SOS-HERMANN GMEINER INTERNATIONAL COLLEGE
DISTANCE INTERVENTION PROGRAMME
(A Learning Support Programme for Candidates Preparing for SOS-HGIC)
Module Tasks for 2019 - 2021
FIRST NAME(S): ....…………………. SURNAME: ……………………..…… GENDER: ………..
COUNTRY: ………………………….. SOS VILLAGE: ……………..………
GRADE/CLASS: …………………….. DATE: ..............................
MATHEMATICS
CODE: MT8C (Algebra)
TIME: 1 hour
INSTRUCTIONS
Answers are to be written in ink in the spaces provided on the question paper.


It is absolutely necessary for candidates to do all exercises on their own without the help of
dictionaries and other textbooks or notes, or the assistance of other persons.
These exercises are not speed tests, but candidates should be encouraged to work as carefully
and quickly as possible within the stipulated time and also go over their work before handing it
in. You should show your working in the space below each question.
Total
Percentage
Section A: (recommended amount of time for this section is 10 minutes)
1. Simplify the expression
Answer: ………………………………………………………………………………. [1]
2. Simplify the expression
Answer: ………………………………………………………………………………. [1]
3. Simplify the expression
Answer: ………………………………………………………………………………. [1]
4. Simplify the expression
Answer: ……………………………………………………………………………….. [1]
5. Simplify
Answer: ……………………………………………………………………………… [1]
6. Simplify
Answer: ……………………………………………………………………………… [1]
2
7. Simplify each of following by collecting like terms and factorising:
Answer: ……………………………………………………………………………… [3]
8. Simplify each of following by collecting like terms and factorising (note there may be more than
one possible answer).
Answer: ……………………………………………………………………………… [2]
9. Simplify each of the following by expanding the following
(
)
Answer: ……………………………………………………………………………… [2]
10. Simplify each of the following by expanding the following and then refactorising
Answer: ……………………………………………………………………………… [2]
3
Section B: (recommended amount of time for this section is 15 minutes)
1. Allison has three boxes of chocolate and five extra pieces of chocolate. Atlas has four boxes of
chocolate and eight extra pieces of chocolate. Suppose each box of chocolate has x pieces of
chocolate.
a. Write an expression for the total number of pieces Allison has.
Answer: …………………………………………………………………………………… [1]
b. Write an expression for the total number of pieces Atlas has.
Answer: …………………………………………………………………………………… [1]
c. Write an expression for the total number of pieces they have together.
Answer: …………………………………………………………………………………… [1]
2. Simplify each of the following inequalities
a.
Answer: …………………………………………………………………………………… [2]
b.
Answer: …………………………………………………………………………………… [2]
4
3. Find the integers which simultaneously satisfy each of the following pairs of inequalities:
Answer: ………………………………………………………………………………. [3]
4.
a. Write the following equation as a quadratic equation:
Answer: ………………………………………………………………………………. [2]
b. Solve the quadratic equation by factorization.
Answer: ………………………………………………………………………………. [3]
5
Section C: (recommended time for this section is 20 minutes)
1. When Claudette stands on a table and Dina stands on the floor, Claudette is 80 cm taller than
Dina. When Dina stands on the table and Claudette stands on the floor, Dina is 1 m taller than
Claudette.
How tall is the table?
Answer: ………………………………………………….… [4]
2. Grandma has calculated that she is four times as old as I am now, but remembers that 5 years
ago she was five times as old as I was at that time.
Calculate Granma’s age now?
Answer: ………………………………………………….… [4]
3. Jane made a mistake when writing down a multiplication, and she multiplied by 54 instead of
45.
Her answer was 198 more than it should have been.
What number did she multiply 54 by?
Answer: ………………………………………………….… [4]
6
4.
a. Sketch the following equation
between x =3 and x = 7 on the grid below.
Do not forget to add axis, number and label your axes.
[5]
7
b. Using or graph or otherwise, calculate the area between the lines
and the x-axis?
Answer: ………………………………………………….…,, [3]
8
Section D: (recommended amount of time for this section is 15 minutes)
1. Two pyramids and a sphere on one side of a pair of scales will just balance a cube on the other
side.
A sphere and a cube together will just balance three pyramids.
How many spheres will just balance a single pyramid?
Answer: ……………………………………………………… [4]
9
2. An athletics club has two types
The 'perimeter' of a cuboid can be measured along three axes.
One 'perimeter' of this cuboid is shown.
If the 'perimeters' of a cuboid are 12 cm, 16 cm and 24 cm, what is the volume of the cuboid
10
Answer: ……………………………………………………… [6]
11