Practice Paper Z
Paper 1 - 42 Marks
You may not use a calculator.
Disclaimer: This is just an example of questions similar to the ones you may come across in the National 5 Exam.
These can be used to help your revision for the National 5 exam but will only form a small part of your overall studies.
1.
Evaluate
2 Marks
2.
Expand and Simplify
(3x – 7)(2x + 3) + 2x(6 – x)
3 Marks
3.
Given that f(x) = 3x – x²
Calculate f(–2)
2 Marks
4
Find the equation of the line that cross through points
A(–7, 17) and B(5, –7)
Give the equation in its simplest form.
3 Marks
5
A parabola has equation y = x² – 6x + 19
a Write the equation in the form y = (x – p)² + q
2 Marks
b Hence, sketch the graph of y = x² – 6x + 19
On your sketch, clearly show the coordinates of the turning point
and the intersection with the y-axis.
3 Marks
6
Determine the nature of the roots of the function f(x) = 3x² – 4x + 7
2 Marks
7
The diagram shows triangle JKL
Calculate the area of triangle JKL
3 Marks
8
Solve algebraically the system of equations
5x + 2y = 4
4x + 3y = 13
3 Marks
9
Express this fraction with a rational denominator.
Give your answer in its simplest form.
3 Marks
10
Evaluate
2 Marks
11.
Change the subject of
to x
3 Marks
12
In the diagram vectors a and b are represented by UT and TS respectively
a Express PT in terms of a and b
1 Mark
b Express QU in terms of a and b
1 Marks
13.
Solve the equation
3 Marks
14
The diagram shows a swimming pool with paving around the outside.
The paving is 1m wide around 3 sides of the pool and 2m on one side.
The area of the pool is 54m².
a Express the length of the pool in terms of x
1 Mark
b Hence, show that 2x² – 7x – 60 = 0
2 Marks
c Algebraically find the value of x
3 Marks
End of Paper