Extended Questions (DP IB Maths: AI SL)

Topic Questions

3 hours12 questions

2 marks

The number of seats a row has at a comedy festival follows a regular pattern where the first row has $u_{1}$ seats and the number of seats in each successive row increases by $d$ seats. In the fourth row there are $25$ seats and in the sixteenth row there are $49$ seats.

Write down an equation, in terms of $u_{1}$ and $d$ , for the number of seats

(i)

in the fourth row

(ii)

in the sixteenth row.

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2 marks

Find the value of $u_{1}$ and the value of $d$ .

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3 marks

The festival has 18 rows of seats in total.

Calculate the total number of seats.

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8 marks

The price for a seat in the first row is $$ 22$ and the price decreases by $5 %$ each successive row.

(i)

Find the row in which the price of a seat first falls below

$ 10

(ii)

Find the total revenue the comedy festival generates if

22

tickets are sold for every row. Give your answer rounded to the nearest dollar.

How did you do?

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Body fat percentage $(x)$	$22.0$	$14.2$	$15.5$	$12.6$	$29.8$	$10.1$
Resting heart rate $(y)$	$65$	$59$	$54$	$68$	$74$	$51$

Number of baskets	$0$	$1$	$2$	$3$	$4$	$5$	$6$
Frequency	$41$	$17$	$34$	$31$	$10$	$15$	$2$

Mouse mass, $x (g)$	19.9	18.3	21.1	19.8	17.5	16.3
Time, $y (seconds)$	18.0	17.7	20.9	18.6	15.0	14.2

	Creativity	Activity	Service	Total
Arts	19	15	7	41
Humanities	9	22	11	42
Sciences	16	8	15	39
Total	44	45	33	122