the following equations simultaneously. (Be sure to Check your solution) 4?? + ?? = 8 ?? = ?? − 2 Solve the following equations using the elimination method. (Be sure to Check your solution) 2?? + ?? = 8 4?? − 3?? = 6 Question 9 (CF/UF - 4 marks) YEAR 10 STANDARD MATHEMATICS – SA5 - EXAM – TERM 4, 2023 - PAGE 1 Question 10 (CU/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 – SA5 - EXAM – TERM 4, 2023 - PAGE 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 (%) 18.5 6.5 5

Answered 1 days AfterNov 13, 2023

Ans 1 a) Equation for a line parallel to the given line is y = 3x – 5 since parallel li

Ans 1 b) Equation for a line perpendicular to the given line y = -1/3x + 5 since perpendicular lines have reciprocal value of slope with opposite sign

Ans 2 a) By solving simultaneous equations graphically we get, x = 4 and y = 3

Ans 2 b) On solving algebraically we get,

2? − ? = 5 ---[1]

Or x = 5 + y/2

? + 1.5? = 9 --- [2]

On solving value of x in equation 2 we get,

Y = 3

And x = 4

Values are same as above.

Ans 3. Graph for inequality x > 12 on the number line below

-15 -12 -9 -6 -3 0 3 6 9 12 15

Ans 4. Solving the following inequality for (2?−3)/5 ≥ 2

We get,

(2?−3)/5 ≥ 2

2x-3 ≥ 2 * 5

2x-3 ≥ 10

2x-3 + 3 ≥ 10 + 3

2x ≥ 13 We get the answer x ≥ 13/2

Ans 5. A) Missing values:

win

draw

loss

total

Home

11

6

3

20

Away

6

8

4

18

total

17

14

7

38

Ans 5. B) Probability that a randomly selected game was won is...

SOLUTION.PDF## Answer To This Question Is Available To Download

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