Elementary Mathematics Test (Intermediate)

20 Questions - Developed by:
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This test consists of 20 questions. (Revised)

It consist of topics tested commonly such as algebraic manipulation, graph analysis, ratio and proportions, angles and circle properties, geometry, trigonometry, practical situations and others.

When the final value is given as an irrational number, round the figure up to 3 significant figures, and angles to 1 decimal place.

• 1
(a³ - a²) ÷ a²
• 2
Y is inversely proportional to x + 1. It is known that the sums of y = 12 when x = 5 and x = 29. Find the value of y when x = 4.
• 3
John sells books at \$25 each. It is known that he makes a profit of 150% per book. Find the cost price.

• 4
Triangle ABC is given. AB = BC is 300 cm while AC is 450 cm. Find ∠ABC.
• 5
With the given information and answer provided from question 4, find the area of triangle ABC. (Round final value up to nearest whole number)
• 6
Sector ABC is given. AB is a radius of 10cm while BC is an arc with (10/9)π cm. Applying circle properties, find the ratio of sector ABC to a circle.

• 7
Find x. Given,
2^x = 36 - 2²

^ means to the power of.
• 8
Alan invested a certain amount of money in a bank for 2 years, paying 5% per annum compound interest. After 2 years, he had received \$8000 worth of interest.

How much did Alan invested?
• 9
It is known that the turning point of the curve is y < 0 and passes through points (-1,0) and (3,0). Find the equation of the curve.
• 10
A car travelled constantly at 20m/s from 0 to 25 seconds and constantly decelerates to the complete stop at the 40th second.

Find the total distance travelled by the car.

• 11
The information below shows the scores of students from an English Test.

Row 1: Marks
Row 2: Students

1. | 5 | 8 | 10 | 9 |
-----------------------
2. |20|10|15|14|

Find the standard deviation.
• 12
The specification of a prism is as follows:
A square base with sides of 10cm, with a circle cut out in the middle, of diameter 4 cm. The height of the prism is 30cm. Find the volume of the prism. (Round the final value off to the nearest whole number)
• 13
Triangle ABC is given. AB = 30 cm, AC = 40 cm. ∠BAC = 90º and BC is the hypotenuse of AB and AC. There is a line extension at C, forming line CD.
Find the value of Cos ∠BCD.
• 14
A triangle consists of sides 5 units. When sides are reduced by 3 units, find the percentage change in the area of the triangle.
• 15
Vector A has coordinates (3,9). Find the length of vector A.
• 16
John was resting at a bench at a park. He stood up and walked 30m North, reaching the playground. He turned a bearing of 150º, walking 60m till he reached a lighthouse. He then walked back to the bench and have a rest.

It is also known that an ice cream cart was somewhere in between the playground and the lighthouse, and also directly opposite to the bench within a short distance.

Hence, find the length of the short distance.

• 17
10 microseconds can be written as 10 x _____ seconds.
• 18
Scale is given as 1:1000000. If the area of the road is 26km², find the area of the road when it is scaled.
• 19
Pi is a/an _____ number.
• 20
There is 1/6 full of oil in a tank. If 40 liters of oil is added into the tank, it will be 2/5 full. How much oil does the tank have before 40 liters of oil was added?