Let Q = , where and
Calculate the exact value of Q.
Give your answer from part (a) correct to
Nina estimates the value of Q to be 2.
Calculate the percentage error in Nina’s estimate.
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Let Q = , where and
Calculate the exact value of Q.
Give your answer from part (a) correct to
Nina estimates the value of Q to be 2.
Calculate the percentage error in Nina’s estimate.
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Let , where and .
Find the value of . Give your answer as a fraction.
Give your answer from part (a) to
Kieran estimates the value of to be -1.
Calculate the percentage error in Kieran’s estimate.
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Consider the numbers and .
Calculate . Give your answer correct to the nearest integer.
Give your answer to part (a) in the form , where and .
Calculate the percentage error if was approximated to be 9000.
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A cylinder has radius of 12.7 cm and height of 14.4 cm.
Calculate the volume of the cylinder correct to
Write your answer to part (a) (ii) in the form , where and .
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A rectangular field has length, , of 25.2 m and width, , of 21.4 m, each correct to 1 decimal place.
Calculate the lower and upper bound for
Calculate the lower and upper bound for the
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Calculate the following, giving your answer in the form , where and
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Consider the following four numbers.
Write down
.
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Five Olympic barbells labelled, “2.2 m in length”, were delivered to an Olympic weightlifting team. The coach measured each barbell to check its length, in metres, and recorded the following:
The weights of the barbells are labelled 20 kg. The coach also weighed each barbell, in kg, and recorded the following:
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In a game show, there is a transparent box filled with identical cubes. Contestants must estimate the number of cubes in the box. The box is 60 cm wide, 80 cm long and 20 cm tall.
Find the volume of the box.
Monica estimates the volume of one cube is 300 cm3. She uses this value to estimate the number of cubes in the box.
Find Monica’s estimated number of cubes in the box.
The actual number of cubes in the box is 280.
Find the percentage error in Monica’s estimated number of cubes in the box.
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Solve the following systems of linear equations using technology.
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Solve the following systems of linear equations using technology.
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Let , where , and .
Calculate the exact value of .
Give your answer from part (a) correct to
Michael estimates the value of to be
Calculate the percentage error of Michael’s estimate.
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Let , where and
Find the value of W. Give your answer as a fraction.
Give your answer from part (a) to
Louis estimates the value of to be 0.03.
Calculate the percentage error of Louis’ estimate.
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A prism has a cross sectional area of and volume of .
Calculate the height of the prism.
Lily estimates the height of the prism to be 7 cm.
Calculate the percentage error in Lily’s estimate.
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Mary has found the exact answer for is .
Write down the exact answer of as a decimal.
Mary rounds her exact answer so that the percentage error is 6.67%.
State the number of significant figures Mary rounded the exact answer to and write down the approximate value of used in calculating the percentage error.
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It is given that and , where and .
Find the size of the angles and .
A circle has radius equal to
Find the area of the circle, giving your answer in terms of .
James rounds the answer from part (b) to the nearest integer.
Calculate the percentage error of James’ estimate.
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A medium rare steak should have an internal temperature of to . Max decides to go to 10 different steak houses, he measures the internal temperature of a medium rare steak at each establishment and records the following:
51.0, 52.1, 62.9, 49.0, 59.8, 50.2, 54.3, 47.7, 48.6, 65.4
Find the mean internal temperature of Max’s recordings.
Max goes to 5 more steak houses and calculates the mean of all 15 restaurants to be
Calculate the mean internal temperature from the 5 additional steak houses Max went to.
Max records one last steak that has an internal temperature of
Calculate the interval of such that the mean internal temperature for all 16 steaks is within the temperature range for a medium rare steak.
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The diameter of Earth is m, correct to four significant figures. The circumference of Mars is m, correct to four significant figures.
Modelling Earth and Mars as perfect spheres, find the difference between the volume of Earth and the volume of Mars, giving your answer in the form , where .
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Solve the following systems of linear equations using technology.
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Consider the numbers .
Giving your answer to 1 decimal place, calculate the value of
Points P and Q have coordinates and respectively.
The formula for the distance, , between two points with coordinates and is given in your formula booklet.
Using your answers from part (a), calculate the distance, , between points P and Q. Give your answer correct to 1 decimal place.
Find the percentage error between the distance, correct to 1 decimal place, found in part (b) and the exact distance between points P and Q.
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Let and , where, ,
Giving your answer to 1 decimal place, calculate the value of
Using your answers to part (a), estimate the value of . Give your answer as a fraction.
Calculate the percentage error between your estimated value of found in part (b) and the exact value of
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A cuboid has length, = 0.102 m, width, = 9.4 cm and height, = 0.25 m.
Calculate the exact volume of the cuboid
Write your answers to part (a) (i) and (ii) in the form , where .
William estimates the volume of the cuboid as being and the percentage error in his estimate is 5%.
Calculate the exact possible values of .
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Let where = , = , = and =
Note: sin2 = (sin )2
Find the value of , giving your answer as a fraction.
Let =
Find the value of giving your answer as a fraction.
Calculate the value of giving your answer as a fraction.
John estimates the value of to be 0.3.
Calculate the percentage error in John’s estimate.
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Consider the numbers and
Giving your answers in the form where calculate
The formula for the distance, between two points with coordinates and is given in your formula booklet.
Using your answers to part (a), estimate the distance between points A and B.
Calculate the percentage error between the estimate of the distance between points P and Q found in part (b) and the exact distance.
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A shop sells bags of potatoes labelled as “5 kg”. The shop owner weighs five bags, in kilograms, at random and recorded the following:
4.96, 4.89, 5.07, 5.11, 5.02
The shop owner shares his findings with his potato supplier, who weighs another five bags and recorded the following:
5.05, 5.01, 4.97, 5.09, X
The supplier allows a maximum percentage error of 1%.
Find the interval for the values of X such that the percentage error from the five bags that the supplier weighed is less than 1%.
Find the interval for the values of X such that the percentage error from all the ten bags weighed is less than 1%.
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Solve the following systems of linear equations using technology.
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