Grade 10 Mathematics Mock 2020 - Copy - copy
Subject
Grade
Mathematics
Grade 10
Points
A 12
D 16
B 13
C 34
Duration
Start time
120 mins
Mar 24, 12:06 pm
Mar 24, 12:06 pm(School TZ)
Knowing and Understanding
Q1
Describe the transformation from A to B.
A1
C1
Explanation
Rotation
clockwise about the origin.
Page 1 of 25
Q2
A1
C1
Explanation
1)
2)
3)
Page 2 of 25
A, B, C and D are points on a circle, center O. AC is a diameter of the circle. AT is a tangent to the
circle. Answer the following questions (1.3 , 1.4)
Q3
A1
Find the size of angle
and . Give reasons for your answer.
C1
Explanation
x = 60
y = 36
Page 3 of 25
Q4
A1
If the length of OD is 4 cm, find the length of CB. Write your answer as an exact value.
C1
Explanation
Radius = 4
Diameter = 8
Page 4 of 25
Q5
A1
C1
Expression
Positive/negative/Zero
a
c
b2 – 4ac (Discriminant)
b
Explanation
'a' is negative as the function is concave down.
'c' is negative as the y-intercept is negative on the graph.
is zero as the graph crosses the x-axis once.
'b' is positive as the vertex has a positive x coordinate, therefore
and 'a' is negative.
Page 5 of 25
Q6
A1
C1
Fill the table and match the Graph with the appropriate description.
Which Graph? (i,ii,iii,iv)
Reason
a)
b)
c)
d)
Explanation
Which Graph?
Reason?
2
a)
ii
-6
3
b)
i
No 'c' value
4
c)
iii
Discriminant is negative
Page 6 of 25
5
d)
iv
'a' is negative, -b/2a is negative,
'c' is positive.
The diagram shows triangle ABC. Point C has coordinates (4, 7) and the equation of the line AB is x + 2y
= 8. Answer the following questions (1.7, 1.8, 1.9)
diagram not to scale
Q7
Find the coordinates of A and B.
A1
C1
Explanation
A(0,4)
B(8,0)
Page 7 of 25
Q8
Show that the distance between A and B is 8.94 correct to 3 significant figures.
A1
C1
Explanation
AB =
Q9
N lies on the line AB. The line CN is perpendicular to the line AB.
Find the equation of CN.
A1
C1
Explanation
CN:
Page 8 of 25
Q10 There are only red marbles and green marbles in a bag. There are 5 red marbles and 3
green marbles.
A1
C1
Dwayne takes at random a marble from the bag. He does not put the marble back in
the bag. Dwayne takes at random a second marble from the bag.
1) Complete the probability tree diagram. (fill the empty spaces or just type the
answers in the space below)
2) Find the probability that Dwayne takes marbles of different colors.
Explanation
1)
,
,
,
2) P(RG)+P(GR)=
Page 9 of 25
Q11 The cumulative frequency graph has been drawn from a frequency table showing the
time (in minutes) it takes a number of students to complete a computer game.
A1
C1
Use the graph,
1) Write down the median time
2) Find the interquartile range.
Explanation
a) Median = 25 minutes.
b) Q1 = 18, Q3= 32
IQR = 32-18 = 14
Page 10 of 25
Q12
A1
C1
Explanation
Level
Frequency
CF
1
5
5
2
8
14
3
16
30
4
18
48
5
x
48+x
6
x-3
45+2x
Median position =
a) Maximum value for x happens when the median position is 48,
b) Minimum value for x happens when the median position is 31
Page 11 of 25
Applying Mathematics in real-life contexts
Task 2: Applying Mathematics in Real life context
In this task, you will use relationships in Mathematics within the global context Globalization
and sustainability with the focus on the impact of decision-making on humankind and the
environment. This task focuses on criterion D (Applying Mathematics in real life context)
and criterion C (Communication).
Anne’s parents are planning to buy a new car. They can either purchase a normal car or an off-peak
car(OPC). Off-peak cars or red plates cars, were introduced in 1994 to ease traffic congestion
during peak hours.There are some restrictions and benefits for using an OPC. In this task, you will
apply your mathematical knowledge to help Anne’s parents decide whether they should purchase a
normal car or an off peak car (OPC).
Reference:
Mark, Geraldine. Columnsshould You Renew The COE For Your Off-Peak Car?. 2020,
https://dollarsandsense.sg/complete-guide- ling-personal-income-tax-2020/. Accessed 19 Mar 2020.
Page 12 of 25
General information about the Off Peak Car (OPC)
Page 13 of 25
Q1
Factor one:
Price of the car
C2
D2
If Anne’s parents are interested in buying a normal car that costs $62800, and
are able to pay $15000 of its price as a down payment, planning to take a loan
from a bank for the remaining amount.
Calculate how much money they need to take from the bank.
Explanation
Amount money they need to take from the bank
62800-15000=47800
Q2
For a car loan, the bank charges a fixed interest of 2.5% per year,
Calculate the amount of interest Anne’s parents will pay for a 1-year loan.
C2
D2
Explanation
Amount of interest paid per year
2.5%
47800=1195
Page 14 of 25
Q3
Calculate the amount of interest Anne’s parents will pay for a 7 years’ loan.
C2
D2
Explanation
Amount of interest paid for 7 years
1195
7=8365
Q4
C2
Calculate the monthly instalments for the 7 years’ car loan
“consider each year to be 12 months”.
D2
Explanation
One year is 12 months
Seven years is 84 months
Amount of interest for 7 years 8365
Total amount of money to be paid for the bank:
Loan amount+interest for 7 years=
47800+ 8365 = 56165
Monthly instalments for 7 years
56165
84= 668.6309
Rounded to (2dp) 668.63
Page 15 of 25
Q5
C2
If the car Anne’s parents are interested to buy was an OPC, Calculate the
monthly instalments for the car.
(Recall that the car costs $62800, down payment is $15000, vehicle tax refund
17000, interest rate is 2.5%, and the loan is for 7 years)
D2
Explanation
Amount of loan:
62800-15000-17000= 30800
Interest for 7 years
30800
2.5%
7= 5390
Total amount of money to be paid to the bank
5390+30800 = 36190
Monthly instalments for 7 years
36190
84= 430.8333333
rounded to 2dp =430.83
Page 16 of 25
Q6
C2
Factor two:
Annual road Tax
To calculate the annual road tax, use the formulae given in the below table that
depends on the capacity of the engine (EC). You will just need to substitute a
number EC in the appropriate formula.
"Remember the OPC has a discount of 500$, subject to a minimum annual road
tax of $70".
D2
If the car they want to buy is a car with an engine capacity (EC) of 1400 cc,
calculate the annual road tax for:
1. a normal car
2. an OPC
Explanation
Normal car road tax
(250+0,375(1400-100))
0.782
625.6
=
OPC road tax
"Remember the OPC has a discount of 500$, subject to a
minimum annual road tax of $70".
so road tax will
625.6-500=125.6
Page 17 of 25
Q7
Factor Three
C2
D2
Expenses involved in owning a car
If her parents are planning to use the car during the weekends, the five public
holidays and on 2 weekdays per week during restricted hours.
Calculate the total annual expenses for buying a normal car.
You will need to use your answers from the previous questions.
(ignore fuel and maintenance costs)
Explanation
Total expenses:
Yearly bank instalments+insurance+ Road tax=
+ 1800 + 625.60= 10,449.171
Rounded to 2dp 10449.17
Page 18 of 25
Q8
C2
Help Anne’s parents make the best choice between a normal car or an OPC.
In your answer you should:
Identify the relevant information. (you may fill the below table) Calculate
the total expenses for buying an OPC for 12 months (52 weeks) and state
whether your answers make sense in the context of the question.
D2
Choose one type of car and justify your choice.
Justify the degree of the accuracy of the calculations.
Yearly bank loan
Annual road tax
instalments
Annual expenses
involved in owning a
car
Normal Car
OPC
Explanation
Identify the relevant information. (you may fill the below table)
Yearly bank loan
instalments
Annual road tax
Annual expenses involved
in owning a car
Normal car
8023.56
625.6
1800
OPC
5169.96
125.6
1650+
Calculate the total expenses for buying an OPC for 12 months (52 weeks) and state
whether your answers make sense in the context of the question.
5169.96+125.6+3730= 9025.56
Choose one type of car and justify your choice.
choosing normal car
No restrictions.
It's total cost is only $1000 more than the cost of OPC.
The annual expenses involved in owning a normal car is almost half the expenses
of owning an OPC, so the $1000 increase in the total cost is due to the loan interest.
Page 19 of 25
Therefore I might think of increasing the amount of down payment to decrease the
amount of the interest.
Choosing OPC car
Help in decreasing the usage of cars, therefore we will decrease the traffic and the
pollution caused by cars.
Its total cost is less than the normal cars.
It will be a good choice if i cannot afford to increase the amount of down
payment due to the vehicle tax refund.
Justify the degree of the accuracy of the calculations.
I rounded to 2 decimal places since it is money and two places are sufficient to
include cents. My answers are considered accurate to a certain extent, as it might
depend on the situation and the usage of the car. these are averages as a
whole.......
Page 20 of 25
Investigating Patterns
Task 3: Investigating patterns:
In this task, apply your understanding of form to investigate patterns and general terms between the
matches shapes. This task focuses on criterion B (Investigating patterns) and criterion C
(Communication).
Page 21 of 25
Q1
B4
Consider the following pattern using matches and ll the table below:
Shape 1
Shape 2
Shape number (n)
Shape 3
Total number of
Added matches (A)
Perimeter (P)
matches used (T )
1
6
---
5
2
11
5
8
3
4
Explanation
n
T
Added
P
1
6
--
5
2
11
5
8
3
16
5
11
4
21
5
14
5
26
5
17
6
31
5
20
Page 22 of 25
Q2
B2
Describe in words any two patterns you have noticed from the table.
C2
Explanation
T starts with 6 and increases by 5
In Added Matches column it stays 5's
P starts with 5 and increases by 3
Or any Pattern make sense and communicated logically
Q3
B1
Write down a general rule for the total number of matches used (T) in terms of n.
Explanation
T= 5n+1
Page 23 of 25
Q4
B1
Verify your general rule in question 3.3
C1
Explanation
n=3
and this matches the table above
n=4
and this matches the table above
Q5
B2
Write down the general rule connecting P and n
Explanation
Q6
B1
Verify your general rule in question 3.5
C1
Explanation
n=3
and this matches the table above
n=4
and this matches the table above
Page 24 of 25
Q7
Investigate to nd a relationship for P in terms of T. In your answer, you should:
predict more values and record these in the table
B2
C2
nd a general rule for P in terms of T
test your general rule for P
Verify your rule
If the perimeter P= 20, nd the total number of matches T.
Explanation
Fill the table and possibly add an extra value
Test when T=1,2 substitute and say matching the result in the table
Verify
and this matches
the result in the table
since 5x20 = 3T+7
100-7=3T
Page 25 of 25