Download Practice Test B

National 5 Maths
Relationships Part 2: Practice Test B
Assessment Standard 1.1: Linear Equations (need 6 out of 11 to pass)
1) A straight line with gradient –6 passes through the point (2, –3). 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 7w – 27 < 3w – 7
(3 marks)
Success criteria:
 Remember to do the opposite when moving to the other side
 Answer begins ‘p < ’
3) Seven large laptops and four small laptops weigh 76kg. Write an equation to
represent this information.
(#2.1)
4) Solve the following system of equations algebraically:
5u + 3v = 53
u + 2v = 19
(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.
6g
9 .
x
Change the subject of the formula to g.
5) A formula is given by: P 
(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 = 5 sin 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 = cos 4x.
(1 mark)
Success criteria:
 Remember units (degrees) in answer (mark will be lost otherwise)
8) Solve the equation 4 tan x° – 9 = 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) Dentists need a piece of equipment that is a perfect right-angled triangle. A
triangle is given with sides of 78cm, 72cm and 150cm. 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 O. PQ is tangent to
the circle at P, and QR is tangent to the
circle at R. Given that angle PQR is 39°,
find the size of angle POR. (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 perfume bottle is 6cm.
The volume it holds is 30ml.
A larger mathematically similar
bottle is 9 cm tall. Calculate the
volume of the larger bottle.
(3 marks)
Success criteria:
 Find linear scale factor by dividing.
 Use correct power (squaring or cubing).
 Answer with units.