Combination of topics
Questions that combine topics and often have a quadratic twist
1
The diagram shows a rectangle garden with lengths as shown.
a Show that the area, A(x) is given by the formula A(x) = x² + 9x + 20
1 Marks
b The area of the garden is 56m².
Determine the value of x.
4 Marks
Show Answer
x= 3
2
A right angled triangle has dimensions as shown
Calculate the length of KH.
Give your answer as a surd in its simplest form
3 Marks
Show Answer
4 root 3 m
3
A vegetable garden consists of a greens patch in the centre and a path around the edge.
The path is x m wide.
The length and breadth of the entire garden are 13m and 11m respectively.
The area of the greens patch is 82m²
a Write an expression in terms of x for the length of the greens area.
1 Mark
b Hence, show that 4x² - 48x + 61 = 0
2 Marks
c Calculate x, the width of the path.
Give your answer correct to 1 decimal place
4 Marks
Show Answer
a 13 - 2x
c 1.4m
4
The diagram shows a plan of a garden.
The grass section is in shape of a rectangle and a the paved section is in the shape of a right angled triangle.
The total area of the garden is 24m².
a Write the length of the paved section in terms of x.
1 Marks
b Hence, show that x² + 10x - 24 = 0
2 Marks
c Determine algebraically, the value of x.
3 Marks
Show Answer
x = 2m
5
Solve the equation x² – 6x – 3 = 0
Give your answer in the form:
4 Marks
Show Answer
3 plusminus 2 root 3
6
In triangle ABC
sin C = 0.5
BC = x + 7
AC = 4x
The area of triangle ABC is 60cm²
a Show that x² + 7x - 60 = 0
2 Marks
b Hence, algebraically determine the value of x.
3 Marks
Show Answer
5cm
7
A right angled triangle is shown below.
It has sides of x cm and 12cm
The hypotenuse if 2x cm
Calculate the value of x
Give your answer as a surd in its simplest form
3 Marks
Show Answer
4r3
8
The two triangles shown are mathematically similar
a Show that x² + 7x - 60 =0
2 Marks
b Hence, determine the value of x
2 Marks
Show Answer
5
9
A rectangular garden has an area of grass and an area of pavement as shown.
The area of grass has length 7m and breadth 5m.
The path around 2 edges of grass has width x m
a Write down an expression for the length of the garden in terms of x
1 Marks
b Hence show that the area of the whole garden is given by A(x) = x² + 12x + 35
2 Marks
The area of the garden is 90m²
b Determine the value of x
3 Marks
Show Answer
a x + 7
c 3m
10
Triangle RST is shown.
Cos R = 0.5
Calculate the side ST.
Give your answer as a surd in its simplest form
3 Marks
Show Answer
3 root 3
11
A force is represented by the vector u
The magnitude |u| of the vector is
a Show that x² + 2x - 15 = 0
3 Marks
b Hence, determine the possible values of x
2 Marks
Show Answer
x = -5 or 3
12
The floor plan of a ball room consists of a rectangle and a segment of a circle as shown,
a Calculate the length of line OK
3 Marks
b A border is to be fitted around the perimeter of the room.
Calculate the length of border required.
4 Marks
Show Answer
b 30.7m