SAT Math Practice Test 1

1. Of the following, which is greater than ½ ?

A. 2/5 B. 4/7 C. 4/9 D. 5/11 E. 6/13

2. If an object travels at five feet per second, how many feet does it travel in one hour?

A. 30 B. 300 C. 720 D. 1800 E. 18000

3. What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?

A. 90 B. 95 C. 100 D. 105 E. 110

4. A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

A. 48 B. 32 C. 24 D. 18 E. 12

5. In a class of 78 students 41 are taking French, 22 are taking German and 9 students are taking both French and German. How many students are not enrolled in either course?

A. 6 B. 15 C. 24 D. 33 E. 54

6. If f(x) = │(x² – 50)│, what is the value of f(-5) ?

A. 75 B. 25 C. 0 D. -25 E. -75

7. ( √2 - √3 )² =

A. 5 - 2√6 B. 5 - √6 C. 1 - 2√6 D. 1 - √2 E. 1

8. 230 + 230 + 230 + 230 =

A. 8120 B. 830 C. 232 D. 230 E. 226

9. Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

A. 10 B. 8 C. 6 D. 4 E. 2

10. In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?

A. 18 B. 13.5 C. 9 D. 4.5 E. 3

SAT Math Practice Test 1 답안지

1.Correct Answer: B

Explanation:

One way to deal with fractions is to convert them all to decimals. (Using your calculator, divide the numerator by the denominator).In this case all you would need to do is to see which is greater than 0.5.Otherwise to see which is greater than ?, double the numerator and see if the result is greater than the denominator. In B, the correct answer, doubling the numerator gives us 8, which is bigger than 7.

2.Correct Answer: E

Explanation:

If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour. Answer = 18000 (E)

3.Correct Answer: C

Explanation:

You could add up all the multiples of 10 (10 + 20 + 30 ....+190), and divide by the number of terms (19). Or you could realize that the average of an evenly spaced series of numbers is equal to the value of the middle term (or the average of the two middle terms if there are an even number of terms). The middle term out of 19 is the tenth term in the series = 100.

4.Correct Answer: A

Explanation:

If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8.Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.

5.Correct Answer: C

Explanation:

You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither78 = (41-9) + (22-9) + 9 + neither.Not enrolled students = 24

6.Correct Answer: B

Explanation:

If x = -5, then (x² – 50) = 25 – 50 = -25But the sign │x│ means the absolute value of x (the distance between the number and zero on the number line). Absolute values are always positive.│-25 │ = 25

7.Correct Answer: A

Explanation:

Expand as for (a + b)2.(√2 - √3)(√2 - √3) = 2 - 2(√2 + √3) + 3 = 5 - 2 √6

8.Correct Answer: C

Explanation:

All four terms are identical therefore we have 4 (230).But 4 = 22, and so we can write 22. 230

Which is equivalent to 232

9.Correct Answer: B

Explanation:

Amy can travel clockwise or anticlockwise on the diagram.Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.Similarly, anticlockwise she has four different routes.Total routes = 8

10.Correct Answer: D

Explanation:

If we take AE as the base of triangle AEC, then the height is CD.The height of the triangle is therefore, 9 (given).To find the base we need to see that triangles AEB and CDE are similar. The ratio AB: CD, is therefore equal to the ratio AE: ED. The given information shows that the ratio is 3:9, or 1:3. Now dividing AD (4) in this ratio gives us AE as 1.The area of AEC = ½ base x height =1/2 x 9 = 4.5

SAT Math Practice Test 2

 

1. Which of the following could be a value of x, in the diagram above?

A. 10 B. 20 C. 40

D. 50 E. any of the above

2. Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?

A. 10 B. 15 C. 20 D. 25 E. 30

3. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?

A. 5 : 1 B. 10 : 5 C. 15 : 2 D. 20 : 2 E. 25 : 2

4. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π B. 3π C. 5π D. 4π E. 10π

5. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

A. 4 B. 7 C. 8 D. 12 E. it cannot be determined from the information given.

6. If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?

A. f(-1) B. f(0)

C. f(1) D. f(3) E. f(4)

7. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?

A. 2.25 B. 3 C. 4 D. 4.5 E. 6

8. If n ≠ 0, which of the following must be greater than n?

I 2nII n²III 2 - n

A. I only B. II only C. I and II only D. II and III only E. None

9. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?

A. 20 B. 15 C. 8 D. 5 E. 3.2

10. n and p are integers greater than 15n is the square of a number75np is the cube of a number.The smallest value for n + p is

A. 14 B. 18 C. 20 D. 30 E. 50

SAT Math Practice Test 2 답안지

1.Correct Answer: B

Explanation:

The marked angle, ABC must be more than 90 degrees because it is the external angle of triangle BDC, and must be equal to the sum of angles BDC (90) and DCB. Also ABC is not a straight line and must be less than 180.Therefore 90 < 5x < 180The only value of x which satisfies this relation is 20.

2.Correct Answer: A

Explanation:

20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.

3.Correct Answer: E

Explanation:

Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2. Now US : Indian = 25 : 10, and Indian : British = 10 : 2Hence the two ratios can be combined and US : British = 25 : 2

4.Correct Answer: C

Explanation:

Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle, and is therefore,

5.Circumference = π.diameter = 5π

5.Correct Answer: D

Explanation:

If two sets of four consecutive integers have one integer in common, the total in the combined set is 7., and we can write the sets asn + (n + 1) + (n + 2) + (n + 3 ) and(n + 3) + (n + 4) + (n + 5) + (n + 6)Note that each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 12

6.Correct Answer: D

Explanation:

You can solve this by back solving – substitute the answer choices in the expression and see which gives the greatest value.satA (-1 + 2) / (-1-2) = -2 / 2 = -1;B (0 + 2) / (0-2) = 2/ -2 = -1;C (1 + 2) / (1-2) = 3/-1 = -3;D (3 + 2) / (3-2) = 5/1 = 5;E (4+ 2) / (4-2) = 6/2 = 3If you had just chosen the largest value for x you would have been wrong. So although it looks a long method, it is actually quick and accurate since the numbers are really simple and you can do the math in your head.

7.Correct Answer: D

Explanation:

(Total area of square - sum of the areas of triangles ADE and DCF) will give the area of the quadrilateral9 - (2 x ½ x 3 x 1.5) = 4.5

8.Correct Answer: E

Explanation:

Remember that n could be positive negative or a fraction. Try out a few cases:In case I, if n is -1, then 2n is less than n.In case II, if n is a fraction such as ½ then n2 will be less than n.In case III, if n is 2, then 2-n = 0, which is less than n.Therefore, none of the choices must be greater than n

9.Correct Answer: C

Explanation:

If after each bounce it reaches 2/5 of the previous height, then after the second bounce it will reach 2/5 x 125. After the third it will reach 2/5 x 2/5 x 125. After the fourth it will reach 2/5 x 2/5 x 2/5 x 125. This cancels down to 2 x 2 x 2 = 8

10.Correct Answer: A

Explanation:

The smallest value for n such that 5n is a square is 5.75np can now be written as 75 x 5 x p.This gives prime factors.... 3 x 5 x 5 x 5 x pTo make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9n + p = 5 + 9 = 14