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National 5 Maths Relationships Part 2: Practice Test A Assessment Standard 1.1: Linear Equations (need 6 out of 11 to pass) 1) A straight line with gradient –3 passes through the point (–5, 4). Determine the equation of this straight line. (2 marks) Success criteria: Use the correct formula Simplify by multiplying brackets and collecting like terms 2) Solve the inequation 6q – 11 < q – 1 (3 marks) Success criteria: Remember to do the opposite when moving to the other side Answer begins ‘q < ’ 3) A family visit a theme park. They paid £48·90 for 2 adult tickets and 3 child tickets. Write an equation to represent this information. (#2.1) 4) Solve the following system of equations algebraically: 5a + 3b = 28 a+ b= 8 (3 marks) Success criteria: Multiply through to get the same coefficient, Take away and solve to get one letter. Substitute in to one of the original equations (the easier one) to get the other letter. 2W 17 . T Change the subject of the formula to W. 5) A formula is given by: D (3 marks) Success criteria: Change side and do the opposite. Use ‘backwards BODMAS’ Do not use × or ÷ signs in your final answer. Assessment Standard 1.5: Trigonometry (need 3 out of 6 to pass) 6) Sketch the graph of y = 7 cos x° for 0 x 360 . (2 marks) Success criteria: Correct shape of graph: sin or cos. Clearly label the correct maximum and minimum on y-axis. Correct number of ‘waves’ in 360° (frequency) Label the numbers at which the graph goes through the x axis. 7) Write down the period of the graph of the equation y = sin 3x. (1 mark) Success criteria: Remember units (degrees) in answer (mark will be lost otherwise) 8) Solve the equation 4 sin x° – 1 = 0, 0 x 360 . (3 marks) Success criteria: Rearrange. Use calculator to get acute angle. Use CAST to get remaining answer(s). Remember units (degrees) in answer. (mark will be lost otherwise) Assessment Standard 1.4: Geometry (need 5 out of 9 to pass) 9) Builders need a tool that is a perfect right angle to measure corners. A metal triangle is given with sides of 18cm, 12cm and 23cm. Use the converse of Pythagoras’ Theorem to decide whether this will be suitable. Explain your answer. (2 marks plus #2.2) Success criteria: Show two sums. Communication (#2.2): decision (‘yes’ or ‘no’) Communication (#2.2): ‘right-angled’ or ‘not right-angled’ Communication (#2.2): ‘because ___ = ____’ or ‘because ___ ≠ _____’ 10) The diagram on the right shows a kite CDEF and a circle with centre D. CF is tangent to the circle at C, and EF is tangent to the circle at E. Given that angle CDE is 156°, find the size of angle CFE. (3 marks) Success criteria: Clearly show where right angle(s) are Know what the angles must add up to. Calculate remaining angle (including degree sign) 11) A box is 40cm wide. The volume it holds is 3600 cm3. A smaller mathematically similar smaller box is 12 cm wide. Calculate the volume of the smaller box. (3 marks) Success criteria: Find linear scale factor by dividing. Use correct power (squaring or cubing). Answer with units.