Trigonometric Graphs

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GCSE MATHEMATICS Trigonometric Graphs X These questions have been taken or modified from previous AQA GCSE Mathematics Papers. Instructions Use black ink or black ball-point pen.

4 unless another value is given in the question. Information The marks for questions are shown in brackets.

1 GCSE MATHEMATICS Trigonometric Graphs X These questions have been taken or modified from previous AQA GCSE Mathematics Papers. Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. Answer all questions. You must answer the questions in the spaces provided. If our calculator does not have a π button, take the value of π to be 3.4 unless another value is given in the question. Information The marks for questions are shown in brackets. The qualit of our written communication is specificall assessed in questions that are indicated with an asterisk (*). Advice Read each question carefull before ou start to answer it. In all calculations, show clearl how ou work out our answer. Use the number of marks for the question as a guide to the amount of time ou need to spend. Look at previous parts of the question, e.g. a), b), c) i) as there ma be information there ou need to answer later parts. Check our answer is realistic and appropriate. For calculator decimal numbers alwas write our full calculator displa in the working out area and then, if ou need to, round the answer on the answer line. This booklet was curated and modified using AQA examination papers between -6, for thecalculatorguide.com, where ou can find man more booklets on further topics. All questions used are reproduced for educational purposes onl.

2 (a) On this grid draw the graph of = + sin x for values of x from º to 36º. The graph of = sin x has been drawn to help ou x (b) On this grid draw the graph of = sin x for values of x from º to 36º. The graph of = sin x has been drawn to help ou. ( mark) x ( mark)

3 (a) Draw the graph of = cos x for º x 36º º 9 º 8 º 7 º 36 º x ( mark) (b) Write down the two solutions to the equation cos x =.5 for º x 36º Answer degrees ( mark) and degrees (c) Draw the graph of = cos x + for º x 36º º 9 º 8 º 7 º 36 º x ( mark)

4 (d) On the grid below, draw the graph of = cos x for º x 36º [ mark] x (e) On the grid below, draw the graph of = cos x for º x 36º [ mark] x

5 3 The graph shows = sin x for º x 36º º 9º 8º 7º 36º x 3 (a) sin x = sin 6º and 9º x 36º Work out the value of x. [ mark] Answer... 3 (b) sin x = sin 6º and 8º x 36º Work out one of the values of x. [ mark] Answer...

6 4 This is a sketch graph of = sin x for º x 36º º 9º 8º 7º 36º x 4 (a) Write down the number of solutions for sin x =.5 for º x 36º [ mark] Answer... 4 (b) sin x = sin Write down the value of x for 9º x 8º [ mark] Answer...

7 6 The depth of water in a harbour is modelled b the equation d = 7 + sin (3t)º d is the depth of water in metres. t is the number of hours after 4. am d The graph shows the depth of water for values of t from to t 6 (a) Complete the table. [ marks] t d (b) On the grid above, draw the graph for values of t from 6 to [ mark] 6 (c) Between what times of da is the depth at least 8 metres? [ marks] Between... and...

8 5 A ball is thrown from point P at an angle xº to horizontal ground. The ball lands a distance d metres from P. The path of the ball is a curve. direction ball is thrown P x horizontal ground d Changing the size of angle x will change the distance d. The connection between x and d is modelled b d = sin x cos x 5 (a) Here is a table of values for x and d. x d On the grid opposite, draw the graph of for values of x from to 9 d = sin x cos x [ marks]

9 d x 5 (b) In this question, ou must show our working on the graph above. Complete this statement. [ marks] For d to be more than 7 metres, x must be between... and...

10 7 The depth of water, d metres, in a harbour at a time, t hours after noon, is given b d = 4 cos(3t) o 7 (a) Complete the table of values. t d (( marks) mark) 7 (b) On the grid, draw the graph of d = 4 cos(3t) o for values of t from to. d t ( marks)

11 7 (c) The depth of water must be at least 9 metres for a ship to enter the harbour. At noon a ship is waiting to enter the harbour. Use the graph to estimate the earliest time the ship can enter. Answer... ( marks) 7 (d) A different ship enters the harbour at 4.5 pm. The ship must leave the harbour before the depth of water falls below 9 metres. Use the graph to estimate the maximum time the ship can sta in the harbour. Give our answer in hours and minutes. Answer...minutes hours (3 marks) 8 The depth of water in a harbour is d metres. d = 5 sin(3t) t is the number of hours after 7. am 8 (a) Here is a table of values for d = 5 sin(3t) t d Show that when t is, the value of d is [ mark]

12 8 (b) On the grid draw the graph of d = 5 sin(3t) for values of t from to [ marks] d t 8 (c) A ship can sta in the harbour when the depth of water is 4 metres or more. Use the graph to work out the maximum time a ship can sta in the harbour. Give our answer in hours and minutes. [ marks] Answer hours minutes

Venn Diagrams 1 GCSE MATHEMATICS. These questions have been taken or modified from previous AQA GCSE Mathematics Papers.

Venn Diagrams 1 GCSE MATHEMATICS. These questions have been taken or modified from previous AQA GCSE Mathematics Papers. GCSE MTHEMTICS Venn Diagrams 1 X These questions have been taken or modified from previous Q GCSE Mathematics Papers. Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. nswer