Sample SAT Math Questions Have a go at these SAT Math questions then visit www.kaptest.co.uk to download the answers and explanations. Sample Questions cover the following topics: • • • • • • • • • • •
Number Properties Averages Ratios and Rates Percents Powers and Roots Advanced Algebra General Word Problems Logic Word problems Triangles Quadrilaterals and Other Polygons Solids
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Number Properties 1.
How many odd integers are between 10 and 62? 3 3 a) 19 b) 18 c) 10 d) 9 e) 8
2.
If the integer P leaves a remainder of 4 when divided by 9, all of the following must be true EXCEPT a) b) c) d) e)
3.
The number that is 4 less than P is a multiple of 9. The number that is 5 more than P is a multiple of 9. The number that is 2 more than P is a multiple of 3. When divided by 3, P will leave a remainder of 1. When divided by 2, P will leave a remainder of 1.
What is the positive difference between the number of distinct prime factors of 152 and the number of distinct prime factors of 643?
Averages 1.
Jerry’s average (arithmetic mean) score on the first three of four tests is 85. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?
2.
If the average (arithmetic mean) of t and s is 25 and the average of r and s is 40, what is the value of r - t? a) b) c) d) e)
65 32.5 30 15 It cannot be determined from the information given.
Ratios and Rates 1.
In a local election, votes were cast for Mr. Dyer, Ms. Frau, and Mr Borak in the ratio of 4:3:2. If there were no other candidates and none of the 1,800 voters cast more than one vote, how many votes did Ms. Frau receive?
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2.
A sporting goods store ordered an equal number of white and yellow tennis balls. The tennis ball company delivered 30 extra white balls, making the ratio of white balls to yellow balls 6:5. How many tennis balls did the store originally order? a) b) c) d) e)
120 150 180 300 330
Percents 1.
The number that is 400 percent greater than 15 is what percent greater than 150 percent of 30? a) b) c) d) e)
15% 25% 33 ⅓ % 66 ⅔ % 166 ⅔ %
Powers and Roots 1.
Which of the following is equal to 85? I. II. III.
25 x 45 215 25 x 210
a) b) c) d) e)
II only I and II only I and III only II and III only I, II and III
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Advanced Algebra 1.
If x ≠-y and x2 – y2 = 13 then x-y = x+y a) b) c) d) e)
2.
√13 7 13 169 It cannot be determined from the information given
The number of foxes on Example Island varies directly as the number of rabbits on the island varies, according to the equation f = kr, where f is the number of foxes, r is the number of rabbits, and k is a constant. If there are 10 foxes on the island when there are 300 rabbits, how many foxes would there be if there were 750 rabbits? a) b) c) d) e)
2.5 15 25 150 250
General Word Problems 1.
Liza took 5n photographs on a certain trip. If she gives n photographs to each of her 3 friends, how many photographs will she have left? a) b) c) d) e)
2n 3n 4n – 3 4n 4n + 3
2.
An hour long test has 60 problems. If a student completes 30 problems in 20 minutes, how many seconds does he have on average for completing each of the remaining problems?
3.
If John gives Allen $5 and Allen gives Frank $2, the 3 boys will have the same amount of money. How much more money does John have than Allen? a) b) c) d) e)
$3 $5 $6 $7 $8
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Logic Word problems 1.
A class of 40 students is to be divided into smaller groups. If each group is to contain 3, 4 or 5 people, what is the largest number of groups possible? a) b) c) d) e)
8 10 12 13 14
Triangles 1.
What is the length of the hypotenuse of an isosceles right triangle with an area of 32? a) b) c) d) e)
4 4√2 8 8√2 √3
Quadrilaterals and Other Polygons 1.
In quadrilateral DEFG, the degree measures of its 4 angles are in the radio of 2:3:5:6. What is the difference in the degree measures between the largest and smallest angles? a) b) c) d) e)
135 112.5 90 67.5 45
Solids 1.
A cube and a rectangular solid are equal in volume. If the lengths of the edges of the rectangular solid are 4, 8 and 16, what is the length of an edge of the cube?
2.
A rectangular block with a volume of 250 cubic inches was sliced into 2 cubes of equal volume. How much greater, in square inches, is the combined surface area of the 2 cubes that the original surfaces area of the rectangular block?
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