Year 10 Common – Term 2 2021
TIME : 60 minutes (plus 5 minutes reading time)
Name:
Teacher: Class:
Directions
• Full working should be shown in every question.
Marks may be deducted for careless or badly arranged work.
• Use permanent black or blue pen only (not pencils) to write your solutions.
• No liquid paper/correction tape is to be used.
If a correction is to be made, one line is to be ruled through the incorrect answer.
• The diagrams are not to scale.
• BOSTES approved calculators are allowed in the exam
(For Teacher use only)
Marking Grid
Coordinate
Polynomials Probability Trigonometry Total
Geometry
7 1-4 5-6
Page 2
/1 /9 /4 /14
10 9 8
Page 3
/3 /2 /7 /12
12,13 11 14
Page 4
/7 /2 /2 /11
15 16
Page 5
/5 /8 /13
17 18,19
Page 6
/3 /5 /8
2,4 5 3 1
Multiple
Choice
/2 /1 /1 /1 /5
Total /13 /14 /22 /14 /63
1 Find the exact value of cos 210° 1 4 Sketch the graph of 2
y = sin x for 0° ≤ θ ≤ 360° .
2 Find the value of 𝑥𝑥, leaving your answer 2 x
to 2 decimal places.
5 Find the equation of a line that has a gradient 2
of 5 and has an x-intercept of 9.
Calculate the exact perpendicular distance 2
from 3 x − y − 10 =0 to the point (4,5).
3 Solve for θ for 0° ≤ θ ≤ 360°
a) cos 𝜃𝜃 = −0.5 2
7 Eight runners are participating in 400 metre 1
race. Assuming all runners have the same
chance of winning, in how many ways can
2 gold, silver and bronze medals be awarded?
b) sin θ = 3 cos θ
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8 9 2
On the diagram above the line 𝐿𝐿1 is parallel Find the shaded area of 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵.
with the 𝑥𝑥-axis and crosses the 𝑦𝑦-axis at 6. Give your answer correct to 2 decimal places.
Lines 𝐿𝐿2 and 𝐿𝐿3 each pass through the origin,
𝑂𝑂, and intersect with the line 𝐿𝐿1 at the points
𝐴𝐴(𝑎𝑎, 6) and 𝐵𝐵(𝑏𝑏, 6) respectively.
The point 𝐶𝐶(−2, −4) lies on the line 𝐿𝐿2 .
a) Show that the equation of the line 𝐿𝐿2 2
is 2 x − y = 0.
10 Given 6 x 3 − 3 x 2 + 2=
x Q( x) × (2 x − 1) + R( x) 3
Find Q( x) and R( x) , where 𝑅𝑅(𝑥𝑥) is the
remainder when divided by 𝑄𝑄(𝑥𝑥).
b) Show that the 𝑥𝑥-coordinate of point 𝐵𝐵 1
is 3.
c) Find the coordinates of point 𝐴𝐴 such 2
that ∠AOB is a right angle.
d) Find the area of ∆AOB . 2
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11 In the Δ𝐴𝐴𝐴𝐴𝐴𝐴, 𝐴𝐴𝐴𝐴 = 9, 𝐵𝐵𝐵𝐵 = 8 and 2
∠𝐶𝐶𝐶𝐶𝐶𝐶 = 60° 13 A bag contains 6 green and 3 red balls.
Two balls are picked at random without
Find all the possible values of ∠𝐴𝐴𝐴𝐴𝐴𝐴 to the replacement.
nearest degree. a) Draw the probability tree. 2
b) What is the probability of getting two 1
green balls?
c) What is the probability of getting at least 1
one red ball?
12 Find P ( A ∩ B ') when 3
P( A=
∪ B) 0.71,= P( A) 0.5 and P ( B ) = 0.4 . 14 Find all possible values 𝑘𝑘 may take if the 2
shortest distance of the line x + 4 y − 7 =0
is 5 units from the point (𝑘𝑘, 3).
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15 Sketch the given polynomial showing its
intercepts with the coordinate axis. 16 Stig leaves home and travels on a bearing of
a) = y x 2 (2 x − 1)3 2 238° for 110 km. He then turns and travels
for 270 km on a bearing of 123°. Stig then
turns and travels home.
a) Put ALL the information above on the 2
diagram below.
b) How far does he travel on the final part of 3
his journey, leaving your answer to
2 decimal places.
b) y =( x + 3)(4 − x 2 ) 3
c) Find the true bearing on which he travels 3
for the final part of his journey. Leaving
your answer to the nearest degree
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17 If a polynomial 𝑃𝑃(𝑥𝑥) is divided by (𝑥𝑥 − 2) 3
the remainder is 5 and if divided by (𝑥𝑥 + 1) 19 A series of 5 games is to be played between 2
the remainder is 2. 2 equally matched teams. The first team to
What is the remainder when 𝑃𝑃(𝑥𝑥) is divided win 3 games becomes the champion and the
by (𝑥𝑥 − 2)(𝑥𝑥 + 1)? game is over. Team A has won the first game.
Find the probability that team A will be the
champion.
18 a) How many ways can 7 people sit around 1
a circular table?
b) How many ways can 7 people sit around
a circular table if 2 particular people want 2
to sit together as a group?
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(D) 305°
~ Multiple Choice ~ 4 Which of the following polynomials have only
Circle the most appropriate answer. one root at 𝑥𝑥 = −4?
1 Which of the following inequations satisfy the
(A) (𝑥𝑥 − 4)(𝑥𝑥 2 + 2𝑥𝑥 + 2)
shaded region?
(B) (𝑥𝑥 − 4)(𝑥𝑥 2 + 2𝑥𝑥 − 2)
(C) (𝑥𝑥 + 4)(𝑥𝑥 2 + 2𝑥𝑥 + 2)
(D) (𝑥𝑥 + 4)(𝑥𝑥 2 + 2𝑥𝑥 − 2)
5 In the universal set of numbers {1, 2, 3, …100},
the sets 𝐴𝐴, 𝐵𝐵 and 𝐶𝐶 are defined below
(A) y ≤ x 2 − 4 and y ≥ 2 x + 4 A{ all numbers are divisible by 2}
B{ all numbers are divisible by 6}
(B) y ≤ x 2 − 4 and y ≤ 2 x + 4 C{ prime numbers}
(C) y ≥ x 2 − 4 and y ≥ 2 x + 4
Which of the following Venn Diagrams best
(D) y ≥ x 2 − 4 and y ≤ 2 x + 4 represent the information above
(A) (B)
2 Which of the following is NOT a polynomial?
(A) 2𝑥𝑥 4 − √7𝑥𝑥 + 2
(B) 𝑥𝑥 5 − 4𝑥𝑥 −4 + 3
1
(C) −𝑥𝑥 2 �𝑥𝑥 2 − 7𝑥𝑥 − 3�
(D) 6 (C) (D)
3 Given sin 𝐴𝐴 is positive and cos 𝐴𝐴 is negative,
which could be the value of 𝐴𝐴?
(A) 141°
(B) 75°
(C) 210°
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~ End of Exam ~
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