ACT-SAT Mathematics Mini Diagnostic Test

omr sat act exam

Think you’re good at ACT-SAT Mathematics? Try the ultimate mini diagnostic test now!

1. If 7a * 9 = 6a + 4, then a =
(where * could symbolise any standard mathematical operation +, -, / or *)

 
 
 
 
 

2. The sum of two different positive integers is 24. One integer is double the other. What is the square of half of the value of the smaller integer?

 
 
 
 
 

3. The price of oil has been fluctuating a lot in 2018. In one week (5 trading days), the price opened on Monday at $52.00 per barrel and then moved up and down as follows: on Monday it closed up 4%; on Tuesday if fell 4%; on Wednesday it moved up 4%; on Thursday down 4%; and on Friday it closed the same as on Thursday (no change). What was the final price on the Friday of that week?

 
 
 
 
 

4. The ratio of flour to sugar in a mixture is 5:6. If the mixture weighs 22 kg, what is the minimum amount of additional flour required to make the ratio flip to 6:5?

 
 
 
 
 

5. A function f(x) is defined as f(x)=(x-3)^2+4. What is the minimum value of f(x)?

 
 
 
 
 

6. What is x in the following equation 3^{(x+3)}=27^{(5x-3)}?

 
 
 
 
 

7. When x= \frac{1}{3} what is the value of \frac{1+x^2}{1-x^2}?

 
 
 
 
 

8. If the average of a and b is 10 and a^2 - b^2= 80, what is the value of b?

 
 
 
 
 

9. If 2y-3x=1 and 5x+4y=2, then what is the value of 6x?

 
 
 
 
 

10. The area of triangle is 40. If its height is 2 units more than its base, what is the length of its base?

 
 
 
 
 

11. ABCD is a parallelogram: AB||CD and AD||BC. M is the midpoint of AC.
parallelogram
Which of the following is true?
1. angle MAB = angle MBA
2. angle MBC + angle MCB = angle AMB
3. angle MAB = angle ACD
4. angle DAB + angle ABC = 180^{\circ}

 
 
 
 
 

12. What is the slope of the line that is perpendicular to the line with equation 3x-7y=1?

 
 
 
 
 

13. In the triangle below what is the value of sin\theta?
triangle

 
 
 
 
 

14. In 2017, a box seat at the theatre cost $84.50 per ticket, and parking costs were $14.50 per vehicle. If, for the 2018 season, box ticket prices went up by 18 percent and parking costs went up by 10 percent, how much more did it cost one person with one vehicle to spend a night at the theatre in 2018?

 
 
 
 
 

15. The imaginary number i is defined as i= \sqrt{-1}. What is the value of i^{20}+ i^{21}- i^{22}?

 
 
 
 
 

16. A mixture requires 5 parts water, 2 parts honey and 1 part lemon juice. In order to make 3 kg of the mixture what is the least amount of lemon juice and water required?

 
 
 
 
 


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