Ch8: Straight Line Graph. x f(x) p 0.5 q 2 4 R 16. (a) Find the values of p, q and r. [3]

Size: px

Start display at page:

Download "Ch8: Straight Line Graph. x f(x) p 0.5 q 2 4 R 16. (a) Find the values of p, q and r. [3]"

Martin Preston
6 years ago
Views:

1 Ch8: Straight Line Graph. Answer the whole of this question on a sheet of graph paper. The table gives values of f() =, for f() p 0.5 q 4 R 6 (a) Find the values of p, q and r. [3] Using a scale of cm to unit on the -ais and cm to unit on the -ais, draw the graph of = f() for 4. [5] (c) Use our graph to solve the equation = 7. [] (d) What value does f() approach as decreases? [] (e) B drawing a tangent, estimate the gradient of the graph of = f() when =.5. [3] (f) On the same grid draw the graph of = + for 0 4. [] (g) Use our graph to find the non-integer solution of = +. []. Answer the whole of this question on one sheet of graph paper. (a) f() =, 0. X f() p q q p Find the values of p and q. [] (i) Draw an -ais for 3 3 using cm to represent unit and a -ais for using cm to represent unit. [] (ii) Draw the graph of = f() for and for [5] (c) Write down an integer k such that f() = k has no solutions. [] (d) On the same grid, draw the graph of = 5 for 3 3. [] (e) (i) Use our graphs to find solutions of the equation, = 5. [3] (ii) Rearrange, = 5 into the form a 3 + b + c = 0, where a, b and c are integers. [] ABBASI MOHAMMED ASIM Page: mdasimabbasi@ahoo.co.in

2 (f) (i) Draw a tangent to the graph of = f() which is parallel to the line = 5. [] (ii) Write down the equation of this tangent. [] 3. Answer the whole of this question on a sheet of graph paper. f() = 3 3, 0. (a) The table shows some values of f(). X F() p q r Find the values of p, q and r. [3] Draw aes using a scale of cm to represent 0.5 units for 3 3 and cm to represent units for 0. [] (c) On our grid, draw the graph of = f() for and [5] (d) Use our graph to solve the equations (i) = 0, [] (ii) = 0. [3] (e) g() = On the same grid, draw the graph of = g() for 3 3. [] (f) (i) Describe briefl what happens to the graphs of = f() and = g() for large positive or negative values of. [] (ii) Estimate the gradient of = f() when = 00. [] A B C 4. 0 NOT TO SCALE The diagram shows a sketch of = + and = 4. (a) Write down the co-ordinates of (i) the point C, [] ABBASI MOHAMMED ASIM Page: mdasimabbasi@ahoo.co.in

3 (ii) the points of intersection of = 4 with each ais. [] Write down the gradient of the line = 4. [] (c) Write down the range of values of for which the gradient of the graph of = + is negative. [] (d) The two graphs intersect at A and B. Show that the co-ordinates of A and B satisf the equation + 3 = 0. [] (e) Solve the equation + 3 = 0, giving our answers correct to decimal places. [4] (f) Find the co-ordinates of the mid-point of the straight line AB. [] 5. Answer the whole of this question on a sheet of graph paper. The table shows some of the values of the function f ( ), 0. X Y p q 3.5 r (a) Find the values of p, q and r, correct to decimal place. [3] Using a scale of cm to represent unit on the -ais and cm to represent unit on the -ais, draw an -ais for 3 3 and a -ais for 6 0. Draw the graph of = f() for 3 0. and [6] (c) (i) B drawing a suitable straight line, find the three values of where f() = 3. [3] (ii) 3 can be written as 3 + a + b = 0. Find the values of a and b. [] (d) Draw a tangent to the graph of = f() at the point where =. Use it to estimate the gradient of = f() when =. [3] ABBASI MOHAMMED ASIM Page: 3 mdasimabbasi@ahoo.co.in

4 6. (a) The table shows some values for the equation for and (i) Write the missing values of in the empt spaces. [3] (ii) On the grid, draw the graph of for and [5] ABBASI MOHAMMED ASIM Page: 4 mdasimabbasi@ahoo.co.in

5 Use our graph to solve the equation. Answer = or = [] (c) (i) B drawing a tangent, work out the gradient of the graph where =. Answer (c)(i) [3] (ii) Write down the gradient of the graph where =. Answer (c)(ii) [] (d) (i) On the grid, draw the line = for 4 4. [] (ii) Use our graphs to solve the equation =. Answer (d)(ii) = or = [] (e) Write down the equation of a straight line which passes through the origin and does not intersect the graph of. 7. A straight line passes through two points with co-ordinates (6, 8) and (0, 5). Work out the equation of the line. 8. A straight line passes through two points with co-ordinates (6, 0) and (0, 7). Work out the equation of the line. Answer (e) [] Answer... [3] Answer... [3] ABBASI MOHAMMED ASIM Page: 5 mdasimabbasi@ahoo.co.in

6 = + 3 A O C 9. B NOT TO SCALE The distance AB is 7 units. (a) Write down the equation of the line through B which is parallel to = + 3. Answer (a).. [] Find the co-ordinates of the point C where this line crosses the ais. Answer (,. ) [] 0. = + 5 A O C B NOT TO SCALE The distance AB is units. (a) Write down the equation of the line through B which is parallel to = + 5. Answer (a)... [] Find the co-ordinates of the point C where this line crosses the ais. Answer (...,...) []. Find the co-ordinates of the mid-point of the line joining the points A(, 5) and B(6, 9). Answer (, ) [] ABBASI MOHAMMED ASIM Page: 6 mdasimabbasi@ahoo.co.in

7 (a) Draw the three lines = 4, = 4 and + = 6 on the grid above. [4] Write the letter R in the region defined b the three inequalities below [] 3. Find the co-ordinates of the mid-point of the line joining the points A(4, 7) and B(8, 3). Answer (, ) [] ABBASI MOHAMMED ASIM Page: 7 mdasimabbasi@ahoo.co.in

QUADRATIC AND CUBIC GRAPHS

NAME SCHOOL INDEX NUMBER DATE QUADRATIC AND CUBIC GRAPHS KCSE 1989 2012 Form 3 Mathematics Working Space 1. 1989 Q22 P1 (a) Using the grid provided below draw the graph of y = -2x 2 + x + 8 for values