Question 1 (10 marks)
(a)
The sum of two consecutive even numbers is 34.
2
Find both of the numbers.
x−3
>8
2
(b)
Solve the inequality
(c)
Solve the following equation:
1
2
2
3
=
x−1
2x + 1
(d)
Find the equation of the line that passes through the midpoint of (3, 1) and (−5, 5),
and is perpendicular to the line x − 2y + 3 = 0.
3
(e)
A chocolate costs $3 more than a lolly. If four chocolates and six lollies cost $68,
find their individual prices.
2
End of Question 1
Matt Cash Mathematics Practice Exam
Year 10 Mathematics
Question 2 (10 marks)
(a)
From the top of a 150 m high building, the angle of depression to the bottom of
a second building is 25◦ while the angle of depression to the top of the building is
12◦ . Calculate the height of the second building to two decimal places.
3
(b)
In a triangle with sides 9 cm, 7 cm and 4 cm, find cos α where α is the smallest
√
angle and hence show that the exact area is 6 5.
3
(c)
The diagram below shows two buildings AY and BX that are 40 m and 50 m tall,
respectively. The bases A and B are x metres apart. An observer due South of B
observes the points X and Y at angles of elevation 34◦ 15′ and 12◦ 40′ respectively.
2
X
Y
50 cm
40 m
B
A
34◦ 15′
12◦ 40′
C
Find the distance between the two buildings.
(d)
Simplify sin (180 + θ) + cos (270 + θ).
End of Question 2
Matt Cash Mathematics Practice Exam
Year 10 Mathematics
2
Question 3 (10 marks)
(a)
Factorise 6x2 − x − 2.
2
(b)
Complete the square for −4x2 − 24x − 39.
3
(c)
Solve the quadratic equation 5x2 + 7x − 12 = 0.
2
(d)
Two numbers a and b differ by 4. Find all possible numbers if one of the numbers
is the other number squared.
3
End of Question 3
Matt Cash Mathematics Practice Exam
Year 10 Mathematics
Question 4 (10 marks)
(i)
How many solutions does the quadratic equation x2 + 6x + 15 = 0 have?
1
(ii)
Hence, sketch the parabola y = x2 + 6x + 15 including all features.
2
Find the values of m such that the line y = mx is a tangent to the parabola
y = 2x2 + 3.
2
(c)
Sketch the parabola y = 4 − 3(x + 1)2 including all features.
3
(d)
Find the minimum value of the expression 3x2 + 12x − 5.
2
(a)
(b)
End of Question 4
Matt Cash Mathematics Practice Exam
Year 10 Mathematics