26 questions · 100 marks · ≈ 2 hours
Ali, Beth and Chari pay rent on a piece of woodland.
The annual rent that they pay is such that
the amount Ali pays : the amount Beth pays : the amount Chari pays = 13 : 8 : 11
The amount that Chari pays = $2563
Calculate how much more rent Ali pays than Beth pays.
$ ......................................................
2 Simplify fully 8 2
(
3
)
x
8
12
x
Without using a calculator and showing all your working, evaluate
2 3
51
÷
5
3
Give your answer as a mixed number in its simplest form.
Ashley takes 3 hours and 36 minutes to walk around a lake.
The distance she walks is 11 520 m.
Calculate Ashley’s average speed.
Give your answer in kilometres per hour.
...................................................... kilometres per hour
Liam started a new job on a salary of $45 500
At the end of 1 year he is given a pay increase of 5.5%
At the end of each subsequent year he is given a pay increase of 1.25%
Calculate, to the nearest $, Liam’s salary at the end of 3 years after he started the job.
$ ......................................................
The straight line L has equation 2y - 5 = 3x
Find the gradient of L
The straight line L has equation 2y - 5 = 3x
Find the coordinates of the point where L meets the y-axis.
(............................ , ............................)
Arthur has 10 cards.
Each card has a letter on it and the letters spell the word PICCADILLY
I
C
C
A
D
I
L
L
Y
P
Arthur selects at random 3 of these cards.
L in that order.
Calculate the probability that he selects P
A
Without using a calculator and showing all your working, solve the inequality
6x2 - x - 12 > 0
The function f is defined by
3
x
≠−
f : x ↦
2
x
2
2
(
)
x
Express the inverse function f –1 in the form f –1 : x ↦ ...
f –1 : x ↦ ......................................................
Without using a calculator and showing all your working, express 6
8
−
2
8
b where a and b are integers.
in the form a +
Given that –3x2 + 6x + 2 can be written in the form a(x + b)2 + c where a, b and c are integers,
find the value of a, the value of b and the value of c.
a = ......................................................
b = ......................................................
c = ......................................................
The incomplete table and pie chart below show information about the favourite type of
chocolate of 440 adults.
Plain
144°
Complete the table and the pie chart.
Here is information about the age, in years, of each of Jelina’s five children when written
in order.
a b b
a
2 +
2b + a + 3 2b + a + 5
It is given that
a is the age of the youngest child
a
b
≠
two of the children have the same age
the mean age of the five children is 10.6 years
Calculate the value of a and the value of b
Show clear algebraic working.
a = ......................................................
b = ......................................................
B
Diagram NOT
accurately drawn
64°
28°
C
A
D
2 cm
The diagram shows a triangle ABC.
The point D lies on AC so that BD is perpendicular to AC.
ÐBAD = 64°
ÐACB = 28°
AD = 2 cm
Calculate the length, in cm to one decimal place, of BC.
...................................................... cm
4
2
−
2
2
−
Calculate 3A - 2B
0
1
5
3
−
1
−
=
=
P
QP
10
17
3
2
−
−
−
Find the matrix Q
P
2.5 cm
K
Diagram NOT
2 cm
74°
accurately drawn
M
3 cm
J
L
The diagram shows a circle JKML.
JKP and LMP are straight lines.
JK = 3 cm, KP = 2.5 cm and PM = 2 cm.
ÐJPL = 74°
Calculate the area, in cm² to 2 decimal places, of triangle LKP.
...................................................... cm²
Write 0.0234 in standard form.
Write 2.40105 as an ordinary number.
Calculate, giving your answer in standard form
101
2 5
. ×
10
98
−
5
10
×
Show your working clearly.
Simplify 3w7y–34w2y3
3
Simplify (25x4)
2
D
Diagram NOT
accurately drawn
B
E
A
C
F
The diagram shows triangle ABC and triangle ADC.
E is the point on BC and AD.
F is the point on AC such that AB, FE and CD are parallel.
Given that AB = 3 cm and that CD = 7 cm,
calculate the length of FE.
...................................................... cm
C
B
A
D
The diagram shows quadrilateral ABCD.
The region R consists of all the points inside the quadrilateral that are
closer to DA than to DC,
less than 3 cm from the side DC,
more than 4 cm from B.
Using ruler and compasses only and showing all your construction lines, construct and
show, by shading, the region R.
Label the region R.
G
Diagram NOT
F
accurately drawn
x°
E
D
x°
C
B
A
The diagram shows a shaded 7-sided shape ABCDEFG.
The points A, B, C, D, E, F and G are 7 vertices of a regular polygon with 11 sides.
ÐGAB = ÐAGF = x°
Calculate the value, to 3 significant figures, of x.
Show your working clearly.
x = ......................................................
A
B
4 cm
4 cm
Diagram NOT
76°
accurately drawn
O
C
The diagram shows a sector OACB of a circle, centre O.
OA = OB = 4 cm
Angle AOB = 76°
Calculate the area, in cm² to 3 significant figures, of the shaded sector OACB.
.....................................................cm²
A
B
4 cm
4 cm
Diagram NOT
76°
accurately drawn
O
C
The diagram shows a sector OACB of a circle, centre O.
OA = OB = 4 cm
Angle AOB = 76°
Calculate the perimeter, in cm to 3 significant figures, of the shaded sector OACB.
.....................................................cm
y is directly proportional to x3
x is inversely proportional to the square root of w.
y = 729 when x = 4.5
x = 25 when w = 0.16
Find a formula for y in terms of w.
(2x + 1), (10x - 10) and (35x - 5) are the first three terms of a sequence.
The first term of the sequence is (2x + 1) where (2x + 1) ≠ 0
After the first term, all other terms of the sequence are found by using the rule
‘multiply the previous term by d’
Given that x is an integer,
find the value of d.
d = ......................................................
C
Diagram NOT
accurately drawn
A
B
ABC is a triangle.
3
→ =
→ =
→ = 5
x
where x > 0 and AC
BC
AB
2
−
5
x
→ as a column vector.
Find AC
Show clear algebraic working.
A small ball is thrown into the air from a point that is 1 m above horizontal ground.
The ball moves vertically upwards so that at time t seconds after the ball was thrown, the
height, h metres, of the ball above the ground is given by
h = 1 + kt - 5t2 where k is a constant.
At time t seconds after the ball was thrown, the velocity of the ball is v m/s.
Find an expression for v in terms of k and t.
Given that the total distance travelled by the ball between the instant when the ball is
thrown and when it hits the ground for the first time is 161 m,
A small ball is thrown into the air from a point that is 1 m above horizontal ground.
The ball moves vertically upwards so that at time t seconds after the ball was thrown, the
height, h metres, of the ball above the ground is given by
h = 1 + kt - 5t2 where k is a constant.
At time t seconds after the ball was thrown, the velocity of the ball is v m/s.
calculate the value of k.
k = .....................................................