Free IB DP Practice Questions | RevisionPrep

1FoundationSAQ-SDefinition and general term of arithmetic sequencess5 marksPaper 1~8 min

A company is designing a rectangular solar panel. The lengths of the sides of the panel, in metres, form an arithmetic sequence with first term

u_1 = 2\,\text{m}

and fourth term

u_4 = 8\,\text{m}

.

(a)

Find the common difference of the arithmetic sequence. [2 marks]

(b)

Find the area of the solar panel. [1 mark]

(c)

A second rectangular panel has the same perimeter as the first panel but has side lengths that are equal. Determine whether the second panel has a greater area than the first panel, justifying your answer. [2 marks]

Solutions

2FoundationSAQ-SDefinition and general term of arithmetic sequencess5 marksPaper 1~8 min

A gardener is building a tiered flower bed. The heights of the tiers, measured in centimetres, form an arithmetic sequence. The first tier has height

30\,\text{cm}

and the fifth tier has height

54\,\text{cm}

.

(a)

Find the common difference of the sequence. [2 marks]

(b)

Find the height of the third tier. [2 marks]

(c)

The gardener has enough soil to build tiers up to a total combined height of

500\,\text{cm}

. Determine whether the gardener can complete a

9

-tier flower bed. [1 mark]

Solutions

3FoundationSAQ-SDefinition and general term of arithmetic sequencess8 marksPaper 1~12 min

The first term of an arithmetic sequence is

18

and the common difference is

-4

.

(a)

Calculate the sum of the first

10

terms. [2 marks]

(b)

Determine the value of

n

for which the

n

th term equals

-50

. [2 marks]

(c)

Find the least value of

n

for which the sum of the first

n

terms is negative. [4 marks]

Solutions

4FoundationSAQ-SDefinition and general term of arithmetic sequencess5 marksPaper 1~8 min

A water tank contains

1200

litres of water. Due to a leak, the volume of water decreases by a constant amount each day. After

8

days, the tank contains

760

litres.

(a)

State what feature of an arithmetic sequence models the daily water loss. [1 mark]

(b)

Calculate the amount of water, in litres, that leaks from the tank each day. [2 marks]

(c)

Determine the day on which the tank will first contain less than

100

litres of water. [2 marks]

Solutions

5FoundationSAQ-SDefinition and general term of arithmetic sequencess7 marksPaper 1~11 min

A cinema has

18

seats in the first row. Each subsequent row has

3

more seats than the row in front. The number of seats in row

n

is

s_n

.

(a)

State the value of

s_1

and the common difference

d

. [1 mark]

(b)

Calculate the number of seats in the

12

th row. [2 marks]

(c)

The last row has

72

seats. Find the total number of rows in the cinema. [2 marks]

(d)

Hence find the total number of seats in the cinema. [2 marks]

Solutions

6FoundationSAQ-SSum of an arithmetic sequences8 marksPaper 1~12 min

A construction company is building a staircase. The first step requires

20

bricks. Each subsequent step requires

4

more bricks than the previous step.

(a)

Find the number of bricks required to build the

12

th step. [2 marks]

(b)

Find the total number of bricks required to build the first

12

steps. [3 marks]

(c)

The company has a total of

750

bricks available. Determine the maximum number of complete steps that can be built, justifying your answer. [3 marks]

Solutions

7FoundationSAQ-SSum of an arithmetic sequences8 marksPaper 1~12 min

A student is training for a race. On the first day she runs

2\,\text{km}

. Each subsequent day she increases her distance by

0.5\,\text{km}

compared to the previous day.

(a)

Find the distance she runs on day

10

. [2 marks]

(b)

Find the total distance she runs over the first

14

days. [2 marks]

(c)

Find the minimum number of days of training required for her total distance to exceed

100\,\text{km}

. [4 marks]

Solutions

8FoundationSAQ-SSum of an arithmetic sequences7 marksPaper 1~11 min

A small business sells handmade candles. In the first week, they sell

20

candles. Each week, sales increase by a constant number of candles. After

12

weeks, a total of

504

candles have been sold.

(a)

State the formula for the sum of the first

n

terms of an arithmetic sequence. [1 mark]

(b)

Find the weekly increase in sales. [3 marks]

(c)

The business aims to sell at least

1000

candles in a single week. Determine the minimum number of weeks required to reach this target. [3 marks]

Solutions

9FoundationSAQ-SDefinition and general term of arithmetic sequencess7 marksPaper 1~11 min

A water tank contains

120

litres of water at the start of day 1. Each day, exactly

7

litres of water are removed from the tank for irrigation. The volume of water in the tank at the end of day

n

is denoted

u_n

litres.

(a)

Write down an expression for

u_n

in terms of

n

. [2 marks]

(b)

Calculate the volume of water remaining in the tank at the end of day

15

. [2 marks]

(c)

Determine the maximum number of complete days for which the tank can supply water before it is empty. [3 marks]

Solutions

10FoundationSAQ-SDefinition and general term of arithmetic sequencess9 marksPaper 1~14 min

A movie theatre has

18

seats in the first row. Each subsequent row has

3

more seats than the previous row. The number of seats per row forms an arithmetic sequence.

(a)

State the first term,

u_1

, and the common difference,

d

, of this arithmetic sequence. [1 mark]

(b)

Find the number of seats in the

15

th row. [2 marks]

(c)

The last row has

72

seats. The theatre has

n

rows in total. Show that

n = 19

. [2 marks]

(d)

A second theatre has the same number of rows. Its first row has

24

seats and its last row has

96

seats, with seats increasing by a constant amount per row. Determine which theatre has more total seats, and by how many. [4 marks]

Solutions

11FoundationSAQ-SSum of an arithmetic sequences7 marksPaper 1~11 min

Tara is training for a charity run. She runs

3\,\text{km}

on the first day and increases the distance she runs each day by a constant amount

d

. She runs a total of

60\,\text{km}

over the first

8

days.

(a)

Find the common difference

d

. [3 marks]

(b)

Find the distance Tara runs on day

8

. [1 mark]

(c)

Tara claims she can maintain this training plan for

20

days. Determine the total distance she would run over

20

days and comment on whether this claim is realistic. [3 marks]

Solutions

12FoundationSAQ-SSum of an arithmetic sequences8 marksPaper 1~12 min

A construction company is building a staircase. The first step requires

120

bricks. Each subsequent step requires

8

fewer bricks than the previous step.

(a)

State the value of the common difference,

d

, for the arithmetic sequence representing the number of bricks per step. [1 mark]

(b)

The staircase has

12

steps. Find the total number of bricks required to build all

12

steps. [3 marks]

(c)

The company has a total of

1200

bricks available. Determine the maximum number of complete steps that can be built. [4 marks]

Solutions

13FoundationSAQ-SDefinition and general term of arithmetic sequencess5 marksPaper 1~8 min

A car rental company charges a fixed fee of USD 50 for the first day. For each additional day, the charge increases by USD 15. The total charge for

n

days is

c_n

dollars.

(a)

Write down the values of

c_1

and the common difference

d

of the arithmetic sequence

c_1, c_2, c_3, \ldots

[1 mark]

(b)

Calculate the charge for a 7-day rental. [2 marks]

(c)

A customer has a budget of exactly USD 200. Determine the maximum number of complete days the car can be rented, and find the unused budget remaining. [2 marks]

Solutions

14FoundationSAQ-SDefinition and general term of arithmetic sequencess7 marksPaper 1~11 min

A small business owner tracks the monthly profit from a new product. In the first month, the profit is

2000

dollars. The profit increases by a fixed amount each month, forming an arithmetic sequence. In the sixth month, the profit is

4500

dollars.

(a)

Find the common difference,

d

, of this arithmetic sequence. [2 marks]

(b)

Find the profit in the twelfth month. [2 marks]

(c)

The owner claims that the total profit over the first twelve months exceeds

54\,000

dollars. Determine whether this claim is correct, showing your reasoning. [3 marks]

Solutions

15FoundationSAQ-SSum of an arithmetic sequences7 marksPaper 1~11 min

An arithmetic sequence has general term

u_n = 5n - 2

, where

n \in \mathbb{Z}^+

.

(a)

Write down the first term

u_1

and the common difference

d

. [2 marks]

(b)

Find

S_{20}

, the sum of the first

20

terms. [2 marks]

(c)

Find the least value of

n

such that

S_n > 2000

. [3 marks]

Solutions

16FoundationSAQ-SDefinition and general term of arithmetic sequencess5 marksPaper 1~8 min

A gardener is planting trees in a straight row. The first tree is planted

5

metres from a fence. Each subsequent tree is planted

3

metres further from the fence than the previous tree. The distance of the

n

th tree from the fence is

u_n

metres.

(a)

State the values of

u_1

and

d

for this arithmetic sequence. [1 mark]

(b)

Calculate the distance from the fence of the

12

th tree. [2 marks]

(c)

The gardener has a row of length

50

metres available beyond the fence. Determine the maximum number of trees that can be planted within this row. [2 marks]

Solutions

17FoundationSAQ-SDefinition and general term of arithmetic sequencess7 marksPaper 1~11 min

A cyclist trains by increasing her cycling distance each day. The distances she cycles on consecutive days form an arithmetic sequence. On day 1, she cycles

12\,\text{km}

. On day 7, she cycles

30\,\text{km}

.

(a)

Find the common difference of the sequence. [2 marks]

(b)

Find the total distance she cycles over the first 7 days. [2 marks]

(c)

Find the minimum number of days of training required for her total cumulative distance to exceed

500\,\text{km}

. [3 marks]

Solutions

18FoundationSAQ-SDefinition and general term of arithmetic sequencess7 marksPaper 1~11 min

A car travels from town A town B. The distances travelled in consecutive minutes form an arithmetic sequence. In the first minute, the car travels

400

metres. In the fourth minute, the car travels

520

metres.

(a)

Find the common difference of the sequence. [2 marks]

(b)

Find the distance travelled in the sixth minute. [2 marks]

(c)

The total distance from town A town B is

9\,\text{km}

. Determine the minute during which the car arrives at town B, justifying your answer. (Assume the sequence continues unchanged.) [3 marks]

Solutions

19FoundationSAQ-SDefinition and general term of arithmetic sequencess5 marksPaper 1~8 min

A farmer plants trees in a straight line. The distance from the first tree to the second tree is

5\,\text{m}

. The distances between consecutive trees form an arithmetic sequence with common difference

d

. The total distance from the first tree to the fifth tree is

38\,\text{m}

.

(a)

Write an expression, in terms of

d

, for the total distance from the first tree to the fifth tree. [1 mark]

(b)

Find the common difference

d

. [2 marks]

(c)

Find the distance between the fourth and fifth trees. [2 marks]

Solutions

20FoundationSAQ-SDefinition and general term of arithmetic sequencess5 marksPaper 1~8 min

A fitness app tracks the number of push-ups a user completes each day. On the first day, the user completes

12

push-ups. Each subsequent day, the user completes

5

more push-ups than the previous day. The number of push-ups completed on day

n

is denoted by

u_n

.

(a)

Write down an expression for

u_n

in terms of

n

. [1 mark]

(b)

Calculate the number of push-ups completed on day

10

. [2 marks]

(c)

On a certain day, the user completes

97

push-ups. Find the value of

n

for this day. [2 marks]

Solutions

Arithmetic and Geometric Sequences · Paper 1 — Free Maths AA SL Practice Questions