Intermediate 2 Revision Unit 3. (c) (g) w w. (c) u. (g) 4. (a) Express y = 4x + c in terms of x. (b) Express P = 3(2a 4d) in terms of a.
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1 Intermediate Revision Unit. Simplif 9 ac c ( ) u v u ( ) 9. Epress as a single fraction a c c u u a a (h) a a. Epress, as a single fraction in its simplest form Epress 0 as a single fraction in its simplest form.. Epress = c in terms of. Epress P = (a d) in terms of a. Epress H = a m in terms of. Epress M = u in terms of. v Epress P= ac d in terms of a. Epress T = v u in terms of v. Epress D = m p n in terms of n. (h) Epress G = u v in terms of v.. Simplif ( ) ( ) ( )( ). Epress ith a rational denominator in its simplest form ( a) 9 8
2 . f() =. Epress f(0) ith a rational denominator in its simplest form. g() = 8. Epress g() ith a rational denominator in its simplest form. 8. Simplif p p a a n n m m a a a 8 (h) a a (i) p 9 p (j) n n n (k) (m ) m (l) ( ) 9 9. Epand the brackets and simplif ( a) ( ) a (a a ) b (b b ) u (u u ) 0. Evaluate Evaluate a hen a = 9 Evaluate hen = 8 Given n = find the value of n. Solve = 0 p = p m = 0 = 0 = 0 n n 8 = 0 a = a 0 (h) = 0 (i) u 0u 8 = 0 (j) =. Solve the equation = 0, giving our ansers correct to one decimal place. Solve the equation 8 = 0, giving our ansers correct to three significant figures. Solve the equation = 0, using an appropriate formula.
3 . Each quadratic function belo has an equation in the form = a. Write don the equation of each function. = a (,) (,) = a = a (,8) (,8) = a. The diagram belo shos the graph of = ( p) q. (,9) Write don the values of p and q. State the equation of the ais of smmetr. Find the coordinates of and.
4 . The diagram belo shos the graph of = ( a) b. P Q (,) Find the values of a and b. State the equation of the ais of smmetr. Find the coordinates of P and Q.. The equation of the parabola in the diagram belo is = ( ). C State the coordinates of the minimum turning point of the parabola. Find the coordinates of C. is the point (,0). State the coordinates of. 8. The equation of the parabola belo is = ( ). C D State the coordinates of the maimum turning point of the parabola. Find the coordinates of and. State the coordinates of C. The point D has the same coordinate as C. State the coordinates of D.
5 9. Factorise Write don the roots of the equation = 0. The graph of = is shon belo. Find the coordinates of the minimum turning point. 0. Solve the equation = 0 The graph of = is shon belo. Find the coordinates of, the maimum turning point of the parabola.. Solve the folloing equations for 0 0 sin = cos = 0 tan = cos tan 0 = 0 sin tan =. Triangle C has area cm. = 8 cm and C = cm, find to values for angle C. 8 cm cm C
6 . The graph belo has equation = asin b. State the values of a and b. 0. The graph belo has equation = acos b. State the values of a and b. 0. The graph belo has equation of the form = acos( b). State the values of a and b. 00. Sketch the folloing graphs for 0 0 = sin = cos = sin( 0) = cos ( )
7 . The diagram belo shos the graph of = sin. The line =. has also been dran on the graph. Find the coordinates of P and Q. 8. The height of a fairground ride, in metres, is given b the formula H =.8.sin (0t)º here t is the time in seconds after the ride starts. What is the maimum height of the ride? What is the height of the ride before it starts? Find the height of the ride after 0 seconds. fter ho man seconds does the ride first reach a height of. metres? 9. The depth of ater, D metres, in a harbour is given b the formula D = sin(t)º. here t is the number of hours after midnight. What is the maimum depth of ater in the harbour? Calculate the depth of ater in the harbour at.0pm. t hat to times is the depth 0.m? 0. satellite is programmed to orbit the Earth. The height of the satellite above the Earth, in kilometres, is given b the formula H = 0 sin(0t) 0 here t is the number of hours after midnight. What is the greatest distance from the Earth that the satellite ill reach? Calculate the height of the satellite at 0.0 p.m. Ho man minutes after midnight ill the satellite first be at a height of. kilometres?
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