Queen Anne High School Maths
Practice Paper 2 - Relationships Unit Assessment (National 5)
1
A straight line with a gradient of 3 passes through the point (4, - 8). Determine the equation
of this straight line in its simplest form.
2
Solve the inequation 9x – 15 < 7x + 3
3
Joe and Jim cycled the 21 miles from Dunfermline to Dollar. At Dollar, they went into Cafe
de Fleurs for refreshments. Joe and Jim ordered up 1 coffee and 2 scones which came to
£8.90. Write an equation which connects the total price to the refreshments purchased.
4
Solve the following system of equations algebraically: 5x + 3y = 1
3x – 2y = 12
5
Change the subject of the formula to x
y = 4x2 - 3
6
The diagram below shows the graph of y = – x
2
The point (-3, k) lies on the graph, find the value of k
PRACTICE 2 - Unit Assessment - Relationships (National 5) Unit
QAHS Maths Website: http://maths.qahs.org.uk > Home Study > National 5
Mr Milton Nov 2014
7
The equation of the quadratic function whose graph is shown below is of the form
y = (x + a)2 + b, where a and b are integers.
Write down the values of a & b
8
Sketch the graph y = x2 + 2x – 8 on plain paper. Mark clearly where the graph crosses the x
and y axes and state the coordinates of the turning point.
9
A parabola has equation y = (x – 7)2 + 9
(a) Write down the equation of its axis of symmetry.
(b) Write down the coordinates of the turning point on the parabola and state whether it is a
maximum or minimum.
10
(a) Factorise
x2 - 6x + 5 = 0
(b) Hence solve the equation
11
Solve the equation x2 - x – 1 = 0 giving your answer correct to 1 decimal place.
12
Determine the nature of the roots of the equation
3x2 – 6x + 3 = 0.
PRACTICE 2 - Unit Assessment - Relationships (National 5) Unit
QAHS Maths Website: http://maths.qahs.org.uk > Home Study > National 5
Mr Milton Nov 2014
13
Use the Converse of Pythagoras’ Theorem to determine whether the triangle below is right
angled.
20 cm
25 cm
15 cm
14
In the diagram below, angles ABC = 35°, BAD = 62°, Points A, B & D touch the circle.
Calculate the size of the shaded angle
PRACTICE 2 - Unit Assessment - Relationships (National 5) Unit
QAHS Maths Website: http://maths.qahs.org.uk > Home Study > National 5
Mr Milton Nov 2014
15
Two jugs are mathematically similar. Find the volume of the larger jug if the volume of the
smaller jug is 0.8 litres
16
Calculate the size of the shaded angle in the regular pentagon shown below :
.
17
Sketch the graph of y = 4 cos x° for 0  x  360 .
18
Write down the Period of the graph of the equation y = cos 3x°.
19
Solve the equation 3 sinx° - 1 = 0, 0  x  360
.
PRACTICE 2 - Unit Assessment - Relationships (National 5) Unit
QAHS Maths Website: http://maths.qahs.org.uk > Home Study > National 5
Mr Milton Nov 2014