Elementary Mathematics Test (Intermediate)

  1. Developed by: Mister Ed

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.

Question 1: (a³ - a²) ÷ a²
A
A^1/2
A - 1
A²

Question 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.
10
12
14.4
16

Question 3: John sells books at $25 each. It is known that he makes a profit of 150% per book. Find the cost price.
$16.67
$10
$18
$20

Question 4: Triangle ABC is given. AB = BC is 300 cm while AC is 450 cm. Find ∠ABC.
82.8º
98.5º
97.2º
41.4º

Question 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)
44689 cm²
43647 cm²
44639 cm²
42432 cm²

Question 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.
1:36
5:9
1:9
1:18

Question 7: Find x. Given,
2^x = 36 - 2²

^ means to the power of.
2
8
4
5

Question 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?
$72562.26
$78048.78
$80000.41
$75862.35

Question 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.
X² - 2x + 3
X² + 2x - 3
X² + 2x + 3
X² - 2x - 3

Question 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.
650m
550m
450m
750m

Question 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.
2.52
2.10
2.06
1.99

Question 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)
3377 cm²
2547 cm²
3028 cm²
2623 cm²

Question 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.
40/30
-40/50
40/50
-30/40

Question 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.
-80%
72%
-84%
84%

Question 15: Vector A has coordinates (3,9). Find the length of vector A.
9.62 units
9.32 units
9.49 units
9.51 units

Question 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.
12m
16m
15m
10m

Question 17: 10 microseconds can be written as 10 x _____ seconds.
10^-6
10^-1
10^-9
10^-3

Question 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.
26cm²
0.00026cm²
0.26cm²
2.6cm²

Question 19: Pi is a/an _____ number.
Composite
Weird
Prime
Irrational

Question 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?
34.6 liters
42.6 liters
68.6 liters
28.6 liters

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