Download d 30 cm 22.5 cm National 5 Maths Homework 1 SECTION A (No

National 5 Maths Homework 1
SECTION A (No calculator allowed – SHOW ALL WORKING)
a) 3.5 – 0.55 x 10
1. Find
b) 7% of £19
c) 12 ½ % of £840
2. Expand and simplify
a) (3x – 4)(x + 3)
b) (3y + 7)(3y - 7)
c) (x - 6)2
3. A semi circle has a radius of 3 cm. Find the a) Area
of the semi-circle. [Leave your answers in terms of π].
4. Factorise the following expressions:
a) 4x + 8
b) 12x – 14
3

e)  m  
m

d) 3(x + 1)2
and
2
b) Perimeter
c) 3x2 – 6x
d) 6x + 10y – 24
5. Find the gradient and the coordinate of the y-intercept for each of the following straight lines;
a) y = 4 x + 6
b) y = 6 + 5x
c) y = -9 + 4x
d) y = -6x -4
e) 4 = y + 5x
SECTION B (a calculator may be used, WORKING MUST BE SHOWN)
6. a) Make an equation and solve it to find the length of each side in the triangle shown;
20
y
12 cm
y+2
b) Then find the area of the triangle.
7.
Calculate the area of the kite sketched here.
8.
Solve 2  5(3 y  2)  4(1  2 y) where y is a positive integer.
9.
A rectangular picture frame is to be made. It is 30 cm high and 22.5cm wide,
as shown in the diagram.
To check that the frame is rectangular, the diagonal, d, is measured.
The diagonal is found to be 37.5cm in length.
20 cm
d
30 cm
Is the frame rectangular? Justify your answer.
2𝑥 2 −6𝑥
22.5 cm
in its simplest form(factorisng will help)
10.
2
3
a) Solve  6 
x
x
11.
Use trigonometry to calculate the angle between the diagonal and the base of the picture frame in Q9.
12.
Find the length of the side marked k.
b) Express
4𝑥−12
k
32˚
12 cm