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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.
Five pipes labelled, “6 metres in length”, were delivered to a building site. The contractor measured each pipe to check its length (in metres) and recorded the following;
5.96, 5.95, 6.02, 5.95, 5.99.
(a) Write the answer to part (a) correct to 2 significant figures.
(b) Calculate the percentage error when the answer to part (a) is written correct to 2 significant figures.
(c) Write your answer to part (c) in the form a ´ 10k where 1 £ a < 10 and k Î .
Given the equation p = r2 + 2qr.
(a) Calculate the exact value of p when q = 3.6 and r = 24.
(b) Write your answer correct to two significant figures.
(c) Express your answer to (b) in the form a ´ 10k where 1 £ a < 10 and k .
(a) Sketch a graph of y = x/2+x for –10 ≤ x ≤ 10.
(b) Hence write down the equations of the horizontal and vertical asymptotes.
The total weight of 256 identical pencils is 4.24 kg. Calculate the weight of one pencil, in kg.
(a) Give your answer exactly.
(b) Give your answer correct to three significant figures.
(c) Write your answer to part (b) in the form a × 10k where 1 ≤ a < 10 and k Î z.
Let x = 6.4 × 107 and y = 1.6 × 108.Find
(a) x/y
(b) y – 2x,
giving your answers in the form a × 10k where 1 £ a < 10 and k Î Z.
A rectangle has length 2.6 × 104 and width 1.9 × 104. Find each of the following, giving your answer in the form a × 10k, where 1 £ a < 10.
(a) The area of the rectangle;
(b) The perimeter of the rectangle.
Two students Ann and Ben play a game. Each time Ann passes GO shereceives $15. Each time Ben passes GO he receives 8% of the amount he alreadyhas. Both students start with $100.
(a) How much money will Ann have after she has passed GO 10 times?
(b) How much money will Ben have after he passes GO 10 times?
(c) How many times will the students have to pass GO for Ben to have more money than Ann?
At the circus a clown is swinging from an elastic rope. A student decides to investigate the motion of the clown. The results can be shown on the graph of the function f (x) = (0.8x)(5 sin 100x), where x is the horizontal distance in metres.
(a) Sketch the graph of f (x) for 0 ≤ x ≤ 10 and –3 ≤ f (x) ≤ 5.
(b) Find the coordinates of the first local maximum point.
(c) Find the coordinates of one point where the curve cuts the y-axis.