(Solved): THANK YOU GUYS 21 - Identifying the graphs Drag and drop each equation to the correct graph. \[ y=2 ...

21 - Identifying the graphs Drag and drop each equation to the correct graph. \[ y=2 \cos x \] Q2 - Characteristics of the graphs Think about the graph of \( y=4 \cos 4 x \) Write down the: maximum value minimum value amplitude period What is the equation of the graph shown here? Q1 - Using the curve \( \begin{array}{lcc}\begin{array}{l}\text { For each equation you are } \\ \text { given one of the } 4 \text { solutions } \\ \text { between }-360^{\circ} \text { and } 360^{\circ} .\end{array} & \tan x=0.649 & \text { or } \\ \begin{array}{l}\text { Use the graph to work out } \\ \text { the other } 3 \text { solutions. }\end{array} & \tan x=-1.072 \\ \begin{array}{l}\text { Round your answers to } \\ \text { the nearest degree. }\end{array} & x=-227^{\circ} \text { or } & \text { or or }\end{array} \) For each equation use your \( \quad \tan x=1.072 \) out the 4 solutions between \( \quad x=\quad \) or \( \quad \) or \( \quad \) or \( \quad \) or \( \begin{array}{l}\text { Round your answers to } \quad x=\quad \text { or } \quad \text { or } \quad \text { or } \\ \text { the nearest degree. }\end{array} \quad x= \) or \( ^{\circ} \quad \) or Q1 - Using the curve Each equation has 4 solutions \( \quad \sin x=0.707 \) between \( -360^{\circ} \) and \( 360^{\circ} \). Q1 Q2 - Using your calculator Work out the missing side \( x \). Give your answers to \( 1 \mathrm{~d} \).p. or better. Work out the missing side \( x \). Give your answers to 1 d.p. or better. \( A B C \) is an isosceles \( A B C D \) is a rectangle. \( \quad A B C \) is a right-angled triangle. triangle, with \( A B=A C \). \( \quad A D \) is a bisector of angle \( B A C \). Angle \( D A C=20^{\circ} \) \( x=C D \). Work out angle \( x \). Give your answers to the nearest whale number. \( x= \) [2] \( \quad x= \) [2] \( x= \) [2] \( \quad x= \) Q1 - Simple questions Work out each of these correct to the nearest metre. The radio mast high, and the a elevation showi Work out the le this cable. From the top of a vertical cliff \( 70 \mathrm{~m} \) high, a boat, \( B \), is seen at an angle of depression of \( 29^{\circ} \). How far from the cliff is the boat? Work out each of these correct to 1 d.p. or better. . A person \( 2 \mathrm{~m} \) high observes the angle From a point at the waters edge, a bridge of elevation to the top of a building to arch \( 55 \mathrm{~m} \) away has an angle of elevation be \( 70^{\circ} \), and the angle of depression to of \( 3^{\circ} \), and the top of a yacht mast \( 15 \mathrm{~m} \) the bottom of the building to be \( 28^{\circ} \). away has an angle of elevation of \( 10^{\circ} \). How tall is the building? \( \quad \) Can the yacht pass under the bridge? heiaht \( =1 \mathrm{~m} \) ra1 bridge \( =\ldots \mathrm{m}[1] \) yacht \( =1 \mathrm{~m}[1] \) Type " \( y \) " (yes) or " \( n \) " (no). Find the length \( x \). Give your answers correct to 1 decimal plana Q2 - Coordinates Find the distance \( A B \). Give your answers correct to 1 decimal place. Find the length \( x \). Give all your answers correct to 1 decimal place. \( x \) is the diagonal of this cuboid. \( \begin{array}{lll}x=\quad \mathrm{cm} \text { [2] } & \begin{array}{l}\text { This shape is a square-based } \\ \text { pyramid. } E \text { is directly above } D .\end{array}\end{array} \) This shape is a corner of a cube. \( x \) is the height of triangle \( A B D \). \( x=\quad \mathrm{cm} \quad[3] \) Q2 - A pyramid and a net Calculate the lengths and give your answers correct to 1 decimal place. The height of this square-based Here is the net for an open box. pyramid is \( 4.2 \mathrm{~cm} \). Find the maximum length of a pencil that can be placed entirely within this box. Find the slant height \( s \). \( s= \) [3] length \( = \) Q1 Q1-General questions ( ) Solve the following equations. \( \begin{array}{ll}2^{x} & =2 \\ \text { Q2 } & x=\end{array} \) \( 8^{x}=1 \) Which of these graphs is exponential? [1] \( x= \) [1] Davida invests \( \$ 1300 \) in a bank account for 5 years at an interest rate \( 10^{x}=0.01 \) of \( 4 \% \) per year. How much money does Davida have in her \( x= \) [2] bank account at the end of the 5 years? Label each graph with the correct equation. \[ y=2^{-x} \] Q1 - Match the graphs Here are the graphs of three equations. Match each equation to the letter shown on its graph. \[ \begin{array}{c} 2 x-y=12 \\ 2 x+y=4 \\ 4 x-3 y=18 \end{array} \] Use the graphs to solve these simultaneous equations \[ \begin{array}{r} 2 x-y=12 \\ 4 x-3 y=18 \end{array} \quad x= \] (The answers are whole numbers) Q2 - Draw the graphs You need graph paper to answer these questions. Draw graphs to solve these simultaneous questions. \[ \begin{array}{r} 2 x+3 y=12 \\ 3 x+y=11 \end{array} \quad x= \] \[ \begin{aligned} 4 x+3 y &=15 \\ x-2 y &=12 \end{aligned} \quad x= \] \[ \begin{aligned} 5 x+3 y &=10 \\ x-y &=-10 \quad x= \end{aligned} \] Q1 - Negative coefficients Work these simultaneous equations out \( \quad \) A bow and arrow cost \( £ 32 \). The bow on paper and write down your answers. costs \( E 23 \) more than the arrow. Q2 - Negative solutions Work these simultaneous equations out on paper and write down your answers. \( \begin{array}{ll}7 c+6 d=-11 & c= \\ -2 c-3 d=-2 & d=\end{array} \) \( \begin{array}{cl}-5 x+4 y=-18 & x= \\ x-3 y=8 & y=\end{array} \) \( 7 v+3 w=26 \quad v= \) \( \begin{array}{ll}7 e+2 f=-21 & e= \\ -3 e-f=8 & f=\end{array} \) \( -5 v+4 w=-37 \quad w= \) \( \begin{array}{cl}5 g+7 h=-8 & g= \\ -5 g+3 h=-32 & h=\end{array} \) [6] Q1 - Multiplying both equations Work these simultaneous equations out on paper and write down your answers. Q2 - With decimals Work these simultaneous equations out The cost of \( 8 \mathrm{CD} \) and 7 DVDs is on paper and write down your answers. \( \quad \$ 100.60 \). Q1 - Understanding simultaneous equations Solve these simultaneous equations. \( \begin{array}{ll}4 \text { pillows and } 4 \text { quilts cost } \$ 56 & 4 p+4 q=56 \\ 8 \text { pillows and } 4 \text { quilts cost } \$ 80 & 8 p+4 q=80\end{array} \) \( \begin{array}{ll}8 \text { pillows and } 4 \text { quilts cost } \$ 80 & p= \\ \text { Find the cost of one of each. } & \text { and }\end{array} \) Find the cost of one of each. \( \begin{array}{ll}4 \text { apple pies and } 4 \text { banoffee cost } \$ 12 & 4 a+4 b=12 \\ 4 \text { apple pies and } 7 \text { banoffee cost } \$ 18 & 4 a+7 b=18 \\ \text { Find the cost of one of each. } & a=\end{array} \) 6 mugs and 5 plates cost \( \$ 54 \) 4 mugs and 5 plates cost \( \$ 46 \) Write down and solve simultaneous \( m= \) and \( p= \) equations ( \( m \) is the cost of a mug and \( p \) is the cost of a plate, in \( \$ \) ). Q2 - More practice Solve these simultaneous equations. Q1 - How many roots Match the descriptions to their graphs by dragging them into place. Estimate the roots from the graphs. For the graph of \( y=x^{2}+4 x+3 \) Find the \( y \)-intercept: \( (0 \), Factorise: \( \quad(x \quad)(x-0 \) The \( x \)-intercepts are: 0) 0) The turning point is: Drag these four points onto the axes, then drag the curve shown in grey to fit. Q1 - Plotting a curve Complete the table of values for \( y=x^{2}+2 \) Drag the crosses to the correct points on the graph. Q2 - Plotting a harder curve Complete the table of values for \( y=-x^{2}-6 x-5 \) Choose five \( x \) values so that you accurately show its shape and plot the points on the graph provided. These should include the turning point and points around it. Drag the crosses to the correct points on the graph. Q1 - Term-to-term rules Find the next three terms in the following sequences, and drag the correct term-to-term rule into place. Q2 - nth term rules The \( n^{\text {th }} \) term of a sequence is \( 8(n+5) \). What are the first four terms? What is the \( 30^{\text {th }} \) term? Which is the first term to be larger than 100? The \( [4] \) [2] (2) The \( n \)th term of a sequence is \( n(n+1) \). What are the first four terms? Is 51 a term in the sequence? Which term is 182 ? The Q1 - Finding gradients and intercepts Write down the gradient and intercept of these lines: \( \begin{array}{lll}y=7 x-9 & \text { gradient }= & \text { intercept }= \\ y=2-x & \text { gradient }= & \text { intercept }=\end{array} \) Rearrange these equations in the form \( y=m x+c \). Write down their gradients and intercepts. \[ \begin{array}{lll} x-y=9 & y= & m= \\ 2 y=6 x-8 & y= & c= \\ 4 x-5 y=17 & y= & m= \\ & m= \end{array} \] Q2 - Matching equations to graphs Write down the letter of the line that matches each equation. \[ \begin{array}{r} 2 x+y+3=0 \\ 2 x+3 y=6 \\ 3 x-2 y=6 \end{array} \] Work out the gradient of a line that is parallel to \[ -2 x+y-3=0 \] Find the gradient of the line \[ 4 x=-5 y+5 \] Q1 Q1-Using more than one letter and powers Q Work out the value of these expressions. 15 Q1 - Using more than one letter and powers Work out the value of these expressions.