1.
Diagnostic Exam
Grade 7 Mathematics
Name:______________________________ Date:__________________
Grade/ Section:_______________________ Teacher:_______________
Choose the best answer:
1.Simplify :
6
5
𝑥
1
4
+ 2 ÷
5
2
a.
11
10
b.
12
10
c.
12
20
d.
11
9
2.Simplify :
2/3 −5/4
1/2 +4/3
a.
−15
10
b.-7
1
22
c.
−7
22
d.24
3.Write
7
12500000
in scientific notation.
a. 5.6x 10−7
b. 5.7x 10−7
c. 4.7x 10−7
d. c. 9.7x 10−7
4.Simplify:2-(1+
1
2
+
1
4
+
1
8
+
1
16
).
a.
1
26
b.
1
16
c.
1
14
d.
1
10
5. Julie’s average for the first four tests is 88.5 .If she wants an average of at least 90 in the five tests, what
score must she gets in her last test?
a. at least 96 b. at least 36 a.at least 45 d. at least 75
6. Alma walks 4.5 kilometers in one hour. What is her speed in meters per minute?
a. 65 m/min b. 95 m/min c. 45 m/min d. 75 m/min
7. The Grade 6 pupils of a school are divided equally into Team A and Team B. The ratio of the number of the
boys to the numbers of girls in Team A is 2:1 and in Team B it is 4:11. What is the ratio of the number of the
boys to the number of girls in Grade 6?
a. 9:8 b. 7:8 c. 3:18 d. 3:8
8. A dress is marked with 12% discount. If the dress is marked at P 1188, how much was it before the discount
was applied?
a. Ph P1350 b. Ph P1050 c. Ph P1950 d. Ph P1370
9. Simplify: (2 −
3
2
)2
− (2 −
3
2
)2
a.-10 b.-42 c.15 d.-12
10. What is the product of three consecutive odd integers if the middle integers is n ?
a. 2𝑛3
-4n b.𝑛3
-24n c. 𝑛3
-4n d. 𝑛2
-4n
11. What number is exactly midway between 3/2 and -9?
a.
−5
4
b.
−15
4
c.
−25
18
d. c.
−25
8
12. The price of a pencil is p pesos and a notebook costs PhP12 more than a pencil.How much do 3 pencils
and 2 notebook cost?
a.6p+25 b.4p+24 c.5p+24 d.7p+3
13.Compute: (1-
2
3
)(1 +
2
3
)(1 +
4
9
)
a.
65
81
b.
1
12
c.
61
12
d.
10
12
14. Subtract 2a-4b+9c from the sum of 3a+5b-3c and a-b+7c.

2.
a.3a+7b-5c b.5a+8b-5c c.3a+7b-4c d.2a+8b-5c
15. If x is twice as far from 5 as it is from -7, what are the possible value for x ?
a.-3 b.-8 c.-6 d.-4
16. What must be added to the product of 3x+1 and 2x -5 to obtain 4x2-5x-6?
a. 2𝑥2
+8x-1 b. 2𝑥2
+18x-1 c.2𝑥2
+8x-11 d. 12𝑥2
+8x-1
17. Let A be the set of all positive even integers less than 10, B the set of all prime number less than 10, and C
the set of all one digit numbers which are NOT multiples of 3. Find C (AUB).
a.{1} b. .{6} c. .{4} d. .{8}
18. In a triangle, the second angle is twice the first angle and the third is 12 degree less than 5 times the first
angle. what is the measure of the largest angle?
a. 510
b.1030
c. 1080
d. 2080
19.Let the universal set U be the set of positive integers less than 20, A the set of odd integers,B the set of
perfect square and C the set of multiples of 3. Determine C (AnB)1
.
a.{3,9,15} b. {3,6,12} c.{3,29,35} d. {3,9,18}
20.In a class of 35 students , 10 speak Ilokano, 18 speak Bicolano, 16 speak Cebuano, 5 speak Both Bicolano
and Ilocano, 2 speak both Ilocano and Cebuano, 9 speak both Bicolano and Cebuano, and 2 speak all three
languages. How many students do not speak any of the three language?
a.7 b.2 c.1 d.4
21.Simplify: 2(5)2-6-2)3+(3-7)3.
a.36 b.34 c.38 d.40
22.How many different lengths of diagonals does a regular decagon have?
a.4 b.8 c.6 d.2
23.Give the solution set for 3{7-2(7x-4)}=-42x+45
a.sets of real no. b.real numbers. c.sets d.R
24. Paul is 20 years older than jason. In 12 years, Paul will be twice as old as Jason will be then.How old is
Paul now?
a.38 b.78 c.28 d.18
25. Karen jogs every morning while Roy cycles on the same route. If Roy’s speed is three times that of Karen
and Roy starts 2 hours after Karen, how long does Roy cycle before she overtakes Karen?
a. 3 hour b. 2 hour c. 5 hour d.1 hour
26. Subtract 2𝑎2
+2ab -ac from the product of a+b and 2a-b+c.
a. 2ac+bc-ab-3 b.2ac+bc-ab-𝑏2
c. 2ac+bc-ab-𝑏3
d. 4ac+bc-ab-𝑏2
27. A cylindrical container with radius 10 cm is filled with water to a height of 2 cm. The water is poured into a
second cylindrical container with radius 4 cm. How high will the water be in the second container?
a. 18.5 cm b. 10.5 cm c. 14.5 cm d.12.5 cm
28.Luis can arrange his stickers 6 or 9 to a page without any stickers left over. If he arranges his stickers 10 to
a page, there are 2 stickers leftover. What is the smallest number of stickers Luis can have?
a.72 b.68 c.45 d.93

3.
29. ABCDEFGH is a regular octagon. What is the measure of angle BAD?
a. 480
b.450
c. 400
d. 350
30. Given rectangle ABCD, let E be the midpoint of side AB and F the midpoint of side BC. What part of the
rectangle ABCD is triangle DEF?
a.9/7 b.4/6 c.3/8 d.8/4
31. At a party, married couple came with their husbands or wives. If half of the woman and ⅙of the men were
single, what is the percentage of the people in the room where married?
a.98% b.75% c.67% d.60%
32. If the length of the of the rectangle is x + 5, its width is 2x-1, and its area is 2x2+5x+7 , what is x?
a.X=2 b.x=3 c.X=9 d.X=4
33.How many four- digit numbers are multiples of 12?
a.980 b.570 c.750 d.705
34. Simplify :( x2-4)(x-2)-(x+3)(x2-4x+4).
a. −4𝑥2
+4x-8 b. −4𝑥2
+6x-4 c. −8𝑥2
+4x-4 d.−𝑥2
+4x-4
35. If n and m are positive integers, what is the value of [(−2)𝑛2
+2m+3-(-2n)n]/ 2m?
a.8 b.9 c.6 d.7
36. Simplify:
(√𝑥 − √2 )(√𝑥 +√2
𝑥2−4
a.
11
𝑥+2
b.
1
𝑥+2
c.
2
𝑥+2
d.
1
𝑥+4
37.A rectangle with dimension 𝜒 by 𝜒+ 10 has the same area as the square with side 𝜒 + 3
what is x ?
a. x=8/4 b.x=9/4 c. x=3/4 d. x=5/4
38. If today is Saturday, what day is 1020
days from now?
a.Friday b.Tuesday c.Monday d.Wednesday
39. Which is larger √75 +1 or 8+√3 ?
a. 8+√3 b. 8+√5 . c. 8+√6 d. √75 +1
40. Which values of 𝜒 satisfy |x+1| = |2x - 4|?
a.x=2 b.x=1 c.x=7 d.x=12
41. What is the value of (1-½)(1-⅓)(1-¼)...(1-1/2013)?
a. 6/2013 b. 8/2013 c. 7/2013 d.1/2013
42. The base of a pyramid is a square and its other faces are equilateral triangles. Which of the following is true?
a. b. c. d.
43. A car leaves A at 8 AM and travels to B at a rate of 60 kph. A bus leaves B at 8:30 AM and
travels to A at a rate of 75 kph. If the car and the bus pass each other midway between A and B,at what time
will the car pass the bus?
a. 10:20 am b. 9:30 am c. 10:30 am d. 12:30 am
44. Which integers values of x satisfy 3x + 1< 2x + 11 ≤4x-3?
a.x=4 b.x=8 c.x=16 d.x=2

4.
45. Find the solution set: 2<|2x-3|≤5
a.[-1, ½) u (5/2 ,4 ] b. (-1, ½] u [5/2 ,4 ) c. (-1, 5/2] u [ ½, 4) d. [-1, 5/2) u ( ½, 4]
46. In a class of 30, ten students have computers at home and 15 have cell phone
are the possible number of students who don't have a computer nor cellphone .
a.from 5 to 15 b. from 5 to 25 c. from 5 to 35 d. from 15 to 45
47. If n is a positive integers, which of the following is a perfect square 3n2
, (−3)3n
, 3(12)n2−1
?
a. 3(12)𝑛2−1
b, 12(3)𝑛2−1
c. 12𝑛2−1
d. 3𝑛2−1
48. If 5n leaves a remainder of 8 when divided by 11, what is the remainder when 4n is divided y 11?
a.3 b.2 c.9 d.4
49. With what polynomial must 6𝑥4
-2𝑥3
+ 𝑥2
+× −5 be divided to get a quotient of 2𝑥2
+5 and a remainder of 6x
+30?
a. 6𝑥2
-x+7 b. 3𝑥2
-4x+7 c. 3𝑥2
-8x+7 d.3𝑥2
-x+7
50.Give the solution set to |3-2x| +|-6+1|<12.
a.(-2,5) b. .(-2,6) c. .(-8,5) d. .(-8,7)
.
GOD BLESS

5.
Answer key
1. a.
11
10
2. c.
−7
22
3. a. 5.6x 10−7
4 b.
1
16
5. a.at least 96
6. d. 75 m/min
7. b. 7:8
8.a. Ph P1350
9. d.-12
10. c. 𝑛3
-4n
11. b.
−15
4
12. c.5p+24
13. a.
65
81
14. d.2a+8b-5c
15. a.-3
16. c.2𝑥2
+8x-1
17. .{1}
18. 𝑐. 1080
19. a.{3,9,15}
20. b.2
21. b.34
22. a.4
23. a.sets of real no.
24. a.4
25. d.1 hour
26. b.2ac+bc-ab-𝑏2

6.
27. d.12.5 cm
28. a.72
29. b.450
30. c.3/8
31. b.75%
32. b.x=3
33. c.750
34. d.−𝑥2
+4x-4
35. a.8
36. b.
1
𝑥+2
37. b.x=9/4
38. c.Monday
39. a.8+√3
40. b.x=1
41. d.1/2013
42. D.
43. c. 10:30 am
44. b.x=8
45. a
46. a.from 5 to 15
47. a
48. b.2
49. d.3𝑥2
-x+7
50. a.(-2,5)