I have a past paper worksheet that I am unable to solve.

Functions and modelling [56 marks] Paper 1: 31 Paper 2: 25 PAPER 2 1a. [1 mark] Urvashi wants to model the height of a moving object. She collects the following data showing the height, ℎ metres, of the object at time seconds. She believes the height can be modeled by a quadratic function, ℎ()= 2+ + , where , , ∈ ℝ. Show that 4+ 2+ = 34 . 1b. [3 marks] Write down two more equations for , and . 1c. [4 marks] Solve this system of three equations to find the value of , and . 1d. [3 marks] Hence find when the height of the object is zero. 1e. [2 marks] the maximum height of the object. PAPER 1 2a. [1 mark] M-Line is a company that prints and sells custom designs on T -shirts. For each order, they charge an initial design fee and then an additional fee for each printed T -shirt. M-Line charges euros per order. This charge is modelled by the linear function ()= 5+ 40 , where is the number of T -shirts in the order. Write down the initial design fee charged for each order. 2b. [2 marks] Find the total amount charged for an order of 94 T-shirts . 2c. [1 mark] EnYear is another company that prints and sells T -shirts. The price, euros, that they charge for an order can be modelled by the linear function ()= 9, where is the number of T-shirts in the order. Write down the number of T -shirts in an order for which EnYear charged 63 euros. 2d. [2 marks] An order of T-shirts will be charged the same price by both M -Line and EnYear. Find the value of . PAPER 1 3a. [4 marks] Consider the function ()= 27 2− 16 , ≠ 0. Sketch the graph of y = f (x), for −4 ≤ x ≤ 3 and −50 ≤ y ≤ 100. 3b. [1 mark] Use your graphic display calculator to find the zero of f (x). 3c. [2 marks] Use your graphic display calculator to find the coordinates of the local minimum point. PAPER 1 4. [4 marks] Consider a function f (x) , for −2 ≤ x ≤ 2 . The following diagram shows the graph of f. On the grid above, sketch the graph of f −1. PAPER 1 5a. [2 marks] Consider the straight lines L1 and L2 . R is the point of intersection of these lines. The equation of line L1 is y = ax + 5. Find the value of a. 5b. [2 marks] The equation of line L2 is y = −2 x + 3. Find the coordinates of R. 5c. [2 marks] Line L3 is parallel to line L2 and passes through the point (2, 3). Find the equation of line L3. Give your answer in the form y = mx + c. PAPER 1 6a. [2 marks] The function is defined by ()= 23+ 5, −2≤ ≤ 2. Write down the range of . 6b. [2 marks] Find an expression for −1(). 6c. [2 marks] Write down the domain and range of −1. PAPER 2 7a. [2 marks] Consider the function ()= 0.33+ 10 + 2−. Calculate (1). 7b. [4 marks] Sketch the graph of = () for −7≤ ≤ 4 and −30 ≤ ≤ 30 . 7c. [2 marks] Write down the equation of the ver tical asymptote. 7d. [2 marks] Write down the coordinates of the -intercept. 7e . [2 marks] Consider a second function, ()= 2− 3. Find the solution of ()= (). PAPER 1 8. [2 marks] The following diagram shows the graph of a function = (), for −6≤ ≤ −2. The points (−6, 6) and (−2, 6) lie on the graph of . There is a minimum point at (−4, 0). Write down the range of .