5.1 Write down the: 5.1.1 Coordinates of D (2) 5.1.2 Range of g (1) 5.2 Calculate the: 5.2.1 Coordinates of A (2) 5.2.2 Values of a and q (4) 5.3 Determine the: 5.3.1 Length of CD (2) 5.3.2 Equation of a straight line through A and D (3) 5. 4 For which values of x … Read more
Samantha is investigating a pattern of dots represented in the diagram below. 4.1 Write down: 4.1.1 The number of dots in the 4th pattern (1) 4.1.2 The number of dots in the 13 th pattern (1) 4.1.3 A formula for the number of dots in the nth pattern (1) 4.2 Hence, or otherwise, calculate the … Read more
The diagram below shows the graphs of f(x)=-x2 + 2x+15 and g(x)=-3x+k. Graph f cuts the x-axis at A(-3 ; 0) and B(5 ; 0), the y-axis at C and has a turning point at D. Graph g cuts the x-axis at B and the y-axis at C. E is a point on g such … Read more
Given: 5.1 Show that f (x) can be written as (2) 5.2 Write down the equations of the asymptotes of f. (2) 5.3 Determine the x-intercept of f. (3) 5.4 Determine the y-intercept of f. (2) 5.5 Sketch the graph of f. Show clearly ALL the intercepts with axes and the asymptotes. (3) 5.6 Determine … Read more
Consider the finite linear pattern: 20 ; 17 ; 14 ;… ; -103 3.1 Write down the 4th term of the pattern. (1) 3.2 Determine the expression for the nth term. (2) 3.3 Calculate the number of terms in the sequence. (2) 3.4 Which term is the first to have a negative value? (3) 3.5 … Read more
4.1 The following number patter is given: 13 ; 27 ; 45 ; 67 ; … 4.1.1 Is this a quadratic number pattern? Justify your answer with relevant calculations. (2) 4.1.2 Determine the general term, Tn , of the quadratic number pattern. (4) 4.1.3 Calculate the value of T100. (2) 4.1.4 The first difference between … Read more
Given the linear pattern: -5 ; 0 ; 5 ; … 3.1 Determine the general term, Tn , of the linear pattern. (2) 3.2 Calculate the value of T12 . (2) 3.3 Which term in the patter has a value of 130? (2) [6]
2.1 Simplify fully, WITHOUT using a calculator: (4) 2.2 Solve for x: 2.2.1 (3) 2.2.2 (3) 2.2.3 (5) 2.3 WITHOUT using a calculator, show that simplifies to (5) [20]