SAT I Math: a collection of medium to hard questions

This post is a collection of medium to hard SAT I Math questions of various subjects and suggested solutions. Getting the full mark in Math part is considered more easily than these other parts of SAT test. This post tries to give you some more preparation so that you won’t be surprised by and can solve tough SAT Math questions in your real test.

Question 1 (Statistics: Average): The average of 5 different integers is 25. The smallest of the 5 integers is 22. The largest of the five integers is N. How many possible values of N are there?

(A) 3        (B) 4          (C) 5        (D) 6         (E) 7

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General approach: To find the number of possible values for N, we first find maximum and minimum value that N could take.
The sum of five integers is 5x25 = 125.
Maximum value of N happens when these other four different integers take their smallest values which are 22, 23, 24, 25. Thus, max of N = 125 – (22+23+24+25) = 31.
Let N(min) be minimum value that N could take. First, straight forward, N(min) > 25. But we want to have a tighter condition for N(min). Note that maximum sum of these 5 different integers now could be: N(min) + N(min)-1 + N(min)-2 + N(min)-3 + 22 = 4xN(min) + 16. This value should be greater than or equal to 125. Thus, N(min) > 27.
Hence, N can be from 28 to 31. For each value of N in that range, we have to find the suitable values for these 3 remaining numbers before we can conclude that the value of N satisfies the question. That can be done pretty easily by balancing each value with the average value 25.
Specifically: 22 + 24 + 25 + 26 + 28 = 125
22 + 23 + 25 + 26 + 29 = 125
22 + 23 + 24 + 26 + 30 = 125
22 + 23 + 24 + 25 + 31 = 125
In summary, N could take 4 possible values (from 28 to 31). (B) is the correct answer.

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Free revision workshops for GCE O level E-Math and A-Math - DEC 2010

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Topic: Trigonometry

Trigonometry is among the most important topics in Elementary and Additional Math which accounts for a high portion in total marks.

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Free Senior Olympiad Training for top scorers

The process includes 2 rounds:

• Round 1: Online test including 5 questions below. Deadline: 25-Nov-2010.
• Round 2: Paper test by invitation, for those who scores well in Round 1 test. The date to be confirmed.

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Full worked solutions for 2010 GCE O level A-Math paper 1 & 2. 

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Simplifying an equation using conjugate surds

Trigonometrical equation

A typical trigonometrical equation which helps students practice important formulas and identities. 

Trigonometry

A Secondary Olympiad question of maximum/minimum type which can be solved by Trigonometry.

fraction and remainder

A question from a top school exam.

A similar question:
Every month Mum gives Cherry 400$ of which she spent 1/10 on transport. 
Her spending on movie is half of her spending on transport and her spending on tuition is five times of her spending on transport and movie. 
What is the remaining amount that Cherry would return to Mum at the end of the month?
1)   40
2)   50
3)   60
4)   30

Total and average

Question below is from a top school exam year 2007

Now try a similar question:

The average cost of some math books in a box was $15 at first. To double the number of books in the box, a number of science books whose total cost is unknown are added to the box. The average cost of books in the box now is 20. Then, all math books are removed from the box. What is average cost of books in the box now?
(1) 15
(2) 20
(3) 25
(4) 30