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1.
The diagram shows the straight lines L1 and L2. The equation of L2 is y = x.
(a)
Find
(i)
the gradient of L1;
(ii)
the equation of L1.
(3)
(b)
Find the area of the shaded triangle.
(3)
(Total 6 marks)
2.
31 pupils in a class were asked to estimate the number of sweets in a jar.
The following stem and leaf diagram gives their estimates.
Stem
Leaf
4
2, 4, 7, 8, 9
5
1, 1, 2, 3, 8, 9
6
0, 2, 2, 4, 6, 6, 7, 8, 8
7
0, 0, 1, 3, 4, 5, 5, 7
8
1, 2, 2
Key: 4 | 7 represents 47 sweets
IB Questionbank Mathematical Studies 3rd edition
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(a)
For the pupils’ estimates, write down
(i)
the median;
(ii)
the lower quartile;
(iii)
the upper quartile.
(3)
(b)
Draw a box and whisker plot of the pupils’ estimates using the grid below.
(3)
(Total 6 marks)
3.
The straight line L passes through the points A(–1, 4) and B(5, 8).
(a)
Calculate the gradient of L.
(2)
(b)
Find the equation of L.
(2)
IB Questionbank Mathematical Studies 3rd edition
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The line L also passes through the point P(8, y).
(c)
Find the value of y.
(2)
(Total 6 marks)
4.
A shipping container is a cuboid with dimensions 16 m, 1
(a)
3
2
m and 2 m.
4
3
Calculate the exact volume of the container. Give your answer as a fraction.
(3)
Jim estimates the dimensions of the container as 15 m, 2 m and 3 m and uses these to estimate
the volume of the container.
(b)
Calculate the percentage error in Jim’s estimated volume of the container.
(3)
(Total 6 marks)
IB Questionbank Mathematical Studies 3rd edition
3
5.
120 Mathematics students in a school sat an examination. Their scores (given as a percentage)
were summarized on a cumulative frequency diagram. This diagram is given below.
(a)
Complete the grouped frequency table for the students.
Examination
Score x (%)
Frequency
0 ≤ x ≤ 20
20 < x ≤ 40
14
26
40 < x ≤ 60
60 < x ≤ 80
80 < x ≤ 100
(3)
(b)
Write down the mid-interval value of the 40 < x ≤ 60 interval.
(1)
IB Questionbank Mathematical Studies 3rd edition
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(c)
Calculate an estimate of the mean examination score of the students.
(2)
(Total 6 marks)
6.
Susi travels from Singapore to Thailand and changes 1500 Singapore dollars (SGD) to Thai
baht (THB). The exchange rate is 1 SGD buys 21.03464 THB.
(a)
Calculate the number of Thai baht Susi buys. Give your answer correct to the nearest
baht.
(2)
Susi leaves Thailand and travels to Indonesia. She has 20 000 THB and uses these to buy
Indonesian rupiah (IDR). The exchange rate is 3.28352 THB buys 1000 IDR.
(b)
Calculate the total number of Indonesian rupiah Susi receives, correct to the nearest
thousand rupiah.
(2)
Susi wants to find the approximate exchange rate between Singapore dollars and Indonesian
rupiah and uses the exchange rates for Thai baht to do this.
(c)
Calculate Susi’s exchange rate between Singapore dollars and Indonesian rupiah.
Give your answer in the form 1 SGD buys x IDR, where x is given correct to the nearest
rupiah.
(2)
(Total 6 marks)
7.
S3
, where S is its surface area.
36 π
The surface area of a sphere is 500 cm2.
The volume of a sphere is V =
(a)
Calculate the volume of the sphere. Give your answer correct to two decimal places.
(3)
(b)
Write down your answer to (a) correct to the nearest integer.
(1)
IB Questionbank Mathematical Studies 3rd edition
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(c)
Write down your answer to (b) in the form a × 10n, where 1 ≤ a < 10 and n 
.
(2)
(Total 6 marks)
IB Questionbank Mathematical Studies 3rd edition
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