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1 Higher Revision Graph Plotting Grade: C. This formula gives the stopping distance, d metres, for a car travelling at x mph. d = x (0 + x) 00 (a) Complete this table. x d Draw the graph of d = x (0 + x) 00 d (c) x Use the graph to estimate the stopping distance when a car is travelling at 56 mph.... m South Wolds Comprehensive School
2 . = x + 5 P O x (a) The line = x + 5 crosses the axis at P. What is the value of at P?... Write down the equation of another line which is parallel to = x (c) S(, 4) and T(5, 0) are two points. Calculate the length ST. Show our method clearl. T (5, 0) Not to scale S (, 4)... []. (a) The equation of a straight line is = x. Write down the coordinates of the point where this line crosses the -axis. (...,...) Rearrange = x to make x the subject.... South Wolds Comprehensive School
3 4. (a) Complete the table below for = 4x x. x Draw the graph of = 4x x on the grid below x (c) Use our graph to solve the equation 4x x =.... South Wolds Comprehensive School
4 5. (a) This graph represents the first part of Ian s journe. Distance from home (km) 4 B 0 A 0 4 Time (minutes) What does the shape of the curve from A to B tell ou about Ian s speed? This graph represents Sarah s journe home. Distance from home (km) Time (minutes) Calculate Sarah s speed. Give our answer in kilometres per hour.... km/h [] South Wolds Comprehensive School 4
5 6. (a) Complete the table below for = x. x Draw the graph of = x. (c) Find the values of x where the graph crosses the x-axis.... South Wolds Comprehensive School 5
6 Grade: B 7. Sketch these graphs. (a) = x = x 8. Here are four equations of straight lines. = x + = x + = x = x + The graphs below show two of these lines. Write the correct equation below each graph x 0 x (a) South Wolds Comprehensive School 6
7 9. (a) Complete the following table for = x + x. x Draw the graph of = x + x x (c) Use our graph to find the solution to the equation x + x = South Wolds Comprehensive School 7
8 0. The table shows some values of x and for the equation = (x ). x (a) Complete the table. Draw the graph of = (x ) for values of x from to x For each of the sketch graphs below, choose the correct equation from this list. = + x = x = x = x (a) 0 x 0 x =... =... South Wolds Comprehensive School 8
9 Grade: A. (a) Find the gradient of a line which is perpendicular to the line = x A line passes through the points (, 4) and (, 5). (i) Find the gradient of this line. (ii) Find the equation of this line. Give our answer in the form = mx + c.. (a) Complete this table for = x +. x Draw the graph of = x x South Wolds Comprehensive School 9
10 (c) The equation x + = 7x can be solved b adding a straight line to the graph, (i) Write down the equation of this line.... (ii) Draw this line on the graph and use it to solve the equation x + = 7x. [] Grade: A* 4. (a) (i) Draw the graphs of x + = 4 and = x +. 0 x [] (ii) The graphs intersect at two points. Write down the coordinates of these points. Give our answers correct to decimal place. (...,...) Solve, algebraicall, these simultaneous equations. Give our answers correct to decimal places. x + = 4 = x + [6] South Wolds Comprehensive School 0
11 x 4 The diagram shows a circle. Which of the following is the equation of the circle? Write Yes under the correct equation. x + = 4 x + = 6 x + = 6 x + = x 5 The curve = x x is drawn on the grid above. South Wolds Comprehensive School
12 (a) (i) Write down the equation of the straight line ou would draw on the grid above in order to solve the equation x x = x (ii) Show that the equation x x = x + simplifies to x x 5 = 0.. Find the equation of the straight line ou would draw on the grid above in order to solve the equation x 4x 4 = B x A 4 5 On the grid the straight line intersects the circle at A and B. 6 (a) Find the equation of the straight line through A and B. Write down the equation of the circle. South Wolds Comprehensive School
13 8. The mass of a radioactive substance is decreasing b 0% a ear. The mass, M grams, after t ears, is given b the formula M = t. (a) Complete this table. t (ears) M (grams) Draw the graph of M = t. M t (c) Use our graph to estimate after how long the mass will be 50 grams.... ears South Wolds Comprehensive School
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