LET Reviewer in General Education

LET Reviewer for General Education |

**PRACTICE TEST FOR GENERAL EDUCATION**

*MATHEMATICS*1. Give the factors of 2x3 + 9x2 + 9x

a. x (2x – 3)(x + 3)

b. x (2x + 3)(x + 3)

c. x (3x – 2)(x + 3)

d. x (2x + 3)(x – 3)

2. Which of the following is/are TRUE?

I. x3 - y3 = (x – y)(x2 + y2)

II. (5x – 2y)(5x – 2y) = 25x2 – 20xy+4y2

III. x2 + y2 = (x + y)(x + y)

a. I only

b. I and III

c. II only

d. I and II

3. If f(x) = x4 – x2 and g(x) = x3 – 3x2 + 2x, then for all values of x for which g(x) ≠ 0, f(x)/g(x)

a. 2(x + 1) / (x – 2)

b. x(x – 1)/ (x – 2)

c. x(x + 1) / (x – 2)

d. x(x – 1)/ (x + 2)

4. If x =-5, what is the value of (x^2-9)/(x+3) ?

a. -8

b. -6

c. 5

d. 7

5. Divide (x^2-9)/y ÷ (2x+6)/8

a. 4(x-3)/y

b. 4(x+3)/y

c. 4(x-9)/y

d. 4(x+9)/y

6. What value of x will satisfy the equation 0.2(2x+1470) = x?

a. 490

b. 560

c. 1470

d. 2130

7. Three times the first of three consecutive odd integers is 3 more than twice the third. Find the third integer.

a. 9

b. 13

c. 11

d. 15

8. The product of 2 whole numbers is 36, and their ratio is 1:4. Which of these is the smaller number?

a. 9

b. 3

c. 2

d. 12

9. A, B, and C are consecutive numbers. If A>B>C, what is the value of (A-B) (A-C) (B-C)?

a. -2

b. -1

c. 1

d. 2

10. Charlie was 40 years when his son Adam was born. How old was Charlie when he was 5 times as old as Adam?

a. 40

b. 45

c. 50

d. 60

11. In 2001, Lior was four times as old as Ezra, and in 2003, Lior was twice as old as Ezra. How many years older than Ezra is Lior?

a. 1

b. 2

c. 3

d. 4

12. A man started painting a wall at 9:00 AM and was able to finish painting 3/5 of it at 10:30 AM. Continuing at this rate, at what time will he finish painting the wall?

a. 11:35 AM

b. 11:30 AM

c. 12:30 AM

d. 12:15 AM

13. If Mary can address a box of envelopes in 5 hours and Jane can address the same box of envelopes in 10 hours, how many minutes will it take Mary and Jane working together to address all the envelopes in the box?

a. 80

b. 160

c. 200

d. 450

14. A father and son working together can finish painting a room in 6 hours. Working alone, a father takes 9 hours to do the painting. How many painting hours will it take the son, working alone, to finish painting the room?

a. 18

b. 75

c. 15

d. 12

15. How much water must be added to 100 cc of 80% solution of punch to reduce it to 50%?

a. 18 cc

b. 1540 cc

c. 36 cc

d. 60 cc

16. How many ounces of pure acid must be added to 20 ounces of a solution that is 5% acid to strengthen it to a solution that is 24% acid?

a. 5

b. 6

c. 10

d. 2 ½

17. Two buses leave the same station at 9:00 pm. One bus travels north at the rate of 30 kph and the other travels east at 40 kph. How many kilometers apart are the buses at 10 pm?

a. 50 km

b. 70 km

c. 100 km

d. 140 km

18. Kath’s grades in three math quizzes are 82, 78, 86. What grade should get in her next quiz to raise her average to 85?

a. 94

b. 90

c. 88

d. 87

19. In the playground for kindergarten kids, 18 children are riding tricycles or bicycles. If there are 43 wheels in all, how many tricycles are there?

a. 7

b. 8

c. 9

d. 11

20. At an amusement park, Lance bought 3 hamburgers and 4 sodas for a total of PhP 150. While paying the same prices, Karen bought 2 hamburgers and 3 sodas for PhP 105. What is the total cost of 1 hamburger and 1 soda?

a. PhP 15

b. PhP 40

c. PhP 30

d. PhP 45

21. What day follows the day before yesterday if 2 days from now will be Sunday?

a. Wednesday

b. Thursday

c. Friday

d. Saturday

22. If July 12, 2003 fell on a Tuesday, on what day will July 12, 2005 fall?

a. Monday

b. Thursday

c. Sunday

d. Friday

23. If January 1, 2008 is a Wednesday, on what day does Christmas day of the same year fall?

a. Thursday

b. Friday

c. Wednesday

d. Saturday

24. What are the missing terms in the series 5, 10, 20 _____, 80, ____320?

a. 40, 160

b. 40, 120

c. 50, 120

d. 35, 135

25. The first 5 numbers in a sequence are 5,6,8,11 and 15. What are the 8th and 10th numbers in the sequence?

a. 27 and 42

b. 26 and 49

c. 33 and 50

d. 32 and 49

26. What is the 500th digit to the right of the decimal point when 15/37 is expressed as a decimal?

a. 0

b. 4

c. 5

d. 7

27. What is the sum of all the two digit numbers which are divisible by 5?

a. 945

b. 950

c. 960

d. 1050

28. What is the 10th term in the progression -8, 4, -2, … ?

a. 1/66

b. 1/65

c. 1/63

d. 1/64

29. In the progression 18, 12, 8…, which term is 512/729?

a. the 8th

b. the 6th

c. the 9th

d. the 7th

30. Which is the sum of the infinite progression 3/2, 1, 2/3, 4/9…?

a. 6 ½

b. 5 ½

c. 4 ½

d. 7 ½

31. If the ratio of sec x to csc x is 1:4, then the ratio of tan x to cot x is ___________

a. 1:4

b. 1:1

c. 4:1

d. 1:16

32. The shadow of an electric pole is 5 meters long when the angle of elevation if the sun is 60°. What is the length of the shadow when the angle of elevation of the sun is 45°?

a. 5√3 meters

b. √3 meters

c. 10√3meters

d. 5 meters

33. A car is parked 120 feet from a building that is 350 feet tall. What is the measure of the angle of depression from the top of the building to the car?

a. 18.9°

b. 37.8°

c. 64.2°

d. 71.1°

34. In triangle ABC, with right angle at B, the sine of A is 4/5. What is the cosine of A?

a. 2/5

b. 4/3

c. 3/5

d. ¾

35. I sin ϴ = 3/5 and 0 ≤ ϴ ≤ Π/2, then tan ϴ =

a. 3/2

b. 4/3

c. 5/4

d. 3/4

36. Find the equation of the line whose slope is 4 and passing through the point (2, -3)

a. 4x – y – 11 = 0

b. 4x – y + 11 = 0

c. 4x + y – 11 = 0

d. 4x + y + 11 = 0

37. What is the equation of the line passing through the points (3,1) and (-5, 4)?

a. 3x + 8y + 17 = 0

b. 3x – 8y + 17 = 0

c. 3x + 8y – 17 = 0

d. 3x – 8y – 17 = 0

38. What is the equation of the line whose x – intercept is 6 and y – intercept is -8?

a. 3x – 4y – 24 = 0

b. 4x – 3y – 24 = 0

c. 3x – 4y + 24 = 0

d. 4x – 3y + 24 = 0

39. If the lines whose equation are y = ax + b and x = cy + d are parallel, which statement must be true?

a. a = -(1/c)

b. c = a

c. a = (1/c)

d. c = - a

40. What is the slope of the perpendicular bisector of line segment AB if A is the point (0, -3) and B is the point (4,0)?

a. –(4/3)

b. –(3/4)

c. 3/4

d. 4/3

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