Name:______
IB Studies Test 1 2016 76 marks
Scientific notation, percentage error, estimation, rounding, currency exchange, coordinate geometry.
- Calculate 3.7 × 16.22 – 500, writing your answer
(a)correct to two decimal places;
(b)(i)correct to three significant figures;
(ii)in the form a × 10k, where 1 ≤ a < 10, k.
(Total 4 marks)
- Let m = 6.0 ×103 and n = 2.4 ×10–5.
Express each of the following in the form a ×10k, where 1 ≤ a < 10 and k.
(a)mn;
(a).
(Total 4 marks)
- (a) A girl’s height is 1.623 m. Write her height to the nearest cm.
(b)The time taken to fill a tank was 2 hours 43 minutes. Write this time to the nearest 5 minutes.
(c)The attendance at a show was 2591 people. How many people, to the nearest 100, were at the show?
(d)The mean distance of the Moon from the Earth is approximately 384 403 km. Write this distance in the form a × 10k where 1 ≤ a < 10 and k.
(Total 4 marks)
The following diagram shows a rectangle with sides of length 9.5 × 102 m and 1.6 × 103 m.
diagram not to scale
(a)Write down the area of the rectangle in the form a × 10k, where 1 ≤ a < 10, k.
(3)
Helen’s estimate of the area of the rectangle is 1 600 000 m2.
(b)Find the percentage error in Helen’s estimate.
(3)
(Total 6 marks)
- (a) Given x = 2.6 × 104 and y = 5.0 × 10–8, calculate the value of w = x × y. Give your answer in the form a × 10k where 1 ≤ a < 10 and .
(b)Which two of the following statements about the nature of x, y and w above are incorrect?
(i)x
(ii)y
(iii)y
(iv)wy
(v)x + y
(vi)x
(Total 8 marks)
- (a) Calculate .
(1)
(b)Express your answer to part (a) in the form a 10k, where
1 a 10 and k.
(2)
©Juan estimates the length of a carpet to be 12 metres and the width to be 8 metres. He then estimates the area of the carpet.
(i)Write down his estimated area of the carpet.
(1)
When the carpet is accurately measured it is found to have an area of 90 square metres.
(ii)Calculate the percentage error made by Juan.
(2)
(Total 6 marks)
7.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)
(Total 4 marks)
8. Ruby moves from the USA to Italy. She transfers 6610 USD into an Italian bank which has an exchange rate of 1 USD = 0.735 euros. The bank charges 1.8 % commission.
Calculate the amount of money Ruby will invest in the Italian bank after commission.
(4 marks)
9.In a television show there is a transparent box completely filled with identical cubes. Participants have to estimate the number of cubes in the box. The box is 50 cm wide, 100 cm long and 40 cm tall.
(a)Find the volume of the box.
(2)
Joaquin estimates the volume of one cube to be 500 cm3. He uses this value to estimate the number of cubes in the box.
(b)Find Joaquin’s estimated number of cubes in the box.
(2)
The actual number of cubes in the box is 350.
c) Find the percentage error in Joaquin’s estimated number of cubes in the box.
(2)
(Total 6 marks)
10.
The diagram shows a wheelchair ramp, , designed to descend from a height of .
(a)Use the diagram above to calculate the gradient of the ramp.
(1)
The gradient for a safe descending wheelchair ramp is.
(b)Using your answer to part (a), comment on why wheelchair ramp is not safe.
(1)
The equation of a second wheelchair ramp, B, is .
(c)(i) Determine whether wheelchair ramp is safe or not. Justify your answer.
(ii) Find the horizontal distance of wheelchair ramp .
(4)
11.
The diagram shows the points M(a, 18) and B(24, 10) . The straight line BM intersects the y-axis at A(0, 26). M is the midpoint of the line segment AB.
(a)Write down the value of .
(1)
(b)Find the gradient of the line AB.
(2)
(c)Decide whether triangle OAM is a right-angled triangle. Justify your answer.
(3)
The straight line, L, has equation. The point A has coordinates (6, 0).
(d)Give a reason why Ldoes not pass through A.
(1)
(e)Find the gradient of L.
(2)
L is a line perpendicular to L. The equation of Lis.
(f)Write down the value of m.(1)
Ldoes pass through A.
(g)Find the value of c.
(2)
12.
Triangle OAB is formed by the following three lines:
, and , where O is the origin and A and B are two other vertices.
(a)Find the coordinates of points A and B.
(2)
(b)Sketch the triangle on the set of axes below.
(5)
(c)Show that is a right angle.
(3)
(d)Find the angle ; to the nearest degree.
(2)
END OF TEST
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